Chapter 20, 21
Magnetism and Electromagnetism
MAGNETISM
Arguable the oldest subject in Physics: ancient Greeks
(near the City of Magnesia) and Chinese realized
certain strange stones attracted iron.
Around 1600, William Gilbert proposed that the Earth
itself is A gigantic magnet.
For a long time, people knew only one source of
magnetism from Iron. In 1821, a Danish physicist,
Oersted noticed that an electrical wire carrying current
made the near-by compass reorient.  First clue of
inter-relation between electricity and
Magnetism.
Ampere, Faraday established the nature of electricity
and magnetism (all from their experimental
observations).
Magnets

Poles of a magnet are the ends where
objects are most strongly attracted
• Two poles, called north and south

Like poles repel each other and unlike
poles attract each other
• Similar to electric charges

Magnetic poles cannot be isolated
• If a permanent magnetic is cut in half repeatedly,
you will still have a north and a south pole
• This differs from electric charges
• There is some theoretical basis for monopoles, but
none have been detected
More About Magnetism

An unmagnetized piece of iron can
be magnetized by stroking it with a
magnet
• Somewhat like stroking an object to
charge an object

Magnetism can be induced
• If a piece of iron, for example, is placed
near a strong permanent magnet, it will
become magnetized
S
S
S
S
N
N
N
N
N
S
N
N
S
Magnets exist in pairs of N-S poles.
A theoretical prediction says that it is possible to have
magnetic mono-poles but they have not been observed!!
Magnetic field cannot be defined as E-field,
FE = qE
FB = qBB
Magnetic Fields




A vector quantity
Symbolized by B
Direction is given by the direction a
north pole of a compass needle
points in that location
Magnetic field lines can be used to
show how the field lines, as traced
out by a compass, would look
Magnetic Field Lines, sketch


A compass can be used to show the
direction of the magnetic field lines (a)
A sketch of the magnetic field lines (b)
Magnetic Field Lines, Bar
Magnet


Iron filings are
used to show the
pattern of the
magnetic field lines
The direction of the
field is the
direction a north
pole would point
Magnetic Field Lines, Unlike
Poles


Iron filings are
used to show the
pattern of the
magnetic field
lines
The direction of
the field is the
direction a north
pole would point
Magnetic Field Lines, Like Poles


Iron filings are
used to show the
pattern of the
magnetic field lines
The direction of the
field is the
direction a north
pole would point
• Compare to the
electric field produced
by like charges
Magnetic and Electric Fields



An electric field surrounds any
stationary electric charge
A magnetic field surrounds any
moving electric charge
A magnetic field surrounds any
magnetic material
Earth’s Magnetic Field


The Earth’s geographic north pole
corresponds to a magnetic south
pole
The Earth’s geographic south pole
corresponds to a magnetic north pole
• Strictly speaking, a north pole should be
a “north-seeking” pole and a south pole
a “south-seeking” pole
Earth’s Magnetic Field

The Earth’s
magnetic field
resembles that
achieved by
burying a huge bar
magnet deep in the
Earth’s interior
S
N
In unifrom field, no force only torque!!!
I
X
Right-handed cork-screw rule
Magnetic Fields

In a magnetic field, a current
carrying wire experiences a magnetic
force
• This force has a maximum value when
the wire is perpendicularly to the
magnetic field lines
• This force is zero when the wire is along
the field lines
Magnetic Fields, cont

One can define a magnetic field in
terms of the magnetic force exerted
on current carrying wire
• Similar to the way electric fields are
defined
F
B  ( I  B)
IL
Units of Magnetic Field

The SI unit of magnetic field is the
Tesla (T)
N
N
Wb
T

 2
A  m C  (m / s) m
• Wb is a Weber
B
I
F
FB = ILB
Magnetic induction
Magnetic flux density
Magnetic field (strength)
[B] = [F/IL]
= Ns/Cm = Tesla
*1 Tesla = 104 gauss
Length of the section in Bfield
?Magnetic force on a current carrying loop
FB = ILB
(1)
(2)
(3)
(4)
A net force on the loop
A net torque on the loop
A net force and torque
nothing, zip
X
S
N
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/mothow.html
DC Electrical Motor
X
X
Magnetic Force on
Moving Charge




