S
S
http://www.youtube.com/watch?v=1wtmehP4IGM
Magnets: HISTORY
S
Rocks containing iron have recorded the history of the
varying directions of Earth’s magnetic field.
Rocks on the seafloor were produced when molten rock
poured out of cracks in the bottom of the oceans.
Magnets: HISTORY
S
The existence of magnets and magnetic fields has been
known for more than 2000 years.
Chinese sailors employed magnets as navigational
compasses approximately 900 years ago.
Throughout the world, early scientists studied magnetic
rocks, called lodestones.
As they cooled, the rocks were magnetized in the
direction of Earth’s field at the time.
S
Magnets: HISTORY
S
In the early nineteenth century, French scientist AndréMarie Ampère knew that the magnetic effects of an
electromagnet are the result of electric current
through its loops.
He proposed a theory of magnetism in iron to explain
this behavior.
Ampère reasoned that the effects of a bar magnet must
result from tiny loops of current within the bar.
wrong, but his basic idea was correct.
1
Magnets: Permanent and TemporaryS
iron, nickel, or cobalt next to a magnet, the element also becomes
magnetic, and it develops north and south poles.
The magnetism, however, is only temporary.
The creation of this temporary polarity depends on the direction of
the external field.
When you take away the external field, the element loses its
magnetism.
The three elements—iron, nickel, and cobalt—behave like
electromagnets in many ways. They have a property called
ferromagnetism.
DOMAINS
S
Magnets: Permanent and Temporary
S
Temporary magnet, after the
external field is removed, the
domains return to their random
arrangement.
Permanent magnet, the iron has
been alloyed with other
substances to keep the
domains aligned after the
external magnetic field is
removed.
DOMAIN FACTORS
S
Each electron in an atom acts like a tiny electromagnet.
When the magnetic fields of the electrons in a group of
neighboring atoms (i.e. 1s) are all aligned in the same
direction, the group is called a domain.
Although they may contain 1020 individual atoms,
domains are still very small—usually from 10 to 1000
microns.
Thus, even a small sample of iron contains a huge
number of domains.
Magnets: Permanent and Temporary
When a piece of iron is not
in a magnetic field, the
domains point in random
directions, and their
magnetic fields cancel
one another out.
S
• materials with some unpaired electrons will have
a net magnetic field and will react more to an
external field. (D & F BLOCK)
• When the magnetic fields of the electrons in a
group of neighboring atoms are all aligned in the
same direction, the group is called a domain
• Factors that determine magnetic domain
– The electron orbital motion
– The change in orbital motion caused by an
external magnetic field
– The spin of the electrons.
S
•The more domains aligned, the stronger the magnetic field.
•When all of the domains aligned, said to be magnetically
saturated.
•Magnetically saturated, no additional amount of external
magnetization force will increase internal level of
magnetization.
placed in a magnetic field,
the domains tend to
align with the external
field.
2
WHY DOES MAGENTISM EXIST?
S
Magnets: Permanent and Temporary
S
A Microscopic Picture of Magnetic Materials
The directions of the domains’ alignments depend on the
direction of the current in the head and become a magnetic
record of the sounds or pictures being recorded.
The magnetic material on the tape allows the domains to keep
their alignments until a strong enough magnetic field is applied
to change them again.
On a playback of the tape, the signal, produced by currents
generated as the head passes over the magnetic particles, goes
to an amplifier and a pair of loudspeakers or earphones.
When a previously recorded tape is used to record new sounds,
an erase head produces a rapidly alternating magnetic field that
randomizes the directions of the domains on the tape.
http://www.youtube.com/watch?v=wMFPe-DwULM
S
Magnets: Permanent and Temporary
S
A Microscopic Picture of Magnetic Materials
• disk drive head
writes a magnetic
pattern
Scientists who first examined seafloor rocks were surprised to
find that the direction of the magnetization in different rocks
varied.
They concluded from their data that the north and south
magnetic poles of Earth have exchanged places many times in
Earth’s history.
The origin of Earth’s magnetic field is not well understood.
How this field might reverse direction is even more of a mystery.
Magnets: Permanent and Temporary
A Microscopic Picture of Magnetic Materials
Electromagnets make up the recording heads of audio cassette
and videotape recorders.
Recorders create electrical signals that represent the sounds or
pictures being recorded.
Magnetism
S
S
Compasses were known to be demagnatized and spoons
magetized in a lightning storm.
It would also orient itself freely in N-S heading if
suspended.
The electric signals produce currents in the recording head that
create magnetic fields.
When magnetic recording tape, which has many tiny bits of
magnetic material bonded to thin plastic, passes over the
recording head, the domains of the bits are aligned by the
magnetic fields of the head.
S
Bar Magnet
S
N
N
3
S
Magnetic Poles
Iron
filings
N
The strength of a magnet is
concentrated at the ends,
called north and south
“poles” of the magnet.
S
A suspended magnet:
N-seeking end and
S-seeking end are N
and S poles.
Field Lines Between Magnets
Unlike
poles
S
Attraction
N
S
Leave N
and enter S
W
N
S
E
S
N
Bar magnet
N
N
N
Repulsion
Like poles
Compass
Magnetic Attraction-Repulsion S
Magnetic Fields – Permanent MagnetsS
Same as the electric field
S
S
N
N
S
S
N
N
N
Magnetic Forces:
Like Poles Repel
S
• Magnetic fields are continuous loops – leaving a
North pole and entering a South pole – passing
through the magnet
Magnetic Field Lines
We can describe magnetic
field lines by imagining a
tiny compass placed at
nearby points.
The direction of the
magnetic field B at any
point is the same as the
direction indicated by
this compass.
• Highest strength near poles (highest concentration of
field lines
Unlike Poles Attract
S
Magnetic Fields Around
Permanent Magnets
S
Note that magnetic field lines, like electric field lines,
are imaginary.
N
S
They are used to help us visualize a field
The number of magnetic field lines passing through a
surface is called the magnetic flux.
Field B is strong where
lines are dense and weak
where lines are sparse.
NUEMONIC CUE: CIVIL WAR –
THE NORTH MARCHES ON THE SOUTH
The flux per unit area is proportional to the strength of
the magnetic field.
The magnetic flux is most concentrated at the poles;
thus, this is where the magnetic field strength is the
greatest.
4
WHY DOES A MAGNET
PICK UP A METAL
S
• INDUCTION
Magnet Properties
S
TYPES OF MAGNETS
• Ferromagnetic
– strongly attracted to magnets.
– iron, cobalt, nickel, gadolinium, and dysprosium.
– can be magnetized and turned into magnets themselves.
– When a magnetizing force is applied, the domains become aligned to
produce a strong magnetic field within the part.
Paramagnetic
– materials are weakly attracted to magnets.
– aluminum, oxygen, sodium, platinum, and uranium.
– Paramagnetic materials include magnesium, molybdenum, lithium, and
tantalum.
– Paramagnetic properties are due to the presence of some unpaired
electrons
• Diamagnetic
– weakly repelled by magnets.
– water, glass, copper, graphite, salt, lead, rubber, diamond,
wood,
– Diamagnetic materials are solids with all paired electron resulting in no
permanent net magnetic moment per atom.
– Most elements in the periodic table
S
• The lines of flux travel through the magnet
• The lines enter the magnet at the south pole.
• A line tangent to any point on a line of flux
shows the direction of the field
• Field line is the direction of the force that
would be exerted on a north pole.
• Where the lines are close together the field is
the strongest.
• The direction of the field is always NORTH
to SOUTH.
S
S
DEMO
• RUB A SPOON WITH A MAGNET AND
MOVE THE SPOON AROUND A
COMPASS AND SEE THAT IT IS
MAGNETIZED.
S
Force Law
B
The three-dimensional shape of the field is visible
B vector – arrow is
the North, tail is the
South
5
Magnetic & Electrostatic S
Forces: There are many similarities between
S
magnetic and electrostatic fields. There are also a
few differences.
• Both obey an inverse square law (just like
gravity does).
• They can both be attractive or repulsive.
• The primary difference between them is that
the electrostatic charge can be a point charge,
but magnets must always have a north and
south pole.
• CANT HAVE A MONOPOLE MAGNET LIKE IN
ELECTRICITY
Large numbers of atom's moments (1012 to 1015) are aligned parallel so that the
magnetic force within the domain is strong.
HOW DIRECTION OF FIELDS
S
DETERMINED
FORCE
• GRAVITY
S
ON
MASS
(attractive only
• ELECTRIC FIELD
(attractive /repulsive)
DIR OF ELECTRIC
FORCE ON A (+)
TEST CHARGE
• MAGNETISM
(attractive /repulsive)
DIR OF
ELECTRIC
FORCE ON THE N
SEEKING POLE
ON ALL THREE FORCES THE INVERSE SQUARE LAW IS
PRESENT: AS DISTANCE INCREASES, FORCE DECREASES.
• Iron (temporary magnet),
after the external field is
removed, the domains
return to their random
arrangement.
• In a permanent magnet,
the iron has been alloyed
with other substances to
keep the domains aligned
after the external magnetic
field is removed.
S
The result if we align the domains
What happens if we bend the magnet
into a horseshoe?
S
Why is it stronger?
6
S
Mechanical Universe
•
•
•
•
•
•
•
•
•
•
Lesson 34: Magnets
William Gilbert, personal physician by appointment to her Majesty Queen
Elizabeth I of England, discovered that the earth behaves like a giant
magnet. Magnetism as a natural phenomenon, the behavior of magnetic
materials, and the motion of charged particles in a magnetic field.
Text Assignment: Chapter 38
Instructional Objectives
Be able to calculate the magnetic force on a current element and on a
moving charge in a given magnetic field.
Know the definition of torque and potential energy for a magnetic dipole.
Be able to explain the concept of domains in ferromagnetic materials.
Be able to use the definition of magnetic flux and discuss the significance of
the result that the net magnetic flux out of a closed surface is zero.
Be able to calculate the magnetic moment of a current loop and the torque
exerted on a current loop in a magnetic field.
Be able to discuss the magnetism of the Earth.
Indicating Direction of B-fields S
One way of indicating the directions of fields perpendicular
to a plane is to use crosses X and dots :
A field directed into the paper
is denoted by a cross “X” like
the tail feathers of an arrow.
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
A field directed out of the paper
is denoted by a dot “” like the
front tip end of an arrow.
Origin of Magnetic Fields
S
Representing Magnetic Field
S
Since no isolated magnetic pole has ever been
found, we can’t define the magnetic field B in
terms of the magnetic force per unit north pole.
We will see instead that
magnetic fields result from
charges in motion—not
from stationary charge or
poles.
E
+
+
v
B^v
S
Force of a B-field
N
(m / s )C
T
Ns
(m)C
1T 1
Right Hand Rule #1 (RHR-1)
B
A magnetic field intensity of one tesla (T) exists in a region of
space where a charge of one coulomb (C) moving at 1 m/s
perpendicular to B-field will experience a force of one newton (N).
T
Magnetic Field
Into Page
Magnetic Field
Out of Page
N
m A
A Tesla is a Newton
meter ampere:
S
•index finger points in
direction of velocity vector
of + charge (or current)
•Thumb points towards
force
+
+
I
F
I
• direction of B vector is
normal to palm (middle
finger up)
• point thumb 180o
opposite direction for
electron (flip hand over)
THIS IS FOR CONVENTIONAL CURRENT, ELECTRON CURRENT WOULD USE
SAME FINGERS & THE LEFT HAND RULE OPPOSITE
7
S
S
If the magnetic field is perpendicular to the wire
(like in the drawing), then the angle is ninety
degrees and the sine of the angle is one.
This is when the current will have its maximum value.
FMax BIl
FB BIl sin
Note that if the field and the current are in the
same direction, no force is exerted on the conductor.
S
What is the force and the direction on 3.5 m long wire that is carrying a
12-A current if the wire is perpendicular to the earths magnetic field
(5.0x10-5)
• Talk about a dot product of vectors to
explain right hand rule
• Place wheel on the desktop wooden
handle down so that it spins like a top
S
FMax BIl
FB (5.5 x10 5 T )(12 A)(3.5m) 2.1x10 3 N
FORCE TO THE LEFT OF WIRE
WIRE IN A MAG FIELD
S
What is the current and the direction on 35 cm long wire perpendicular
to a magnetic field of 8.5T if the force that results is 125 N and forces the
wire to the left.
S
FMax BIl
I
FB
F
Bl
(125)
42 A
(8.5T )(.35m)
CURRENT UPWARDS
8
A wire has a current of 12.5 A. It goes east to west.
The magnetic field goes north to south. The magnetic
field strength is 55 T. Find the force acting on a 25cm
length of wire.
S
S
• Electrostaics
• Can have a mono pole
• Positive seeks negative
• If you keep cutting a metal bar in half, all the way down to an
electron you will still have a magnetic pole on that electron. You
can’t cut it so that there is no dipole.
The magnetic field is perpendicular
to the direction of the current, so we
have a maximum force.
F BIl
Magnetism
Always have dipole
North seeks south
• The electrons charge is through to come from the magnetic spins of
the electrons around the proton
55 x 106 T 12.5 A 0.25 m
1 . 7 x10
4
N
• As the electrons are random – no magnetically charge bar, but if we
move the electons in a similar order we develop a magnetic field
FORCE TO INTO THE PAGE
Repeat the previous problem but change the
direction of the wire to Enter the magnetic field
with an angle of 25o into the magnetic field
S
B
•index finger points in
direction of velocity vector
of + charge (or current)
25
FB BIl sin
( 55 x10 6 T )(12 . 5 A )( 0 . 25 m )(sin 25 )
(55 x10 6 T )(12.5 A)(0.25m)(sin 25)
(17 x10 5 T )(sin 25 )
•Thumb points towards
force
+
+
v
F
7 . 26 x10 5 N
FORCE TO INTO THE PAGE
FB BIl sin
FB Bqv sin
m
qv( B) C ( B) A m( B )
s
Il
• point thumb 180o
opposite direction for
electron (flip hand over)
I
FOR A ELECTRON THE VELOCITY USE SAME FINGERS & THE LEFT HAND RULE
FIELD, CURRENT(v), FUMB
S
Cm
A m
s
T ( A m) N
• direction of B vector is
normal to palm (middle
finger up)
+
+
F B
Middle Finger
+
N
N
A m
N
A m
S
RIGHT HAND RULE
Thumb
ION IN A MAG FIELD
S
Right Hand Rule #1 (RHR-1)
The right hand rule gives the direction for the force
v
+
S
acting on a particle
that has a positive charge.
If the charge on the particle is negative,
then the direction of the force will be in the opposite direction. Or you could
use your left hand in the same way.
Both formulas leave us with Newton's when multiplying by Teslas
I is same as v for a proton Opposite is v for and electron
9
Magnetic Forces on a Moving CationS
Imagine a tube that
projects charge +q
with velocity v into
perpendicular B field.
F
S
B
v
+
N
S
Upward magnetic force F
on charge moving in B field.
Experiment shows:
F qvB
Force and Angle of Path
S
• The force on the charged particle is at a maximum
when the velocity is perpendicular to the magnetic
field.
• Note that if the velocity is in the direction of the
magnetic field, the magnetic force will be zero.
+
Force and Angle of Path
N
S
N
S
N
S
S
Deflection force greatest
when path perpendicular
to field.
+
+
Least at parallel.
• The force is always perpendicular to the velocity
and the magnetic field, B.
WHAT IS THE CHARGE ON EACH PARTICLE
S
Practice With Directions:
S
What is the direction of the force F on the charge in
each of the examples described below?
X
X
X
X
F
X X X
Up
X+ X v X
X X X
X X X
X
X
Left
X
X
v
X X
FX X
+
X X
X X
X
X
X
X
F
v Up
F
Right
negative q
v
10
A 2 nC + charge is projected with velocity 5 x 104
m/s at an angle of 300 with a 3 mT (milliTesla)
magnetic field as shown. What is the magnitude
and direction of resulting force?
S
Circular Motion in B-field
S
v
+
30o
F qvB sin
(2 x10 9 C )(5 x10 4 m / s )(3x10 3 T )(sin 30)
1.5 x10 7 N
Using right-hand rule, the force is seen to be into paper.
A proton moving at 5.5 x 107 m/s along the x - axis
enters an area where the magnetic field is 3.5 T
directed at an angle of 45 to the x - axis lying in the
xy plane.
(a) What is magnitude of force?
(b) What is direction of force?
(c) What is the acceleration acting on the proton?
S
S
(a) The force is given by:
F qvB sin
m
F 1.6 x 1019 C 5.5 x 107 3.5 T sin 45
s
11
F 2.2 x10
N
http://www.youtube.com/watch?v=1sldBwpvGFg
(b)Using the right hand rule:
Force is in the z direction.
(c) To find the acceleration we use the second law:
S
Circulating Charged Particles S
• electric field will cause parabolic
path parallel to field
F ma
a
F
m
2.2 x 1011 N
1.67 x 10 27 kg
1.3x1016 m / s
• magnetic field will cause circular
path since FB is ALWAYS
perpendicular to B and v
11
S
FC
mv2
;
R
FC F B
Beam of electrons moving in a circle, due to the
presence of a magnetic field. Purple light is
emitted along the electron path, due to the
electrons colliding with gas molecules in the bulb.
S
S
The magnetic force F on a moving charge is always
perpendicular to its velocity v. Thus, a charge moving
in a B-field will experience a centripetal force.
F B qvB ;
Centripetal Fc = FB
mv2
qvB
R
The radius of
path is:
mv
R
qB
X
X +X
X
X
X
+
X
X
X X X
X RX X X
X
X FX
X
X
X
X
+
c
X
+
X
X
X
X
X
X
X
An electron travels at 5.0x107m/s perpendicular to a uniform mag field
Of 10 T. Describe the path.
S
FC FB
mv 2
qvB
r
(9.1x10 31 kg )(5.0 x107 m / s)
(1.6 x10 19 C )(10T )
r
r 2.8 x10 5 m
S
A proton with a velocity of 6.8 x 106 m/s zooms through
the CERN magnetic field. (55 T).
What is the max magnetic force acting on the proton?
A proton with a velocity of 6.8 x 106 m/s zooms through
the CERN magnetic field. (55 T).
What is the max magnetic force acting on the proton?
S
FMax qvB
m
FMax 1.6 x 1019 C 6.8 x 106 55 x 106 T
s
F 598 x10 17 N 6.0 x10 17 N
12
S
S
q1
A proton travels at 1.0x107m/s perpendicular to a uniform mag field
and remains in a circular pattern of .01 meter. Describe the radius.
v
FB
r
FC FB
FB
mv 2
qvB
r
v
Particle follows
circular path
(1.67 x10 27 kg )(1.0 x107 )
(1.6 x10 19 C )( B )
.01
If the initial direction of particle’s velocity is not perpendicular to the magnetic field, then
there will be an angle between the field and the velocity. The path will end up being
a type of spiral called a helix. This would be the general path of a charged
particle in a magnetic field. The circular path is a special case that occurs only
when the direction of the particle’s velocity is perpendicular to the field.
B 10.4T
A proton travels through a perpendicular to a uniform mag field
of 20T and remains in a circular pattern of .01 meter. What is the velocity?
S
FC FB
mv 2
qvB
r
Circular Path of Particle
This constant force acting to
change the direction of the particle
acts as a centripetal force.
UCM of charged particle in B field S
Fb
qvB
This image cannot currently be display ed.
1.67 x10 27 kg (v)
(1.6 x10 19 C )(20T )
.01m
V= 1.9x107 m/s
v
2 r
T
T
m2
qB
mv 2
mv
r
r
qB
THE PERIOD IS
INDEPENDENT
OF THE VELOCITY
mass of particle (identity) can be determined
from B strength and period of UCM
S
A proton with a velocity of 6.8 x 106 m/s zooms through
the CERN magnetic field. (55 T).
What is the B field required of CERN proton at speed of
light?
OK SO WHY DOES THAT SILLY THING
SPIRAL DOWN THE MAG FIELD
S
13
Helical motion of charged particle S
• axis of helix is parallel to B
field vector
S
Q2. Draw the magnetic field lines around a straight section of wire carrying a
current horizontally to the left.
The magnetic field lines circle around the wire and get weaker as you get farther
away from the wire. To determine the direction, use the Right Hand Rule. Notice,
if the wire was laid horizontally on this piece of paper in a left-right direction and
the current was moving to the left, the magnetic field lines would be pointing into
the paper above the wire and coming out of the paper below the wire. If the wire
was placed perpendicular to this page with the current coming out of the end of
the wire facing us, the magnetic fields would point around the wire in a
counterclockwise direction.
• v causes UCM
• v causes helix
I
•CD demo
THIS HAPPENS!
S
Q7. The magnetic field due to current in wires in your home can affect a compass.
Discuss the effect in terms of currents, including if they are ac or dc.
S
F
v
+ particle
v of
B
Magnetic Field
WHY DOES THE PATH CHANGE BUT THE
VELOCITY NOT CHANGE?
WHY DOES IT HAPPEN?
Typical current in a house circuit is 60 Hz AC. Due to the
mass of the compass needle, its reaction to 60 Hz (changing
direction back and forth at 60 complete cycles per second)
will probably not be noticeable. A DC current in a single wire
could affect a compass, depending on the relative orientation
of the wire and the compass, the magnitude of the current,
and the distance from the wire to the compass. A DC current
being carried by two very close wires in opposite directions
would not have much of an effect on the compass needle,
since the two currents would cause magnetic fields that
tended to cancel each other.
V and B angle less than 90 deg
AN ELECTRON WOULD HAVE THE SAME SHAPE BUT AN OPPOSITE SPIN
WHY DOES IT SPIN?
WHO KNOWS?
S
• Place a + charged up balloon in a magnetic field
– nothing happens. Magnetic fields don’t
affect stationary charges.
• But a moving charge traveling through a
magnetic field will experience a FORCE.
• The force exerted will be perpendicular to the
motion of the charge and perpendicular to the
direction of the field.
• The result of the force is to cause a deflection of
the charged particle. It gets pushed to the side.
• A helium balloon (+ charged) that ascends into a
magnetic field would spin along the magnetic
field with the right hand rule.
Q8. If a negatively charged particle enters a region of uniform magnetic field which is
perpendicular to the particle’s velocity, will the kinetic energy of the particle increase,
decrease, or stay the same? Explain your answer. (Neglect gravity and assume there is
no electric field.)
S
The magnetic force will be exactly perpendicular to the
velocity, and so also perpendicular to the direction of
motion. Since there is no component of force in the
direction of motion, the work done by the magnetic
force will be zero, and the kinetic energy of the particle
will not change. The particle will change direction, but
not change speed.
14
S
Magnetic Work
10.The maximum magnetic force as given in Eq. 20-4 can be used since
the velocity is perpendicular to the magnetic field.
S
W F cos s
Fmax qvB 1.60 1019 C 8.75 105 m s 0.75T 1.05 1013 N
Magnetic Force and Work: For work to be done, a
force has to act on an object
A magnetic field could do work on a moving charged
particle since it does exert a force on it.
By the right hand rule, the force must be directed to the North.
But force and the displacement are not in the same
direction.
WORK BY A MAG FIELD
S
Magnetic Work
S
• The cosine of a ninety degree angle is zero.
• Magnetic work will be zero since the angle
between the force and the motion is 90.
• A magnetic field does no work on a
moving charged particle.
Magnetic Force
S
VIDEO
S
• EXPLAIN HOW A MASS SPECTROMETER
WORKS
• EXPLAIN HOW A STAR CHAMBER WORKS
Charge moving perpendicular to B field
experiences maximum force
• EXPLAIN HOW A CYCLOTRON WORKS
FB proportional to component of velocity vector
• MIT #13
FORCE IS ALWAYS PERPENDICULAR TO THE
MAGNETIC FIELD EVEN IF VELOCITY IS NOT
15
eV (WORK/ENERGY)
10-19
S
joules
S
eV (WORK/ENERGY)
S
S
one eV = 1.602 x
A volt is not a measure of
energy.
An electron volt is a
measure of energy.
An electron volt is the
kinetic energy gained by an
electron passing through a
potential difference of one
volt.
KE
1 2
mv
2
2 KE
v
m
mv
r
qB
Bqv
m
mv 2
r
http://www.youtube.com/watch?v=J-wao0O0_qM
2 KE
m
qB
http://www.youtube.com/watch?v=wyL7TRWAmzk&feature=related
A proton is fired by 10.MeV through a perpendicular to a uniform mag field
of 20T and remains in a circular pattern. What is the radius?
S
r
2 KE
v
m
Bqv
2 KE
r
qB
mv
r
qB
mv
r
S
2
This image cannot currently be display ed.
m
2 KE
m 2 KEm
qB
qB
2(10.0 x106 eV )(1.6 x10 19 J / eV )(1.67 x10 27 kg
(1.6 x10 19 C )(20T )
• Bombard Molecule with high KE electrons
Which knocks another electron lose (forms
a radical cation.)
The magnetic force F=qvbsinonly works
on charged particles
Lone magnetic field deflects the lightest
atoms the most.
r .022m
16
S
A proton in a mass spectrometer is fired beyond an efield
X mag field at 5x107 m/s. What radius will it strike the
mass spectrometer if the B field is 1.0T?
mv 2
qvB
r
r
r
Crossed E, B fields
S
Using FB with and FE to accelerate an ion
mv
qB
E vB
(1.67 x10 27 kg )(5 x10 7 m / s )
(1.6 x10 19 C )(1.0T )
This allows an ion to move through
Without alters course with the Efield, but
Accellerates
r .52m
OR
S
Crossed E, B fields
What B field would B required to accelerate a proton to a
speed of 6x107m/s and with an Efield of 108 N/C?