The direction of the
magnetic force is
always perpendicular
to both v and B
F = qvB (vB)
Force is smaller when
v is not perpendicular
to B
F = 0 when v is
parallel to B
Right Hand Rule




Hold your right hand
open
Place your fingers in
the direction of B
Place your thumb in
the direction of v
The direction of the
force on a positive
charge is directed out
of your palm
• If the charge is
negative, the force is
opposite that
determined by the right
hand rule
CRT TV
Nam June Paik
http://www.paikstudios.com/
X
x
X
q
x
x
x
x
x
x
Xq
x
x
F
x
X
x
x
x
X
x
x
qx
x
x
x
x
q
x
x
v
x
q
X
x
F = q v B┴
Force by a magnetic field on a moving charge is always
Perpendicular to the direction of motion.
NO WORK DONE BY THE FIELD!!!
X
x
X
x
X
x
r
x
x
x
x
x
x
x
x
x
x
x
v
X
x
x
q
x m
X
x
x
x
B
FB = q v B
Force by B-field
This force causes a circular motion.
Centrepetal force = FB
Fc = mv2/r = q v B = FB
r = mv/qB
Since there is no work done by the field, in vacuum,
The charge will make a circular motion forever!!!
Bubble Chamber
B = 0.36 T
r = 0.4 m
Mass m?
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A univalent ion with mass m
Came into the field region with
Speed v = 6 x 105 m/s.
Mass spectrometer
An object with +e charge
And mass m kg
http://www.geo.mtu.edu/weather/aurora/images/aurora/jan.curtis/index4.html
http://science.nasa.gov/headlines/y2002/23sep_auroraseason.htm
Magnetic Fields –
Long Straight Wire


A current-carrying
wire produces a
magnetic field
The compass needle
deflects in directions
tangent to the circle
• The compass needle
points in the direction
of the magnetic field
produced by the
current
Direction of the Field of a Long
Straight Wire

Right Hand Rule
#2
• Grasp the wire in
your right hand
• Point your thumb in
the direction of the
current
• Your fingers will
curl in the direction
of the field
Magnitude of the Field of a Long
Straight Wire


The magnitude of the field at a
distance r from a wire carrying a
current of I is
 oI
B
2r
µo = 4  x 10-7 T m / A
• µo is called the permeability of free
space
I
x
x
x
x
x
x
x
x
x
o
o
o
o
o
o
o
o
o
For infinitely long solenoid
B = onI
n: number of turns/m
http://www.bugman123.com/Physics/Physics.html
A solenoid electro-magnet is energized as shown in the figures.
Since current flows through wire in the presence of magnetic fields,
the solenoid will feel force. Which figure correctly describes the force acting
on the solenoid?
Induced emf

A current can be produced by a changing
magnetic field
• First shown in an experiment by Michael
Faraday


A primary coil is connected to a battery
A secondary coil is connected to an ammeter
Faraday’s Experiment




The purpose of the secondary circuit is to
detect current that might be produced by
the magnetic field
When the switch is closed, the ammeter
deflects in one direction and then returns
to zero
When the switch is opened, the ammeter
deflects in the opposite direction and then
returns to zero
When there is a steady current in the
primary circuit, the ammeter reads zero
Faraday’s Conclusions



An electrical current is produced by a
changing magnetic field
The secondary circuit acts as if a
source of emf were connected to it
for a short time
It is customary to say that an
induced emf is produced in the
secondary circuit by the changing
magnetic field
INDUCTION
Michael Faraday (1791 – 1867)
…it appeared very extraordinary, that as every
electric current was accompanied by a corresponding
intensity of magnetic action at right angles to the current,
good conductors of electricity, when placed within the
sphere of this action, should not have any current induced
through them, or some sensible effect produced equivalent
in force to such a current.
Primary Coil
Secondary coil
G
?
Summary of Experimental Findings
EMF is induced in the secondary coil
Only when the magnetic field through it changes.
EMF induced is bigger if the area of coil is bigger.
EMF is induced always in the opposite direction of
change in magnetic field.
Vind = - A (dB/dt)
= - d/dt
 = A B : magnetic flux
Magnetic Flux