S
balancing the FB with and FE from
electric field
FE FB
E vB
qE qvB
108 N / C (6 x107 m / s ) B
This allows an ion to move through
Without altering course
E vB
OR
B 1.66
V
vB
d
DISTANCE IN FIELD IS
IRRELEVANT
• DO WE NEED TO KNOW DISTANCE IN
FIELD?
•
NO DISTANCE IN THE FIELD IS THE
SAME FOR BOTH FIELDS – SO THEY
BOTH GET THE SAME TIME TO DO
WORK (THE B FIELD JUST DOESN’T
GET CREDIT FOR IT.
S
Ns
1.66T
mC
MASS SPECTROMETER
A
S
V
17
MASS SPECTROMETER
A
S
V
R
S
A particle with an unknown mass and charge moves with a constant speed of
v = 2.2 x 106 m/s as it passes undeflected through a pair of parallel plates
as shown. The plates are separated by a distance of d = 5.0 x 10-3 m, and
a constant potential difference V is maintained between them. A uniform
magnetic field of B = 1.20 T directed into the page exists between the plates
and to the right of them as shown. After the particle passes into the region
to the right of the plates where only the magnetic field exists, it trajectory is
circular with radius r = 0.10 m.
(a) What is the sign of the particle’s charge? Explain your answer.
(b) On the drawing, indicate the direction of the electric field provided by the
plates.
(c) Determine the magnitude of the potential difference between the plates.
(d) Determine the ratio of charge to mass (q/m) of the particle.
A
V
R
What will be the radius if the B field isS
1.66T and velocity is 6x107m/s?
FC FB
S
(a)Finding the potential difference between the plates:
V
The electric field is given by
2
mv
qvB
r
(a)If the particle is positive, the magnetic force would be up and particle
would curve above the plates. Since it goes the other way, it must have
negative charge. Between the plates, the negative particle is deflected
downwards. Therefore the electric field must force the negative particle up.
The direction of the field is the direction a positive test charge would go so
the field must be down. This way the particle will be deflected upward by
the electric field of the plates.
mv
r
qB
E
The electric force from the plates is:
Set the two forces equal:
4
r 2.1x10 m
V vBd
A proton drifts through with 1 MeV
S
and is accelerated into a B field of
1.0T.
2qV
m
r
2 KEm
qB
v 1.4 x10 7 m / s
r
2(1 / 2mv 2 )m
qB
r .05m
qvB qE
V
d
V
qvB q
d
qvB
F qE
m
V 2.2 x 106 1.20 T 5.0 x 103 m
s
for E:
13.2 x 103V
S
(C) Finding the ratio of charge to mass q/m :
From the circular path of the particle in the magnetic
field, we know that:
The centripetal force = the magnetic force in the field
Set these two things equal to each other:
KE qV 1 / 2mv 2
v
d
The magnetic force from the magnetic field is: F
mv 2
qvB
r
Solving for q/m (the charge to mass ratio):
q v2
m rvB
v
rB
q
m
1
2.2 x 106
m
s 0.10 m 1.20 T
1 .8 x 1 0 7
C
kg
18
Q8.
If a negatively charged particle enters a region of uniform magnetic
field which is perpendicular to the particle’s velocity, will the kinetic energy of
the particle increase, decrease, or stay the same? Explain your answer.
(Neglect gravity and assume there is no electric field.)
S
The magnetic force will be exactly perpendicular to the velocity, and so also
perpendicular to the direction of motion. Since there is no component of force in
the direction of motion, the work done by the magnetic force will be zero, and the
kinetic energy of the particle will not change. The particle will change direction,
but not change speed.
The kinetic energy of the proton can be used to find its velocity.
The magnetic force produces centripetal acceleration, and from this the radius can be
determined.
KE 12 mv 2
r
9. Alpha particles of charge
q 2e
mv
qB
m
7
2 KE
qvB
m
2 KE
m
qB
S
and mass m 6.6 10 27 kg
are emitted from a radioactive source at a speed of 1.6 10 m s .
What magnetic field strength would be required to bend them into a
circular path of radius 0.25 m?
S
14. A 5.0-MeV (kinetic energy) proton enters a 0.20-T field, in a plane
perpendicular to the field. What is the radius of its path?
2 KE m
qB
mv 2
r
1.60 10
2 5.0 106 eV 1.60 1019 J eV 1.67 1027 kg
19
C 0.20 T
Oersted
1.6 m
S
In this scenario, the magnetic force is causing centripetal motion, and so
must have the form of a centripetal force. The magnetic force is perpendicular to
the velocity at all times for circular motion.
Fmax qvB m
v2
r
B
mv
qr
6.6 10 kg 1.6 10 m s 1.3T
2 1.60 10 C 0.25 m
27
7
19
https://www.youtube.com/watch?v=-w-1-4Xnjuw
13. An electron is projected vertically upward with a speed of
1.70 10 6 m s
S
into a uniform magnetic field of 0.350 T that is directed horizontally away from
the observer. Describe the electron’s path in this field.
20-6, 20-8
S
13. The magnetic force will cause centripetal motion, and the electron will
move in a clockwise circular path if viewed in the direction of the magnetic
field. The radius of the motion can be determined.
Fmax qvB m
v2
r
r
mv
qB
9.1110 kg 1.70 10 m s 2.77 10
1.60 10 C 0.350 T
31
6
19
5
m
19
CURRENT THROUGH WIRE
S
S
Instead, Oersted was amazed
to see that the needle
rotated until it pointed
perpendicular to the wire, as
shown in the figure at right.
The forces on the compass
magnet’s poles were
perpendicular to the direction
of current in the wire.
A CURRENT (EVEN AN MOVING ELECTRON) CAN ILLICIT A MAGNETIC FIELD
Oersted also found that when
there was no current in the
wire, no magnetic forces
existed.
S
S
The strength of the field also varies inversely with the
distance from the wire.
A compass shows the direction of the field lines.
If you reverse the direction of
the current, the compass
needle also reverses its
direction
I
S
S
In 1820, Danish physicist Hans Christian Oersted
was experimenting with electric currents in wires.
Oersted laid a wire across the top of
a small compass and connected the
ends of the wire to complete an
electrical circuit, as shown.
He had expected the needle to point toward the wire
or in the same direction as the current in the wire.
+
r
B
Right Hand Rule
20
S
What is the direction of the magnetic field around this conductor
S
Right hand
e-
Current
S
So with DC, once the field is built up, it doesn’t change
and remains constant. If the current varies, the magnetic
field will also vary.
S
Strength of Magnetic Field: The magnetic field
strength around a straight section of a current carrying
conductor is given by this equation:
A compass needle is a magnet that can rotate to align
itself with a magnetic field.
I
B
0 I
2 r
I
B is the magnetic field strength,
0 is the permeability of free space,
I is the current, and r is the distance to
the center of the conductor.
Field around
Conductor
No Current
0 4 x 107
Current
S
• A current carrying wire passes between the
magnet and a force is exerted on it, pushing it
up.
• Point your fingers from north to south
(direction of the field) and your thumb in the
direction of the current. Your palm points up
and this is the direction of the force. Just like
we did with a single charged particle.
T m
A
A long straight wire has a current of 1.5 A.
Find the magnitude of the magnetic field at a point that is
5.0 cm from the wire.
I
B 0
2 r
7 T m
1.5 A
4 x 10
A
2 0.050 m
S
6.0 x 106 T
21
Magnetic Fields due to Currents
S
Force on current-carrying wire
S
Oersted’s discovery
• use RHR-1 for force
direction
• thumb in direction of
current
This discovery lead to some very powerful things that
basically changed the world! Oersted reported the
phenomenon, and then forgot about it.
S
Ampere’s
Law F on parallel wires S
wire 1
wire 2
But other scientists picked up on it.
R
B2
off
on
Two competing influences when
determining force on wire 2 due to
current in wire 1 and wire 2
reverse
current
x
x
x
x
x
x
x
x
i2
F1
I’s in same direction
S
Johann Salomo Cristoph Schweiger (1779 - 1857) showed
that the amount of deflection of the needle in the Oersted
experiment was proportional to the strength of the current
flowing through the conductor. He thus created the first
electric current meter, the galvanometer.
B1
0i1
2R
F2 is increasing linearly with
current in wire and B1 it is in
F2
i1
These drawings represent Oersted's experiment.
B1
B1 is increasing linearly with
current but decreasing with
separation distance R
F2 i2 LB1
0i1i2
L
2 R
OPEN THESE WITH MEDIA
PLAYER
S
2 wr dif I.php
2 wr same I.php
http://www.youtube.com/watch?v=43AeuDvWc0k
22
Force between parallel wires
anti-parallel currents
repel
S
S
parallel currents
attract
Ampere’s Law and +/- current
S
Force Between Parallel Conductors: Ampere found
that when two current carrying conductors are in the
vicinity of each other, they will exert magnetic forces
upon one another.
S
Each of the conductors creates its own magnetic field.
These fields, depending on their direction, will either
attract or repel each other. Wire number two sets up a
magnetic field, B2
l
loop 1
loop 2
ienclosed = 1i
ienclosed = 0
in is +, out is
out is +, in is
B2
The French physicist, Andre-Marie Ampere (1775 - 1836) set up
two parallel wires. One of them was free to move sideways,
back and forth. When both of the wires carried current in the
same direction, they attracted each other. If the current flowed
in opposite directions, they repelled each other.
Permeability: Permeability is a property of a material
that has to do with how it changes the flux density in a
magnetic field from the permeability value of air.
1.Some materials (like iron) are very permeable to lines
of flux.
2.lines of flux are attracted to the material and pass
through it rather than through air.
3.material with low permeability would have little effect
on lines of flux,
4.material with a high permeability would dramatically
change the flux density of the magnetic field.
S
0 I 2
2 d
B2
S
N
S
In the drawing above, you can see what happens when a
permeable object is placed in the field. The lines of force will
concentrate in highly permeable materials.
F1
This field exerts a force on wire number one =
F BIl
so
F1 B2 I1l
I
0 2 I1l
2 d
0 I 2 I1l
2 d
F1
A 5.00 cm length of wire has a current of 3.50 A. It is
12.0 cm from a second 5.00 cm length of wire that has a
current of 4.95 A in the same direction. Find the force
of attraction between the two wires.
The magnetic field around the second wire is:
S
B
0 I
2 r
B2
0 I 2
2 r
The force it exerts on the first wire is:
o
FB BIl sin
or since 90
F1 B2 I1l
Plug in the equation for the magnetic field:
soft iron ring
N
I1
I2
d
F1 B2 I1l
B2
0 I 2
2 r
I
F1 0 2 I1l
2 r
7 T m
4 x 10
4.95 A 3.50 A 0.0500 m
A
F1
2 0.120 m
0 I 2 I1l
2 r
1.44 x 106 N
23
S
Mechanical Universe
• Faraday law video
• Run Magnet through a loop hooked to
galvanometer
29.A vertical straight wire carrying an upward 24-A current exerts an attractive force
per unit length of 8.8 10 4 N m on a second parallel wire 7.0 cm away.
What current (magnitude and direction) flows in the second wire?
S
29.
Since the force is attractive, the currents must be in the same direction,
so the current in the second wire must also be upward. Use Eq. 20-7 to calculate
the magnitude of the second current.
F2
I2
0 I1I2
2 d
S
Do this the day before induction
S
28. A long straight wire carries current I out of the page toward you.
Indicate, with appropriate arrows, the direction of B at each of the points C, D, and E
in the plane of the page.
To find the direction, draw a radius line from the wire to the field point.
Then at the field point, draw a perpendicular to the radius line, directed so
that the perpendicular line would be part of a counterclockwise circle.
l2
2 F2 d
0 l2 I1
C
2
4 10
7
8.810
TmA
4
D
2
10 m
13A upward
7.024A
Nm
I
E
S
30.
(I) Determine the magnitude and direction of the force between two parallel
wires 35 m long and 6.0 cm apart, each carrying 25 A in the same direction.
S
30.Since the currents are parallel, the force on each wire will be attractive,
toward the other wire.
F2
0 I1 I 2
2 d
l2
4 10
7
TmA
2
25 A 35 m 7.3 10
6.0 10 m
2
2
2
N, attractive
24
SOLENOID
S
Ideal Solenoid
S
• Hollow cylinder with coil wrapped around exterior
• Ideal solenoid, like ideal emf source, has assumed properties
that real ones do not.
Magnetic flux lines add together.
The field increases with each added loop.
SOLENOID
• External B field = 0, only field along longitudinal axis
S
acts like bar
magnet
SOLENOID
• This is a coil that has a hollow core (these are often
called "air cores").
• Adjacent to the coil is a soft iron or steel rod that fits
into the hollow core.
• When the solenoid is energized it develops a strong
magnetic field and pulls the rod into it.
• can turn switches on and off and control all sorts of
things. Cars, appliances, weapons systems, &tc.
all make great use of solenoids.
S
current i through each coil
n coils (turns) per meter
S
S
Magnetic Field Produced by a Coil
Many loops build up high flux density
Electromagnets ferromagnetic core makes up the
center of the coil
The magnetic field is even greater
Several advantages over permanent magnets:
- Very intense magnetic fields - much
stronger than permanent magnet fields.
- Can be switched on and off.
25
S
S
X
●
X
●
X
●
X
●
X
X
X
X
X
X
X
X
●
●
●
●
●
●
●
●
http://www.youtube.com/watch?v=3jXRZMuyjnQ&feature=related
• DEMO THE ELECTROMAGNET HERE
S
DIAGRAM THE FIELD OF THES
ELECTROMAGNET
TORQUE ON A CURRENT LOOP
S
Forces Caused by Magnetic Fields
S
Electric Motor
26
S
S
S
S
http://www.youtube.com/watch?v=so4d71HGflA&NR=1
S
TORQUE ON A CURRENT LOOP
S
27
TORQUE ON A CURRENT LOOP S
S
S
TORQUE ON A CURRENT LOOP S
TORQUE ON A MOTOR
•The Torque on the loop will rotate the loop to a smaller
Θ until the torque becomes 0 at Θ=0.
•If the loop turns past Θ=0 and the current remains the
same the torque reverses and the turns the loops
opposite and back to Θ=0
•For continuous rotation the current must
systematically reverse.
•In AC motors this reversal is natural
•DC Motors: as the loop becomes perpendicular to B
the torque becomes zero, but gaps at this
position provide the loop to continue on and not
decelerate back.
• In DC motors, a split ring commutator is used
SPLIT COMMUNICATOR
S
A coil of wire has an area of 2.0x10-4m2, consists of 100 loops/turns and
contains a current of 0.045A. The coil is placed in a uniform magnetic field of
magnitude 0.15T. (a) Determine the magnetic moment of the coil. (b) Find the
maximum torque that the magnetic field can exert on the coil.
S
(b)( NIA) BSin (9.0 x10 4 A m 2 )(0.15T ) sin 90
1.4 x10 4 N m
28
S
Conversion between CGS and SI magnetic units.
SI Units
SI Units
S
CGS Units
(Somm
Conversion
units.
(Gaussi
Quantity between CGS and SI magnetic
(Kennel
erfeld)
Forces Caused by Magnetic Fields
S
ly)
an)
Field
H
A/m
A/m
oersteds
Flux Density
(Magnetic
Induction)
tesla
tesla
gauss
Flux
weber
weber
maxwell
Magnetization
M
A/m
-
erg/Oe-cm3
Tape recorder
S
Galvanometers
The wire coil in an electric motor is called the armature. The
armature is made of many loops mounted on a shaft or axle.
The total force acting on the armature is proportional to nILB, where
n is the total number of turns on the armature, B is the strength
of the magnetic field, I is the current, and L is the length of wire
in each turn that moves through the magnetic field.
The magnetic field is produced either by permanent magnets or by
an electromagnet, called a field coil.
The torque on the armature, and, as a result, the speed of the motor,
is controlled by varying the current through the motor.
The Hysteresis Loop and Magnetic Properties
S
• When a mylar tape covered with fine iron dust
passes near a small electromagnet that has a
varying mangtic field, according to an electrical
signal, the dust become magnetized in different
directions. The electrical signal could be from a
radio or microphone.
• The tape then is a record of the electrical signal.
When it passes by another small electromagnet,
it creates an electrical signal, duplicating that of
the original signal. This signal can be amplified
and played back through loudspeakers.
Magnetic Media
S
29
Magnetic Media
S
Each bit is identified as either a 0 or a 1. How are these bits
stored?
When the read/write head passes over the spinning storage
disk, as in the figure below, the domains of atoms in the
magnetic film line up in bands.
Loud Speakers: Another cool application of the force
exerted by a magnetic field on a conductor is the
classic loudspeaker.
Here are the parts of a speaker: a flexible cone –
made of paper or thin plastic, a magnet base, and a coil.
S
N
The surface of a computer storage disk is covered with an
even distribution of magnetic particles within a film.
FMax BIl
S
N
Speaker exploded
Speaker assembled
This is a signal that varies with the music, that is, the
current increases and decreases with the music. The
amount of force exerted on the coil by the magnetic field
varies with the strength of the current.
Forces Caused by Magnetic Fields
S
Storing Information with Magnetic Media
The orientation of the domains depends on the direction of the
current.
Two bands code for one bit of information. Two bands
magnetized with the poles oriented in the same direction
represent 0.
When the current increases, the force increases, when
the current decreases, the force decreases and so on.
The coil sits in a slot cut into the magnet.
The force exerted on the coil causes it to move back
and forth – with the music. This also vibrates the cone,
which puts the sound into the air.
S
cone
to amplifier
coil
Two bands represent 1 with poles oriented in opposite
directions.
magnet
The recording current always reverses when the read/write
head begins recording the next data bit.
SPEAKERS
S
Forces Caused by Magnetic Fields
S
The Force on a Single Charged Particle
Charged particles do not have to be confined to a wire, but can
move across any region as long as the air has been removed to
prevent collisions with air particles.
A picture tube, also called a
cathode-ray tube, in a
computer monitor or television
set uses electrons deflected
by magnetic fields to form the
pictures on the screen, as
illustrated in the adjoining
figure.
30
S
S
S
S
S
What is causing this to happen?
S
http://www.youtube.com/watch?v=KXNELXRaBc4&feature=related
31
S
S
S
S
Q3.
In what direction are the magnetic field lines surrounding a straight wire
carrying a current that is moving directly away from you?
The magnetic field lines form clockwise circles centered on the wire.
S
1. (a) What is the magnitude of the force per meter of length on a straight wire
carrying an 8.40-A current when perpendicular to a 0.90-T uniform magnetic field?
(b) What if the angle between the wire and field is 45.0°?
S
(a)
Use an angle of 90 degrees and a length of 1 meter.
F IlB sin
F
l
IB sin 8.40 A 0.90T sin 90o 7.6 N m
(b)
F
l
IB sin 8.40 A 0.90 T sin 45.0o 5.3 N m
32
2. Calculate the magnitude of the magnetic force on a 160-m length of straight wire
stretched between two towers carrying a 150-A current. The Earth’s magnetic field of
5.0 10 5 T makes an angle of 65° with the wire.
S
S
F IlB sin 150 A 160 m 5.0 105 T sin 65o 1.1N
NEED A 2 WIRE HW PROBLEM
3. How much current is flowing in a wire 4.80 m long if the maximum force on it is
0.750 N when placed in a uniform 0.0800-T field?
S
S
The image part with relationship ID rId10 was not found in the file.
Fmax IlB I
Fmax
lB
0.750 N
4.80 m 8.00 102 T
1.95 A
49. A 30.0-cm-long solenoid 1.25 cm in diameter is to produce a
field of 0.385 T at its center. How much current should the
solenoid carry if it has 975 turns of the wire?
S
S
48. Use Eq. 20-8 for the field inside a solenoid.
B 0 IN l
4 10
7
T m A 2.0 A 420
0.12 m
8.8 103 T
49. Use Eq. 20-8 for the field inside a solenoid.
B 0 IN l I
Bl
0 N
0.385T 0.300 m
4 107 T m A 975
94.3A
33
S
Solenoid
S
A solenoid is a single wire wrapped in multiple loops or “windings”. It is
characterized by the number of windings per meter, n, the current, i, its length L
and its cross sectional area A.
In the limit of an infinitely long solenoid, the field outside the coil vanishes.
We can apply Ampere’s law to find B inside the coil.
Note that B is uniform; INDEPENDENT OF DIAMETER; similar to electric field
created by parallel plates
S
S
S
S
34
WHY DOES THIS HAVE TO S
SPIN TO GET CURRENT
S
• Batteries were not the ultimate answer however (they still
aren’t). They are expensive – metals and acids are costly –
and they don’t last long. Even today, battery power is much
more expensive than the electricity the power company delivers
to your house through the power lines.
• A really cheap source of electricity would be very useful.
• In 1831 two physicists, working independently, found a way to
make cheap electricity. Joseph Henry (in the good old US of A)
and Michael Faraday (in England) discovered electromagnetic
induction
Induced current can be induced in two separate ways: a
conductor can be physically moved through a magnetic field or
the conductor can be stationary and the magnetic field can be
moved (this is what happened in Faraday's experiment). The
production of current depends only on the relative motion
between the conductor and the magnetic field. In the drawing
below a magnet is dropped through a conductor formed into a
coil. As the magnet's lines of flux move through the loops in the
coil, it induces current. The amount of current depends on
several factors. One factor is the speed of relative motion. The
faster the motion, the greater the current. If you move the
magnet very slowly, you won't produce hardly any current at all.
If the motion is very rapid, more current is produced. Double the
speed and you double the current. Double the magnetic field and
you would also double the induced current.
S
Induced Current
S
Right-hand force rule shows current outward for
down and inward for up motion.
Down
I
B
I
B
Up
S
S
Another factor with a coil is the number of turns in
the coil. The more turns, the more voltage. Pushing
the magnet through twice as many loops produces
twice the voltage. And so on.
Sounds like something for nothing, but that ain't the
case. It takes energy to push the magnet through
the coil. The more loops, the more energy it takes to
push the magnet through them. So you have to put
work into the system to induce the electricity.
35
Electromotive Force, emf: The induced voltage is called the emf.
The symbol for emf is
Induction actually creates electromotive force
S
Mechanical Universe
•
•
which really isn’t a force, although they call it that.
We learned about internal resistance in batteries and earlier when we studied curr
In the problems we will be doing,
internal resistance of the loop (or loops) will usually be negligible,
so voltage and emf are essentially the same. Figure
•
•
•
•
V emf 0
•
•
•
.
S
Lesson 37: Electromagnetic Induction
After Oersted's 1820 discovery that electric currents create magnetism, it
was obvious that in some way magnetism should be able to create electric
currents. The discovery of electromagnetic induction, in 1831, by Michael
Faraday and Joseph Henry was one of the most important of the 19th
century, not only scientifically, but also technologically, because it is the
means by which nearly all electric power is generated today.
Text Assignment: Chapter 41
Instructional Objectives
Be able to state Faraday's law and use it to find the emf induced by a
changing magnetic flux.
Be able to state Lenz's law and use it to find the direction of the induced
current in various applications of Faraday's law.
Be able to state the definitions of self inductance and mutual inductance.
Be able to state the expression for the energy stored in a magnetic field and
the magnetic energy density.
Be able to apply Kirchhoff's laws to obtain the differential equation for an LR
circuit and be able to discuss the behavior of the solution.
In AP B this is normally the case.
Magnetic Flux: Emf is induced by a change in a
quantity called the magnetic flux rather than by a
change in the magnetic field. Think of the flux as the
strength of a magnetic field moving through an area of
space, such as a loop of wire. For a single loop of wire in
a uniform magnetic field the magnetic flux through the
loop is given by this equation:
S
BA cos
S
• PUT A PICTURE OF THE WIRES
BURNED
is the magnetic flux, B is the magnetic field
strength, A is the area of the loop, and is the angle
between B and a normal to the plane of the loop.
Self-Induction & Inductance
Faraday’s Law cases have been for
an external magnetic field causing
an induced emf in a separate loop
or solenoid.
S
HOW IS A GENERATOR S
DIFFERENT THAN A MOTOR
When current through a solenoid is
changing this produces a flux change
through itself which induces an emf.
This process is called self
induction.
36
Faraday’s Law of Electromagnetic InductionS
Faraday’s Law of Electromagnetic InductionS
When flux through a loop changes with time an emf is
induced in the loop causing current to flow in the loop
The magnetic flux is proportional to the number of lines
of force passing through the loop. The more lines the
bigger the flux.
Area
normal
normal
q
When flux through a loop changes with time an emf is
induced in the loop causing current to flow in the loop
S
q
q
S
S
S
N
B
Loop in field
Side view
If the loop is perpendicular to the magnetic field ( = 0)
then the magnetic flux is simply:
S
BA
This is the maximum value that the flux can have.
On the AP Physics Test, you will have the flux equation
in this form:
m B A BA cos
q=0
= BA
q = 90
=0
B
Side view of loops
in magnetic field
N
B
S
Magnetic Flux Density
• Magnetic flux lines
are continuous
and closed.
B
A
A
• Direction is that
of the B vector at
any point.
Magnetic Flux
density:
When area A is
perpendicular to flux:
B
; = BA
A
The unit of flux density is the weber per square meter.
37
Application of Faraday’s Law
S
A change in flux can
occur by a change in area or
by a change in the B-field:
= B A
A loop of wire measures 1.5 cm on each side.