The emf is actually induced by a
change in the quantity called the
magnetic flux rather than simply by
a change in the magnetic field
Magnetic flux is proportional to both
the strength of the magnetic field
passing through the plane of a loop
of wire and the area of the loop
B
 = A B┴
A
= (0.3 x 0.2)(0.175 sin(40))
= 0.06 x 0.112
= 0.0067 T.m2
B = 0.175 T
B┴
B
40
B//
0.3 m
+
+
+
+
-
Vind = - d/dt
Vt = -3 d/dt
Net number of loops
Example 23.2
150 turn loop with a 0.75 cm2 cross-section
Magnetic field: 0 T  0.25 T in 3.6 s
5 Ohm
What is the induced current in the coil?
Faraday’s Law and
Electromagnetic Induction


The instantaneous emf induced in a
circuit equals the time rate of change of
magnetic flux through the circuit
If a circuit contains N tightly wound
loops and the flux changes by dΦ
during a time interval dt, the average
emf induced is given by Faraday’s Law:
d B
  N
dt
Faraday’s Law and Lenz’ Law

The change in the flux, ΔΦ, can be
produced by a change in B, A or θ
• Since ΦB = B A cos θ

The negative sign in Faraday’s Law is
included to indicate the polarity of the
induced emf, which is found by Lenz’ Law
• The polarity of the induced emf is such that it
produces a current whose magnetic field opposes
the change in magnetic flux through the loop
• That is, the induced current tends to maintain the
original flux through the circuit
AC Generator
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/motorac.html#c2
James Clerk Maxwell


Electricity and
magnetism were
originally thought to
be unrelated
in 1865, James Clerk
Maxwell provided a
mathematical theory
that showed a close
relationship between
all electric and
magnetic phenomena
Maxwell’s Starting Points




Electric field lines originate on positive
charges and terminate on negative
charges
Magnetic field lines always form closed
loops – they do not begin or end
anywhere
A varying magnetic field induces an emf
and hence an electric field (Faraday’s Law)
Magnetic fields are generated by moving
charges or currents (Ampère’s Law)
Maxwell’s Predictions




Maxwell used these starting points and a
corresponding mathematical framework to
prove that electric and magnetic fields play
symmetric roles in nature
He hypothesized that a changing electric field
would produce a magnetic field
Maxwell calculated the speed of light to be
3x108 m/s
He concluded that visible light and all other
electromagnetic waves consist of fluctuating
electric and magnetic fields, with each
varying field inducing the other
Hertz’s Confirmation of
Maxwell’s Predictions

Heinrich Hertz was
the first to
generate and
detect
electromagnetic
waves in a
laboratory setting
James Clerk Maxwell’s Equations
(1867)
E-field comes
out from p-charge and
Pre-Maxwell
terminates at negative charge.
 
E 
B-field cannot do like E-field.
o
No magnetic monopole!

B  0

Faraday’s law

B
 E  
t
Ampere’s law


  B  o J
 
E 
o

B  0


B
 E  
t



E
  B   o J   o o
t
The velocity of transverse undulations in our hypothetical
medium, calculated from the electromagnetic experiments,
agrees so exactly with the velocity of light calculated from
the optical experiments, that we can scarcely avoid the
inference that light consists in the transverse undulation
of same medium which is the cause of electric and magnetic
Phenomena.
v
1
 o o

1
(8.851012 C 2 / N  m2)(4 107 N / A2 )
2.9986 x 108 m/s
Hertz’s Experiment
(1887)
Hertz’s Experimental Apparatus



An induction coil is
connected to two
large spheres
forming a capacitor
Oscillations are
initiated by short
voltage pulses
The inductor and
capacitor form the
transmitter
Hertz’s Experiment

Several meters away from the
transmitter is the receiver
• This consisted of a single loop of wire
connected to two spheres
• It had its own inductance and
capacitance

When the resonance frequencies of
the transmitter and receiver
matched, energy transfer occurred
between them
Hertz’s Conclusions

Hertz hypothesized the energy
transfer was in the form of waves
• These are now known to be
electromagnetic waves

Hertz confirmed Maxwell’s theory by
showing the waves existed and had
all the properties of light waves
• They had different frequencies and
wavelengths