A uniform magnetic field is applied perpendicularly to the
loop, taking 0.080 s to go from 0 to 0.80 T.
(field is perpendicular to the loop)
Find the magnitude of the induced emf in the loop.
S
BA
= A B
Rotating loop = B A
m B A BA cos
Loop at rest = A B
n
n
t
0.80 T 0.015 m 0
2
0.080 s
0.0022 V
n
Parallel Coils
S
LENZ’S LAW
• Current induced by changing flux flows in such a
direction to oppose the change that caused it
S
act in same way as
parallel current
carrying wires
•Lenz’s law is a manifestation of the law of COE.
•It is the change in the field and not the field itself that
is opposed by the induced magnetic effects.
LENZ’S LAW
S
LENZ’S LAW
S
Faraday couldn’t explain why the induced current was
opposite what would be expected. Then stepped Lenz.
t
Lenz’s law: An induced current will be in such a direction
as to produce a magnetic field that will oppose the
motion of the magnetic field that is producing it.
If the magnet is turned so that a south pole approaches the coil,
the induced current will flow in a clockwise direction.
38
Changing Magnetic Fields Induce EMF
S
Opposing Change
S
Magnet falling through copper tube
The animation below is an example of how Lenz’s law works.
http://www.youtube.com/watch?v=JDCgxZ87oNc
http://www.youtube.com/watch?v=iABmUEH5s0k&feature=fvw
http://www.youtube.com/watch?v=glCNP6qH_Dc&NR=1&feature=fvwp
http://www.youtube.com/watch?v=c3asSdngzLs
DEMO Magnet move swiftly over
an aluminum can
1. No Current
S
Induced EMF: Observations S
B
Flux lines in Wb
Faraday’s observations:
2. Induced Current
Opposes Field
• Relative motion induces
emf.
1. No Current
• Direction of emf depends
on direction of motion.
N turns; velocity
2. Induced Current
• Emf is proportional to
rate at which lines
are cut (v).
Faraday’s Law:
Opposes Field D
1. No Current
N
SLOWING TRAIN W/ EDDY
S
CURRENTS
• During braking, the metal wheels are
exposed to a magnetic field from an
electromagnet, generating eddy currents
(induction) in the wheels.
• The magnetic interaction between the
applied field and the eddy currents acts to
slow the wheels down.
• faster the wheels spin = stronger the effect,
• producing a smooth stopping motion.
http://www.youtube.com/watch?v=Bkbdm66UQis&feature=related
• Emf is proportional to
the number of turns N.
E = -N
t
The negative sign means
that E opposes its cause.
A coil has 200 turns of area 30 cm2. It flips from
S
vertical to horizontal position in a time of 0.03 s. What
is the induced emf if the constant B-field is 4 mT?
A = 30 cm2 – 0 = 30 cm2
N = 200 turns
n
= B A = (3 mT)(30 cm2)
= (0.004 T)(0.0030 m2)
= 1.2 x
10-5
N
B
S
Wb
B = 4 mT; 00 to 900
E N
1.2 x 10 Wb
(200)
t
0.03 s
-5
E = -0.080 V
The negative sign indicates the polarity of the voltage.
39
Calculating Flux When Area S
is Not Perpendicular to Field
The flux penetrating the area
A when the normal vector n
makes an angle of with the
B-field is:
n
A
If a generator produces only a small current, then the opposing
force on the armature will be small, and the armature will be
easy to turn.
If the generator produces a larger current, the force on the larger
current will be greater, and the armature will be more difficult
to turn.
BA cos
S
Changing Magnetic Fields Induce EMF
Opposing Change
B
A generator supplying a large current is producing a large amount
of electric energy.
The angle is that the plane of the area (the normal makes
with B field. ) THIS IS NOT THE PLANE OF THE LOOP.
A current loop has an area of 40 cm2 and is placed in
a 3-T B-field at the given angles. Find the flux S
through the loop in each case.
x
x
x
x
x x
x x
A
x x
x x
n
x
x
x
x
A = 40 cm2
n
change B intensity
(a) = BA cos 00 = (3 T)(0.004 m2)(1);
12.0 mWb
(b) = BA cos
0 mWb
= (3 T)(0.004
m2)(0);
S
•
S
change current in
solenoid
pull loop into/out of B
generator: rotating
coil in fixed B field
(c) = BA cos 600 = (3 T)(0.004 m2)(0.5); 6.00 mWb
•
•
Many ways to change flux through a loop
n
(a) = 00 (b) = 900 (c) = 600
900
The opposing force on the armature means that mechanical
energy must be supplied to the generator to produce the
electric energy, consistent with the law of conservation of
energy.
slide a bar across a rail system
causing loop to increase in size
http://www.youtube.com/watch?v=e0pAHF1yamg&feature=related
and more
to come!
S
Superconductors
An extreme example of a diamagnet is a superconductor. These materials are known primarily through their
electrical properties - at some relatively low temperature their electrical resistance is exactly zero. Thus, one can
establish a current in a superconductor and it will never die away due to resistance, even when the source of
potential difference that started the current is removed. Superconductors also have interesting magnetic
properties; they are perfect diamagnets: when an applied magnetic field is applied, eddy currents in the
superconductor induce a magnetic field which exactly cancels the applied magnetic field. This is the Meissner
effect. This effect is responsible for the magnetic levitation of a magnet when placed above a superconductor.
Suppose, as in Fig. 9.17, we place a magnet above a superconductor. The induced magnetic field inside the
superconductor is exactly equal and opposite in direction to the applied magnetic field, so that they cancel within
the superconductor. What we then have are two magnets equal in strength with poles of the same type facing
each other. These poles will repel each other, and the force of repulsion is enough to float the magnet. Such
magnetic levitation devices are being tried on train tracks in Japan; if successful, this would make train travel much
faster, smoother, and more efficient due to the lack of friction between the tracks and train (in some cases, rather
than superconductors, strong electromagnets are used to provide the magnetic levitation).
Despite these interesting properties, superconductors are not widely used in today's world, outside of as
electromagnets to generate strong magnetic fields in certain medical diagnostic devices and in particle
accelerators. The reason for this is that superconductors exist only below a certain critical temperature, and
above that temperature they behave like normal materials. When first discovered these critical temperatures were
of the order of 10 K (about -260o C), which was (and still is) fairly difficult to reach (this is about the temperature at
which helium liquefies). However, recently high temperature superconductors have been discovered which
have critical temperatures of the order of 100 K and above (about -170o C). This is about the temperature that
nitrogen liquefies, and is relatively easy to reach with today's technology - ``dry ice'' is liquid carbon dioxide at this
temperature. These developments has spurred research into other uses of superconductors such as in magnetic
levitation devices and as circuit elements in computers to increase speed by cutting down on resistance.
40
S
Directions of
Forces and EMFs
An emf E is induced by
moving wire at velocity v
in constant B field. Note
direction of I.
From Lenz’s law, we see
that a reverse field (out) is
created. This field causes a
leftward force on the wire
that offers resistance to the
motion. Use right-hand
force rule to show this.
INDUCED EMF
Blv
(T )(m)(
(
m
)
s2
I
B
v
Induced
emf
x x x
x x
x x x
x x
x x x
x x
x x x
I
v
B
Lenz’s law
S
S
S
S
N m
A s
( )( )
J
A s
J
C
s
s
J
C
V
Binduced points opposite
X X
X
X
X X
X
X
X X
X
X
B increasing
out of page
X X
X
X
X X
X
X
X X
X
X
B increasing
into page
x
N
m
)(m)( )
A m
s
Identify direction of changing B
B increasing
into page
S
x x x x x x x x x
x x x x x xI x x
x x x x x x x x x
x xI x x x x x x
v v
x x x x x Lx x x x
x x x x x x x x
x x x x x x x x x
B decreasing
out of page
41
Rail Gun, 0.20 m long, moves at a constant speed of 7.0 m/s
perpendicular to a magnetic field of strength 8.0×10−2 T.
S
S
a. What EMF is induced in the wire?
b. The wire is part of a circuit that has a resistance of 0.50 Ω.
What is the current through the wire?
c. If a different metal was used for the wire, which has a
resistance of 0.78 Ω, what would the new current be?
http://www.youtube.com/watch?v=-uV1SbEuzFU
a.ɛ = BLv
Motional EMF in a Wire In B S
F = qvB;
Work = FL = qvBL
E=
Work qvBL
q
q
E = BLv
x x x x x x x
I
x x x x x x
x x x x x x x
x Ix x x x x
x x x x L
x xv x
x x x x x x
x x x x x x x
x
If wire of length L moves with
velocity v an angle with B:
E = BLv sin
x x x
x
x x B
x
x x
x x x
x xv
x x x
Fx
I
v
b.
Substitute V = E
B
Lenz’s law
I
I
R
R
= 0.22 A
v
Induced Emf E
Motional EMF & FB
Substitute EMF = 0.11 V, R1 = 0.50 Ω
B
v sin
S
ɛ = (8.0×10−2 T)(0.20 m)(7.0 m/s)
ɛ = 0.11 T·m2/s
ɛ = 0.11 V
Force F on charge q in wire:
Using the right-hand rule, the direction of the current is
counterclockwise.
S
I
S
R
Substitute E = 0.11 V, R2 = 0.78 Ω
= 0.14 A
The current is counterclockwise.
42
A 0.50-m length of wire moves at a constant speed
of 25 m/s with a 4.0T B-Field. What is the magnitude
and direction of the induced emf in the wire?
BLv sin
(4.0T )(.5m)(25m / s)(sin 90)
E = 50 V
S
x x x x x x x
I
x x x x x x
x x x x x x x
x Ix x x x x
x x x x L
x xv x
x x x x x x
x x x x x x x
x
classic Lenz’s law demonstrations (unless you’re reading ahead, if
that’s the case [and what are the odds] then stand by). One of
these involved a falling magnet in a thick walled aluminum pipe.
You actually saw two different cylinders dropped down the pipe.
The first was an aluminum slug. It fell through the pipe at a rate
determined by g. The magnet behaved very differently. As it fell –
pulled down by the force of gravity – the lines of magnetic flux
around the magnet cut through the aluminum wall of the pipe.
This changing flux induced an emf. The current sort of swirled
around and around in the pipe walls, which gives them their name
eddy currents. The eddy currents build up their own magnetic
fields, which oppose the magnetic field of the magnet. This
generates an upward force that slows the magnet down and it
ends up taking a really long time to fall through the pipe.
To determine the direction of the induced magnetic field, you use
the right hand rule as before, but you reverse the direction of
current flow in you final answer. Remember you only do this
reversal in electromagnetic induction.
S
S
What is the current if a .5Ω resistor is placed in
circuit?
10V
V IR I
I 20 A
.5
S
FM
FA
How many electrons would be stored in a 5μF
capacitor is placed in circuit (Resistor removed)?
Q CV
e
Q (10V )(5 x10 6 F ) 5 x10 5 C
5 x10 5 C
1.6 x10 19 e / C
e 3.125 x1014
A 0.20-m length of wire moves at a constant speed
of 5 m/s in at 1400 with a 0.4-T B-Field. What is the
magnitude and direction of the induced emf in the
wire?
BLv sin
(0.4T )(0.20)(5m / s )(sin 140)
v
S
North
B
A 6.0 cm by 6.0 cm square loop of wire is attached to
a cart that is moving at a constant speed of 12 m/s.
It travels through a uniform magnetic field of 2.5 T.
(a) What is the induced emf after it has traveled 5.0 cm
into the field? (b) What is the direction of the current,
clockwise or counterclockwise? (c) If the resistance of
the loop is 1.0 , what is the current in the loop?
S
6.0 cm
E = 0.257 V
South
v
(a) Calculating emf:
Hand pulls the west in the diagram. Using righthand rule, point fingers to right, thumb in
direction of current / induced emf—to North
Blv
m
2.5 T 0.060 m 12
s
10.0 cm
1.8 V
(b) The current is clockwise in the loop.
43
S
S
(c) Calculating the current. Use Ohm’s law. We know
the emf, we assume that the emf is equal to the
potential difference V. We also know the resistance of
the loop.
V IR
V 1.8V
I
R 1.0
1.8 A
I
S
TRANSFORMERS
S
25 cm
A rectangular loop enters a magnetic field of 5.25 x 102 T. It
is moving at a constant speed. The induced emf when it
enters the field is 10 V. What is the velocity of the cart?
v
85 cm
v
Bl
10V
v
5.25 X 102 T (.25m )
v .076m / s
S
When the energy reaches your, step-down
transformers, provide appropriately low voltages
for your Ipod.
Does Voltage Matter?
S
5 cm
A a similar rectangular loop cart enters a magnetic field of
1.0 x 102 T. It is moving at a constant speed. The induced
emf when it enters the field is 10 V. What is the velocity
of the cart?
the current in the electrical lines outside
your house are around 1,100V AC
v
85 cm
v
Bl
v
10V
5.25 X 10 2 T (.05m)
v 2m / s
44
S
HOW TRANFORMERS WORK
P IV
S
• The strength of the magnetic field is proportion
to the input voltage and the number of turns
around the core (called the primary coil).
• By reversing the rule, the output voltage is
proportional to the strength of the changing
magnetic field and the number of turns (called
the secondary coil).
HOW TRANFORMERS WORK
S
• The greater the number of turns around
the iron core the greater the strength of an
electromagnet.
S
In an ideal transformer, the electric power
delivered to the secondary circuit equals the
power supplied to the primary circuit.
PS PP
• The strength is approximately proportional
to the number of turns.
P IV
An ideal transformer dissipates no power itself,
and can be represented by:
• Triple the number of turns and you triple
the strength of the electromagnet.
HOW TRANFORMERS WORK
HOW TRANFORMERS WORK
VP I P VS I S
S
The EMF induced in the secondary coil
(AKA the secondary voltage) is proportional
to the primary voltage.
HOW TRANFORMERS WORK
S
If the secondary voltage is larger than the primary
voltage, the transformer is called a
Step-Up Transformer
The secondary voltage also depends on the
ratio of the number of turns on the
secondary coil to the number of turns on the
primary coil
Vs N s
Vp N p
45
HOW TRANFORMERS WORK
If the secondary voltage is smaller than the
primary voltage, the transformer is called a
Step-Down Transformer.
S
S
Another way to understand this is to consider
a transformer as 100 percent efficient, as is
typically assumed in industry.
Therefore, in most cases, it may be assumed
that the input power and the output power
are the same.
In college you will look at efficiency, not here.
For all transformers, the ratios of:
S
IS VP NP
IP VS NS
Some transformers can function either as
step-up transformers or step-down
transformers, depending on how they are
hooked up.
S
The turn ratio is directly proportional to the
voltage ratio
The turn ratio is inversely proportional to the
current ratio
S
S
Transformers cannot increase the power
output, a voltage decrease corresponds to a
current increase.
A step-up transformer increases voltage.
= corresponding decrease in current through
the secondary
A step-down transformer decreases voltage
= corresponding decrease in current
through the secondary
46
S
A step-up transformer has a primary coil
consisting of 200 turns and a secondary coil S
consisting of 3000 turns. The primary coil is
supplied with an effective AC voltage of 90.0 V.
a. What is the voltage in the secondary
circuit?
b. The current in the secondary circuit is 2.0 A.
What is the current in the primary circuit?
http://www.youtube.com/watch?v=gJ1Mz7kGVf0
S
a.
This is a step-up
transformer – the emf
in the secondary coil
is larger than the emf
in the primary:
S
Step-Up Transformers
= 1350 V
b. The power in the primary and secondary circuits
are equal assuming 100 percent efficiency.
VpIp = VsIs
= 30 A
Transformers and Transmission of Power
Energy must be conserved; therefore, in the
absence of losses, the ratio of the currents
must be the inverse of the ratio of turns:
S
EVERYDAY USES OF TRANSFORMERS
S
Long-distance transmission of electrical energy
is economical only if low currents and very
high voltages are used.
Step-up transformers are used at power sources
to develop voltages as high as 480,000 V.
High voltages reduce the current required in the
transmission lines, keeping the energy lost to
resistance low.
47
EVERYDAY USES OF TRANSFORMERS
S
Transformers in home appliances further adjust
voltages to useable levels.
S
30. A transformer is designed to change 120 V into 10,000 V, and there are 164 turns
in the primary coil. How many turns are in the secondary coil?
VS
IPOD Charger……...
VP
NS
NP
VS
NS N P
164
VP
10, 000 V rpm
120 V
13, 700 turns
A transformer of the type discussed in this
chapter is contained inside of that block.
In this case, it is probably reducing the household
voltage of about 120 V to something in the 3-V
to 26-V range.
EVERYDAY USES OF TRANSFORMERS
S
Not all transformers are step-up or step-down.
Transformers can be used to isolate one circuit
from another.
31.
(I) A transformer has 320 turns in the primary coil and 120 in the secondary coil.
What kind of transformer is this, and by what factor does it change the voltage? By what
factor does it change the current?
S
Because Ns < Np , this is a step-down transformer. find the voltage ratio, find the
current ratio.
VS
VP
This is possible because the wire of the primary
coil never makes direct contact with the wire of
the secondary coil.
NS
IS
IP
NP
NP
NS
120 turns
320 turns
0.375
320 turns
120 turns
2.67
This type of transformer would most likely be
found in some small electronic devices.
S
TEST QUESTION AREAS
Diagramming Mfield of magnet, coil, wire,
MField between 2 wires & around 1 wire
Proton/Electron through a field / by a wire
Rolling Cart through B field (induced EMF)
Rail Generator in a B field (induced EMF)
Current Carrying Loop in a B Field (Motor)
Faraday Discovery / Law (conceptual)
Motor/Generator Question (conceptual)
Transformer
Mass Spectrometer (conceptual)
S
32. A step-up transformer increases 25 V to 120 V. What is the current in the secondary
coil as compared to the primary coil?
IS
IP
VP
VS
25 V
120 V
0.21
48
S
36. A transformer has 330 primary turns and 1340 secondary turns. The input voltage is
120 V and the output current is 15.0 A. What are the output voltage and input current?
S
33.
(I) Neon signs require 12 kV for their operation. To operate from a 240-V line,
what must be the ratio of secondary to primary turns of the transformer? What would the
voltage output be if the transformer were connected backward?
NS
NP
VS
VP
12000 V
240 V
50
Relate the voltage and current ratios.
VS
VP
NS
NP
VS VP
NS
NP
120 V
1340 turns
15.0 A
1340 turns
330 turns
487 V
If the transformer is connected backward, the role of the turns will be reversed:
IS
NS
NP
VS
VP
VS
1
50
240 V
IP
NP
NS
I P IS
NS
NP
330 turns
4.8 V
S
S
34.
(II) A model-train transformer plugs into 120-V ac and draws 0.35 A while
supplying 7.5 A to the train. (a) What voltage is present across the tracks? (b) Is the
transformer step-up or step-down?
(a) Relate the voltage and current ratios.
VS
VP
NS
NP
;
IS
IP
NP
NS
VS
VP
IP
VS VP
IS
IP
IS
60.9 A
120 V
0.35 A
7.5 A
5.6 V
(b) Because Vs<Vp, this is a step-down transformer.
S
35.
(II) The output voltage of a 95-W transformer is 12 V, and the input current
is 22 A. (a) Is this a step-up or a step-down transformer? (b) By what factor is the
voltage multiplied?
• The loudspeakers in your radio, television or stereo system consists
of a permanent magnet surrounding an electromagnet that is
attached to the loudspeaker membrane or cone.
• By varying the electric current through the wires around the
electromagnet, the electromanget and the speaker cone can be
made to back and forth. If the variation of the electric current is at
the same frequencies of sound waves, the resulting vibration of the
speaker cone will create sound waves, including that from voice and
music.
•
• Cutout of a loudspeaker
• If you examine the back area of a loudspeaker, you should be able
to see the permanent magnet and coil of wire for the electromagnet.
Some loudspeakers use an electromagnet without the iron core,
which is called a solenoid.
VIDEO AC vs. DC
S
(a) We assume 100% efficiency, and find the input voltage from P=IV
P I PVP VP
P
IP
95 W
22 A
4.318 V
(b) Since Vp<Vs , this is a step-up transformer.
VS
VP
12 V
4.318 V
2.8
49
Tape recorder
S
• When a mylar tape covered with fine iron dust
passes near a small electromagnet that has a
varying mangtic field, according to an electrical
signal, the dust become magnetized in different
directions. The electrical signal could be from a
radio or microphone.
• The tape then is a record of the electrical signal.
When it passes by another small electromagnet,
it creates an electrical signal, duplicating that of
the original signal. This signal can be amplified
and played back through loudspeakers.
S
Forces Caused by Magnetic Fields
Storing Information with Magnetic Media
S
The current through the wire induces a
magnetic field in the core. When the
read/write head passes over the spinning
storage disk, as in the figure below, the
domains of atoms in the magnetic film line
up in bands.
Forces Caused by Magnetic Fields
S
Storing Information with Magnetic Media
The orientation of the domains depends on the direction of the
current.
Two bands code for one bit of information. Two bands
magnetized with the poles oriented in the same direction
represent 0.
Two bands represent 1 with poles oriented in opposite
directions.
The recording current always reverses when the read/write
head begins recording the next data bit.
Forces Caused by Magnetic Fields
S
Storing Information with Magnetic Media
Data and software commands for computers are processed
digitally in bits.
Each bit is identified as either a 0 or a 1. How are these bits
stored?
The surface of a computer storage disk is covered with an even
distribution of magnetic particles within a film.
The direction of the particles’ domains changes in response to a
magnetic field.
Forces Caused by Magnetic Fields
S
Storing Information with Magnetic Media
To retrieve data, no current is sent to the read/write
head.
Rather, the magnetized bands in the disk induce current
in the coil as the disk spins beneath the head.
Changes in the direction of the induced current are
sensed by the computer and interpreted as 0’s and
1’s.
During recording onto the disk, current is routed to the disk drive’s
read/write head, which is an electromagnet composed of a
wire-wrapped iron core.
50
CURRENT FROM GENERATOR S
Water Dam turbines, in turn, turn coils of
conductors in a magnetic field, thereby
inducing an EMF.
The electric generator, invented by Michael Faraday, converts
mechanical energy to electrical energy.
An electric generator consists of a number of wire loops placed in a
strong magnetic field.
The wire is wound around an iron core to increase the strength of the
magnetic field.
The iron and the wires are called the armature, which is similar to that
of an electric motor.
21.5 Electric Generators
CURRENT FROM GENERATOR S
Generators and motors are almost identical in
construction, but they convert energy in
opposite directions.
A generator converts mechanical energy to
electrical energy, while a motor converts
electrical energy to mechanical energy.
S
CURRENT FROM GENERATOR S
S
S
A generator is the opposite of a motor – it
transforms mechanical energy into electrical
energy. This is an ac generator:
The axle is rotated by an
external force such as
falling water or steam.
The brushes are in
constant electrical
contact with the slip
rings.
21.5 Electric Generators
A dc generator is
similar, except that it
has a split-ring
commutator instead of
slip rings.
51
CURRENT FROM GENERATOR S
The current is greatest when the motion of the loop is
perpendicular to the magnetic field, that is, when
the loop is in the horizontal position
In this position, the component of the loop’s velocity
perpendicular to the magnetic field is greatest.
CURRENT FROM GENERATOR S
The current changes smoothly
from zero to some maximum
value and back to zero
during each half-turn of the
loop. Then it reverses
direction.
A graph of current versus time
is shown in the figure.
S
Does the entire loop contribute to the induced
EMF? Look at the figure, where all four sides
of the loop are depicted in the magnetic field.
S
As the loop rotates from the
horizontal to the vertical position,
as shown in the figure, it moves
through the magnetic field lines at
an ever-increasing angle.
Thus, it cuts through fewer magnetic
field lines per unit of time, and the
current decreases.
CURRENT FROM GENERATOR S
When the loop is in the vertical position, the wire
segments move parallel to the field and the
current is zero.
As the loop continues to turn, the segment that
was moving up begins to move down and
reverses the direction of the current in the
loop.
This change in direction takes place each time
the loop turns through 180°.
CURRENT FROM GENERATOR S
Because the conducting loop is rotating in a circular
motion, the relative angle between a point on the
loop and the magnetic field constantly changes.
The electromotive force can be calculated by the
electromotive force equation given earlier, EMF =
BLv(sin θ), except that L is now the length of
segment bc.
The maximum voltage is induced when a conductor is
moving perpendicular to the magnetic field and
thus θ = 90°.
52
HOMEMADE GENERATOR
S
Section Check
S
Question 2
Define electromotive force.
A. Electromotive force is the speed with which a charge moves
through the circuit.
http://www.youtube.com/watch?v=k7Sz8oT8ou0&feature=related
B. Electromotive force is the force given to the charges by a
battery.
C. Electromotive force is the potential difference, or voltage, given
to the charges by a battery.
D. Electromotive force is the current supplied to the charges by a
battery.
Section Check
S
Section Check
Question 1
Answer 2
What is electromagnetic induction?
Answer: C
A. The process of generating a magnetic field through a circuit in
which there is a relative motion between the wire and the
magnet.
B. The process of generating a magnetic field when a current is
passed through a wire.
C. The process of generating a current through a circuit in which
S
Reason: While studying electric circuits, we learned that a source of
electric energy, such as a battery, is needed to produce a
continuous current. The potential difference, or voltage,
given to the charges by a battery is called the
electromotive force, or EMF. Electromotive force, however,
is not actually a force; instead, it is a potential difference
and is measured in volts.
there is a relative motion between the wire and the magnetic
field.
D. The process of generating a current through a wire when it is
kept in a magnetic field.
Section Check
S
Section Check
Answer 1
Question 3
Answer: C
A straight wire, 25-m long, moves at a speed of 2.0 m/s in a
perpendicular direction through a 1.0-T magnetic field. What is the
EMF induced in the wire?
Reason: Faraday found that to generate current, either the
conductor can move through a magnetic field or a
magnetic field can move past the conductor. It is the
relative motion between the wire and the magnetic field
that produces the current. The process of generating a
current through a circuit in this way is called
electromagnetic induction.
A.
C.
(1.0 T)(25 m)(2.0 m/s)sin 90º
B. (1.0 T)(25 m)(2.0 m/s)cos 90º
D.
(1.0 T)(25 m)(2.0 m/s)tan 90º
S
53
Section Check
S
Changing Magnetic Fields Induce EMF
Answer 3
In this section you will:
Answer: C
Apply Lenz’s law.
Reason: Electromotive force is given by:
Explain back-EMF and how it affects the operation of motors
and generators.
EMF = Blv(sin )
S
Explain self-inductance and how it affects circuits.
Electromotive force is equal to the magnitude of the magnetic
field, times the length of the wire times the component of the
velocity of the wire in the field perpendicular to the field.
Solve transformer problems involving voltage, current, and turn
ratios.
In the above case,
EMF = Blv(sin ) = (1.0 T)(25 m)(2.0 m/s)sin 90
EMF is measured in volts.
Section Check
S
Changing Magnetic Fields Induce EMF
S
Question 4
Lenz’s Law
Explain how EMF is induced in an electric generator.
In a generator, current is produced when the armature turns through
a magnetic field.
The act of generating current produces a force on the wires in the
armature.
In what direction is the force on the wires of an armature produced?
Section Check
S
Changing Magnetic Fields Induce EMF
Answer 4
Motors and Lenz’s Law
An electric generator consists of a number of wire loops placed in a
strong magnetic field. The wire is wound around an iron core to
increase the strength of the magnetic field. The iron and the wires
together are called the armature. The armature is mounted so that it
can rotate freely in the magnetic field. As the armature turns, the
wire loops cut through the magnetic field lines and induce an EMF.
Lenz’s law also applies to motors.
S
When a current-carrying wire moves in a magnetic field, an EMF is
generated.
This EMF, called the back-EMF, is in a direction that opposes the
current.
When a motor is first turned on, there is a large current because of the
low resistance of the motor.
As the motor begins to turn, the motion of the wires across the
magnetic field induces a back-EMF that opposes the current.
Therefore, the net current through the motor is reduced.
54
Changing Magnetic Fields Induce EMF
S
Lecture PowerPoint
Motors and Lenz’s Law
Chapter 21
If a mechanical load is placed on the motor, as in a situation in which
work is being done to lift a weight, the rotation of the motor will
slow.
Physics: Principles with
Applications, 6th edition
This slowing down will decrease the back-EMF, which will allow more
current through the motor.
Note that this is consistent with the law of conservation of energy: if
current increases, so does the rate at which electric power is being
sent to the motor.
This power is delivered in mechanical form to the load.
If the mechanical load stops the motor, current can be so high that
wires overheat.
Changing Magnetic Fields Induce EMF
Giancoli
© 2005 Pearson Prentice Hall
This work is protected by United States copyright laws and is provided solely for
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Dissemination or sale of any part of this work (including on the World Wide Web)
will destroy the integrity of the work and is not permitted. The work and materials
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S
Chapter 21
Motors and Lenz’s Law
As current draw varies with the changing speed of an electric motor,
the voltage drop across the resistance of the wires supplying the
motor also varies.
S
S
Electromagnetic Induction
and Faraday’s Law
Another device, such as a lightbulb, that is in parallel with the motor,
also would experience the drop in voltage.
This is why you may have noticed some lights in a house dimming
when a large motorized appliance, such as an air conditioner or a
table saw, starts operating.
Changing Magnetic Fields Induce EMF
S
Motors and Lenz’s Law
Units of Chapter 21
S
• Induced EMF
When the current to the motor is interrupted by a switch in the circuit being
turned off or by the motor’s plug being pulled from a wall outlet, the
sudden change in the magnetic field generates a back-EMF.
• Faraday’s Law of Induction; Lenz’s Law
This reverse voltage can be large enough to cause a spark across the
switch or between the plug and the wall outlet.
• Changing Magnetic Flux Produces an Electric
Field
• EMF Induced in a Moving Conductor
• Electric Generators
• Back EMF and Counter Torque; Eddy
Currents
• Transformers and Transmission of Power
55
Units of Chapter 21
S
• Applications of Induction: Sound Systems,
Computer Memory, Seismograph, GFCI
S
21.1 Induced EMF
Therefore, a changing magnetic field induces
an emf.
• Inductance
Faraday’s experiment used a magnetic field
that was changing because the current
producing it was changing; the previous
graphic shows a magnetic field that is
changing because the magnet is moving.
• Energy Stored in a Magnetic Field
• LR Circuit
• AC Circuits and Reactance
• LRC Series AC Circuit
• Resonance in AC Circuits
21.1 Induced EMF
S
Almost 200 years ago, Faraday looked for
evidence that a magnetic field would induce
an electric current with this apparatus:
21.2 Faraday’s Law of Induction;
Lenz’s Law
S
The induced emf in a wire loop is proportional
to the rate of change of magnetic flux through
the loop.
Magnetic flux:
(21-1)
Unit of magnetic flux: weber, Wb.
1 Wb = 1 T·m2
21.1 Induced EMF
He found no evidence when the current was
steady, but did see a current induced when the
switch was turned on or off.
S
21.2 Faraday’s Law of Induction;
Lenz’s Law
S
This drawing shows the variables in the flux
equation:
56
21.2 Faraday’s Law of Induction;
Lenz’s Law
S
The magnetic flux is analogous to the electric
flux – it is proportional to the total number of
lines passing through the loop.
21.2 Faraday’s Law of Induction;
Lenz’s Law
21.2 Faraday’s Law of Induction;
Lenz’s Law
S
Magnetic flux will change if the area of the
loop changes:
S
Transformers and Transmission of Power
S
Transformers work only if the current is
changing; this is one reason why electricity
is transmitted as ac.
Faraday’s law of induction:
[1 loop] (21-2a)
[N loops] (21-2b)
21.2 Faraday’s Law of Induction;
Lenz’s Law
S
The minus sign gives the direction of the
induced emf:
21.2 Faraday’s Law of Induction;
Lenz’s Law
S
Magnetic flux will change if the angle between
the loop and the field changes:
A current produced by an induced emf moves in
a direction so that the magnetic field it
produces tends to restore the changed field.
57
21.2 Faraday’s Law of Induction;
Lenz’s Law
S
Problem Solving: Lenz’s Law
21.3 EMF Induced in a Moving ConductorS
The induced emf has magnitude
1. Determine whether the magnetic flux is increasing,
decreasing, or unchanged.
2. The magnetic field due to the induced current points in
the opposite direction to the original field if the flux is
increasing; in the same direction if it is decreasing; and
is zero if the flux is not changing.
3. Use the right-hand rule to determine the direction of the
current.
(21-3)
Measurement of
blood velocity from
induced emf:
4. Remember that the external field and the field due to the
induced current are different.
21.3 EMF Induced in a Moving ConductorS
This image shows another way the magnetic
flux can change:
21.4 Changing Magnetic Flux Produces anS
Electric Field
A changing magnetic flux induces an electric
field; this is a generalization of Faraday’s
law. The electric field will exist regardless of
whether there are any conductors around.
21.3 EMF Induced in a Moving ConductorS
The induced current is in a direction that tends
to slow the moving bar – it will take an external
force to keep it moving.
21.5 Electric Generators
S
A sinusoidal emf is induced in the rotating
loop (N is the number of turns, and A the area
of the loop):
(21-5)
58
21.6 Back EMF and Counter Torque; EddyS
Currents
An electric motor turns because there is a
torque on it due to the current. We would
expect the motor to accelerate unless there is
some sort of drag torque.
21.8 Applications of Induction: Sound
Systems, Computer Memory,
Seismograph, GFCI
S
This microphone works by induction; the
vibrating membrane induces an emf in the coil
That drag torque
exists, and is due to
the induced emf, called
a back emf.
21.6 Back EMF and Counter Torque; EddyS
Currents
Section
25.1
S
Electric Current from Changing Magnetic Fields
Induced EMF
Are the units correct?
A similar effect occurs in a generator – if it is
connected to a circuit, current will flow in it,
and will produce a counter torque. This
means the external applied torque must
increase to keep the generator turning.
Volt is the correct unit for EMF. Current is measured in
amperes.
Does the direction make sense?
The direction obeys the fourth right-hand rule: v is the direction
of the thumb, B is the same direction as the fingers, and F is
the direction that the palm faces. Current is in the same
direction as the force.
Is the magnitude realistic?
The answers are near 10−1. This agrees with the quantities
given and the algebra performed.
21.6 Back EMF and Counter Torque; EddyS
Currents
Induced currents can flow
in bulk material as well as
through wires. These are
called eddy currents, and
can dramatically slow a
conductor moving into or
out of a magnetic field.
CURRENT FROM GENERATOR S
The armature is mounted so that it can rotate freely in the
magnetic field.
As the armature turns, the wire loops cut through the magnetic
field lines and induce an EMF.
Commonly called the voltage, the EMF developed by the
generator depends on the length of the wire rotating in the
field.
Increasing the number of loops in the armature increases the
wire length, thereby increasing the induced EMF.
Note that you could have a length of wire with only part of it in
the magnetic field. Only the portion within the magnetic field
induces an EMF.
59
CURRENT FROM GENERATOR S
Section
25.2
Changing Magnetic Fields Induce EMF
S
Lenz’s Law
When a generator is connected in
a closed circuit, the induced EMF
produces an electric current.
In Chapter 24, you learned that a wire carrying a current through
a magnetic field will experience a force acting on it.
This force results from the interaction between the existing
magnetic field and the magnetic field generated around all currents.
The animation shows a singleloop generator without an iron
core.
The direction of the induced
current can be found from the
third right-hand rule.
As the loop rotates, the strength
and the direction of the current
change.
Section
25.2
Changing Magnetic Fields Induce EMF
S
Section
25.2
Lenz’s Law
25.2
Changing Magnetic Fields Induce EMF
Lenz’s Law
An EMF, equal to BLv, will be
induced in the wire.
If the magnetic field is out of the
page and velocity is to the right,
then the fourth right-hand rule
shows a downward EMF, as
illustrated in the figure, and
consequently a downward
current is produced.
S
Lenz’s Law
Consider a section of one loop that moves through a magnetic
field, as shown in the figure.
Section
Changing Magnetic Fields Induce EMF
To determine the direction of this force, use the third right-hand
rule: if current, I, is down and the magnetic field, B, is out, then
the resulting force is to the left, as shown in the figure.
S
Section
25.2
Changing Magnetic Fields Induce EMF
S
Lenz’s Law
This means that the direction of
the force on the wire opposes
the original motion of the wire, v.
That is, the force acts to slow
down the rotation of the
armature.
The method of determining the
direction of a force was first
demonstrated in 1834 by H.F.E.
Lenz and is, therefore, called
Lenz’s law.
60
S
S
S
GENERATORS
S
Mechanical Universe
•
•
•
•
•
•
•
•
•
•
S
S
Lesson 38: Alternating Current
Electromagnetic induction makes it easy and natural to generate alternating current.
Use of transformers makes it practical to distribute ac over long distances. Although
Nikola Tesla understood all this, Thomas Edison chose not to, and thereby hangs a
tale. Alternating current circuits obey a differential equation identical to the harmonic
oscillator resonance equation.
Text Assignment: Chapter 42
Instructional Objectives
Be able to state the definition of rms current and relate it to the maximum current in
an ac circuit.
Know the phase relationships between voltages and currents for elements of an LRC
circuit.
Be able to discuss the relationship between an LRC circuit and a harmonic oscillator.
Be able to describe a step-up and a step-down transformer.
Be able to discuss the relationship between power transmission and voltage.
Be able to state the resonance condition for an LRC circuit and to sketch the power
versus angular frequency.
61
S
The AC Generator
• An alternating AC current is
produced by rotating a loop
in a constant B-field.
• Current on left is outward
by right-hand rule.
Rotating Loop in B-field
B
I
The simple ac generator
can be converted to a dc
generator by using a single
split-ring commutator to
reverse connections twice
per revolution.
v I
v
B
• The right segment has an
inward current.
E
Operation of AC Generator
Commutator
t
• When loop is vertical, the
current is zero.
I in R is right, zero, left, and then zero as loop rotates.
S
The DC Generator
DC Generator
For the dc generator: The emf fluctuates in magnitude,
but always has the same direction (polarity).
S
S
The Electric Motor
In a simple electric motor, a current loop experiences a
torque which produces rotational motion. Such motion
induces a back emf to oppose the motion.
I=0
Applied voltage – back emf
= net voltage
Eb
V – Eb = IR
I=0
Sinusoidal Current of GeneratorS
x
x
.
.
-E
The emf varies sinusoidally with max and min emf
E = -N
Electric Motor
S
t
A change in flux can
occur by a change in area or
by a change in the B-field:
= B A
= A B
Calculating flux through an area in a B-field:
B
For N turns, the EMF is:
V
Summary
Faraday’s Law:
+E
I
Since back emf Eb increases with
rotational frequency, the starting
current is high and the operating
current is low: Eb = NBA sin
; = BA
A
BA cos
E NBA sin
62
S
Summary (Cont.)
FORMULAS GIVEN ON AP
S
Lenz’s law: An induced current will be in such a direction
as to produce a magnetic field that will oppose the
motion of the magnetic field that is producing it.
Induced B
Induced B
Left motion
I
N
I
Right motion
S
Flux increasing to left induces
loop flux to the right.
N
S
Flux decreasing by right move
induces loop flux to the left.
Summary (Cont.)
S
S
S
S
The ac generator is
shown to the right. The
dc generator and a dc
motor are shown below:
V
DC Generator
Electric Motor
Summary (Cont.)
http://www.youtube.com/watch?v=PLeQ6R2S-Fs&feature=related
The rotor generates a back
emf in the operation of a
motor that reduces the
applied voltage. The
following relationship exists:
Applied voltage – back emf
= net voltage
V – Eb = IR
Motor
63
S
EXAM TIME
S
http://www.youtube.com/watch?v=4OqlTXwLG40&feature=related
S
S
http://www.youtube.com/watch?v=y54aLcC3G74&feature=related
EXTRA SLIDES
S
Maxwell’s Equations
S
http://www.youtube.com/watch?v=1ix62_oBGtg&feature=related
implies that magnetic field lines MUST be
closed loops, not lines, that both enter
and exit the Gaussian surface
64
Armature and Field
Windings
S
S
In the commercial motor,
many coils of wire around
the armature will produce
a smooth torque. (Note
directions of I in wires.)
Series-Wound Motor: The
field and armature wiring
are connected in series.
Motor
Shunt-Wound Motor: The field windings and the
armature windings are connected in parallel.
A series-wound dc motor has an internal resistance of 3
S
. The 120-V supply line draws 4 A when at full speed.
What is the emf in the motor and the starting current?
Eb
V
F qv B
F qvB sin
V – Eb = IR
Recall that:
I
S
Magnetic Force
120 V – Eb = (4 A)(3
The back emf
in motor:
v
Eb = 108 V
Note that since the force is always perpendicular to the
velocity, the magnetic force does no work and
cannot increase or decrease the speed of a charge.
The starting current Is is found by noting that Eb = 0
in beginning (armature has not started rotating).
120 V – 0 = Is (3
E = BLv sin
S
Magnetic Field created by circular loop
S
B
v sin
v
Induced Emf E
In general for a coil of N turns of area A rotating
with a frequency in a B-field, the generated emf
is given by the following relationship:
For N turns, the EMF is:
B
X FB into
page
Is = 40 A
Summary (Cont.)
An emf is induced by a wire
moving with a velocity v at an
angle with a B-field.
vsin
θ
E NBA sin
OR RHR-3
Fingers curl,
thumb is
North pole of
field
Resembles B field created by
a permanent bar magnet
65
Section
25.1
S
Electric Current from Changing Magnetic Fields
Section
25.1
Alternating Current Generators
The figure shows how an
alternating current, AC, in
an armature is transmitted
to the rest of the circuit.
The figure shows a graph of
the power produced by an AC
generator.
Note that power is always
positive because I and V are
either both positive or both
negative.
The brush-slip-ring
arrangement permits the
armature to turn freely
while still allowing the
current to pass into the
external circuit.
Section
25.1
S
Electric Current from Changing Magnetic Fields
Average Power
Average power, PAC, is half
the maximum power; thus,
S
Electric Current from Changing Magnetic Fields
Section
25.1
Alternating Current Generators
S
Electric Current from Changing Magnetic Fields
Effective Voltage and Current
As the armature turns, the alternating current varies between
some maximum value and zero, as shown in the graph.
It is common to describe alternating current and voltage in
terms of effective current and voltage, rather than referring to
their maximum values.
Recall from Chapter 22 that P = I2R. Thus, you can express
effective current, Ieff, in terms of the average AC power as
PAC = Ieff 2R.
Section
25.1
S
Electric Current from Changing Magnetic Fields
Average Power
The power produced by a generator is the product of the current
and the voltage.
Because both current and voltage vary, the power associated with
an alternating current varies.
Section
25.1
S
Electric Current from Changing Magnetic Fields
Effective Voltage and Current
To determine Ieff in terms of maximum current, Imax, start with
the power relationship,
and substitute in I2R.
Then solve for Ieff .
Effective current is equal to
times the maximum current.
66
Section
25.1
S
Electric Current from Changing Magnetic Fields
Wire #1 (length L) forms a
one-turn loop, and a bar
magnet is dropped
through. Wire #2 (length
2L) forms a two-turn loop,
and the same magnet is
S
dropped through.
N
Compare the magnitude
of
the induced voltages in
these two cases.
Effective Voltage and Current
Similarly, the following equation can be used to express
effective voltage.
Effective voltage is equal to
times the maximum voltage.
Effective voltage also is commonly referred to as RMS (root
mean square) voltage.
Section
25.1
ConcepTest 21.6a Voltage
and Current I1) V > V S
S
Electric Current from Changing Magnetic Fields
1
3) V1 = V2 0
4) V1 = V2 = 0
S
N
ConcepTest 21.6a Voltage
and Current I1) V > V S
Wire #1 (length L) forms a
one-turn loop, and a bar
magnet is dropped
through. Wire #2 (length
2L) forms a two-turn loop,
Faraday’s
law:same
N
magnet
and the
is
t
S
dropped
through.
depends
on N (number
of loops)
so the induced emf is twice as
N
Compare the magnitude of
large in the wire with 2 loops.
the induced voltages in
these two cases.
Effective Voltage and Current
In the United States, the voltage generally available at wall
outlets is described as 120 V, where 120 V is the magnitude of
the effective voltage, not the maximum voltage.
The frequency and effective voltage that are used vary in
different countries.
2
2) V1 < V2
1
2
2) V1 < V2
3) V1 = V2 0
4) V1 = V2 = 0
B
Section
25.1
S
Electric Current from Changing Magnetic Fields
Effective Voltage and Current
In this section, you have explored how moving wires in magnetic
fields can induce current.
However, as Faraday discovered, changing magnetic fields
around a conductor also can induce current in the conductor.
In the next section, you will explore changing magnetic fields
and the applications of induction by changing magnetic fields.
S
N
ConcepTest 21.6b Voltage
S
and Current II1) I > I
Wire #1 (length L) forms a
one-turn loop, and a bar
magnet is dropped
through. Wire #2 (length
2L) forms a two-turn loop,
and the same magnet is
S
S
dropped through.
Compare the Nmagnitude ofN
the induced currents in
these two cases.
1
2
2) I1 < I2
3) I1 = I2 0
4) I1 = I2 = 0
67
ConcepTest 21.6b Voltage
S
and Current II1) I > I
Wire #1 (length L) forms a
one-turn loop, and a bar
magnet is dropped
through. Wire #2 (length
2L) forms a two-turn
loop,
Faraday’s law:
N
t
and the same magnet
is
S
says that the induced emf is twice
dropped
through.
as
large in the wire
with 2 loops.
The current is given by Ohm’s law:
N
the
of
I Compare
= V/R. Since wire
#2 magnitude
is twice as
long as wire #1, it has twice the
the induced currents in
resistance, so the current in both
wires
is thetwo
same.cases.
these
1
2
2) I1 < I2
3) I1 = I2 0
4) I1 = I2 = 0
B
S
N
ConcepTest 21.7a Falling
S
Magnet I
A bar magnet is held
above the floor and
dropped. In 1, there is
nothing between the
magnet and the floor.
In 2, the magnet falls
S
through a copper
loop.
How will the magnet
in
N
copper
case 2 fall in
loop
1) it will fall slower
2) it will fall faster
3) it will fall the same
S
N
comparison to case 1?
ConcepTest 21.7a Falling
S
Magnet I
A bar magnet is held
above the floor and
dropped. In 1, there is
nothing between the
magnet
and
the floor.
When
the magnet
is falling
from above
the loop in 2, the induced current will
In
2,
the
magnet
falls
produce a North pole on top of the loop,
which
repels
the
magnet.
through a copper loop.
When the magnet is below the loop, the
How current
will the
magnet
in
induced
will produce
a North
pole on the bottom of the loop, which
casethe
2 South
fall in
attracts
pole of the magnet.
ConcepTest 21.7b Falling
S
Magnet II
If there is
1) induced current doesn’t need any energy
induced
current,
doesn’t that
cost
energy?
Where
would that
energy
come from
in case 2?
2) energy conservation is violated in this case
3) there is less KE in case 2
4) there is more gravitational PE in case 2
S
S
N
copper
loop
N
ConcepTest 21.7b Falling
S
Magnet II
If there is
1) induced current doesn’t need any energy
2) energy conservation is violated in this case
induced
3) there is less KE in case 2
current,
4) there is more gravitational PE in case 2
doesn’t that
cost
In both cases, the magnet starts with
the
same initial gravitational PE.
energy?
In case 1, all the gravitational PE has
S
S
Where
been
converted into kinetic energy.
In case 2, we know the magnet falls
would that
N
N
slower, thus there is less KE. The
copper
difference
energyin energy goes into making
loop
the induced current.
come from
in case 2?
ConcepTest 21.8a Loop
S
and Wire I
1) it will fall slower
A wire loop is being
1) clockwise
2) it will fall faster
pulled away from a
2) counterclockwise
3) it will fall the same
3) no induced current
current-carrying
wire. What is the
direction of the
S
S
N
copper
loop
Follow-up:
What happens
in case 2
if you flip the magnet
comparison
to case
1?
so that the South pole is on the bottom as the magnet falls?
N
induced current in
the loop?
I
68
ConcepTest 21.8a Loop
S
and Wire I
ConcepTest 21.9 Motional
S
EMF
A conducting rod
A wire loop is being
1) clockwise
pulled away from a
2) counterclockwise
slides on a conducting
3) no induced current
track in a constant B
current-carrying
1) clockwise
2) counterclockwise
3) no induced current
field directed into the
wire. What is the
page. What is the
The magnetic flux is into the page on the
direction of the
right side of the wire and decreasing due
to the fact that the loop is being pulled
induced current in
away. By Lenz’s Law, the induced B field
will
oppose
this decrease. Thus, the new
the
loop?
B field points into the page, which
requires an induced clockwise current to
produce such a B field.
direction of the
x x x x x x x x x x x
induced current?
x x x x x x x x x x x
x x x x x x x x x x x
I
ConcepTest 21.8b Loop
S
and Wire II
What is the induced
current if the wire
v
x x x x x x x x x x x
1) clockwise
ConcepTest 21.9 Motional
S
EMF
A conducting rod
2) counterclockwise
slides on a conducting
3) no induced current
track in a constant B
1) clockwise
2) counterclockwise
3) no induced current
field directed into the
loop moves in the
page. What is the
direction of the
The B field points into the page.
of the since the
Thedirection
flux is increasing
areainduced
is increasing.
The induced
current?
B field opposes this change and
therefore points out of the page.
Thus, the induced current runs
counterclockwise according to
the right-hand rule.
yellow arrow ?
I
current if the wire
x x x x x x x x x x x
x x x x x x x x x x x
v
x x x x x x x x x x x
Follow-up: What direction is the magnetic force on the rod as it moves?
ConcepTest 21.8b Loop
S
and Wire II
What is the induced
x x x x x x x x x x x
ConcepTest 21.10
Generators
1) clockwise
A generator has a
1) increases
2) counterclockwise
coil of wire
2) decreases
rotating in a
4) varies sinusoidally
3) no induced current
loop moves in the
S
3) stays the same
magnetic field. If
The magnetic flux through the loop
direction of the
the rotation rate
arrow
? parallel
isyellow
not changing
as it moves
increases, how is
to the wire. Therefore, there is no
the maximum
induced current.
output voltage of
I
the generator
affected?
69
ConcepTest 21.10
Generators
A generator has a
1) increases
coil of wire
2) decreases
rotating in a
S
3) stays the same
4) varies sinusoidally
magnetic field. If
the rotation rate
The maximum voltage is the leading
NBA sin(t )
increases,
how
term
that multiplies
sin(t)is
and is
given
= NBA. Therefore, if
the bymaximum
increases, then must increase
output voltage of
as well.
the generator
affected?
S
70
