AP Physics
Chapter 19
Magnetism
Chapter 19: Magnetism
19.1 Magnets, Magnetic Poles, and Magnetic
Field Direction
19.2 Magnetic Field Strength and Magnetic Force
19.3 Electromagnetism – The Source of Magnetic
Fields
19.4 Omitted
19.5 Magnetic Forces on Current-Carrying Wires
19.6 Applications of Electromagnetism
19.7 Omitted
Homework for Chapter 19
• Read Chapter 19
• HW 19.A: p.626-627: 6,9-13,15,24,25,28,29.
• HW 19.B: p.629-631:52-56,58,61,62,75,76,78,79.
19.1 Magnets, Magnetic Poles, and
Magnetic Field Direction
static cling
bar magnet
electromagnet
electric generator
pole–force law or law of poles
- like magnetic poles repel each other,
and unlike magnetic poles attract each other.
• The north pole of a compass is the north-seeking end
.
dipole
- poles always occur in pairs, never singly (monopole). If you
break a magnet in half, you end up with two smaller dipole magnets.
magnetic field (B)
- The direction of a magnetic field (or B field) at any
location is the direction that the north pole of a compass at that location would
point.
• Magnetic field lines always point
from north to south
.
• Magnetism and electricity are two
aspects of a fundamental force, the
electromagnetic force
.
19.2 Magnetic Field Strength and
Magnetic Force
• A magnetic field can exert forces only on moving
charges.
• When a charged particle enters a magnetic field, the particle experiences a
force that is evident because the charge is deflected from its original path.
• The electron beam in a cathode ray tube (made visible by fluorescent paper) is
normally horizontal between the end electrodes but is deflected here because of
the magnet.
• We will use the convention:
X
X
X
X
X
X
X
X
is into the page and
●
●
●
●
●
●
●
●
is out of the page.
On Gold Sheet
Right Hand Force Rule: For a positively
charged particle the force is in the direction
your palm is facing; for a negatively charged
particle, the force is in the direction of the
back of your hand.
Example 19.1: An electron moves with a speed of 4.0 x 106 m/s along the +x-axis. It
enters a region where there is a uniform magnetic field of 2.5 T, directed at an angle
of 60° to the x axis and lying in the xy plane. Calculate the initial force and
acceleration of the electron.
A larger mass will have a larger radius.
Fc = mac
qvB = mv2
r
Example 19.2: A proton has a speed of 4.5 x 106 m/s in a direction perpendicular to
a uniform magnetic field, and the proton moves in a circle of radius 0.20 m. What is
the magnitude of the magnetic field?
Check for Understanding
1. When the ends of two bar magnets are near each other, they attract one
another. The ends must be
a)
b)
c)
d)
e)
one north, the other south
one south, the other north
both north
both south
either a or b
Answer: e
2. If you look directly down on the S pole of a bar magnet, the magnetic field
points
a) to the right
b) to the left
c) away from you
d) toward you
Answer: c
Check for Understanding
3. A proton moves vertically upward in a uniform magnetic field and deflects to
the right as you watch it. What is the magnetic field direction?
a)
b)
c)
d)
directly away from you
directly toward you
to the right
to the left
Answer: b, according to the right hand rule
Check for Understanding
Check for Understanding
19.3 Electromagnetism – The
Source of Magnetic Fields
Although a bit unlikely, the idea is that by jarring the domains in
the presence of the earth’s magnetic field, they will align with it.
On Gold Sheet
Right-Hand Source Rule: If a currentcarrying wire is grasped with the right
hand with the extended thumb pointing
in the direction of the current (I), the
curled fingers indicate the circular
sense of the magnetic field direction.
● Since magnetic field is a vector, you must use vector addition to find the net
field if there are contributions from two or more sources.
Example 19.3: What current is required for a long straight wire to produce a
magnetic field of magnitude equal to the strength of the Earth’s magnetic field of
about 5.0 x 10-5 T at a location 2.5 cm from the wire?
Example 19.5: Two long parallel wires carry currents of 20 A and 5.0 A in opposite
directions. The wires are separated by 0.20 m.
a) What is the magnetic field midway between the two wires?
b) At what point between the wires are the magnetic fields from the two wires the
same?
Check for Understanding
1. A long, straight wire is parallel to the ground and carries a steady current to
the east. At a point directly below the wire, what is the direction of the
magnetic field the wire produces?
a)
b)
c)
d)
north
east
south
west
Answer: a, according to the right hand source rule.
2. A long, straight current-carrying wire is oriented vertically. On its east side, the
field it creates points south. What is the current direction?
a) up
b) down
Answer: b, according to the right hand source rule.
Homework for Chapter 19
• HW 19.A: p.626-627: 6,9-13,15,24,25,28,29.
19.5 Magnetic Forces on
Current-Carrying Wires
no current in
the wire
X
X
X
On Gold Sheet
a) Use the right hand force rule to determine the
direction of force. Point the thumb in the direction
of the conventional current I and the fingers in the
direction of the B-field. The force F is the direction
of the palm.
b) Here the current is flowing in the opposite
direction. Point the thumb in the direction of the
current I and the fingers in the direction of B. F is
the direction of the palm.
• Forces exist between two parallel current-carrying wires. This is because the
magnetic field produced by the current in one wire exerts a force on the other
wire.
• If the currents are in the same direction, the forces attract. If the currents are in
opposite directions, the forces repel. Use the right hand rule for
Example 19.6: A wire carries a current of 6.0 A in a direction 60° with respect to the
direction of a magnetic field of 0.75 T. Find the magnitude of the magnetic force on
a 0.50 length of the wire.
Torque on a Current-Carrying Loop
• A magnetic field can exert torque on a current-carrying loop.
• Suppose that the loop in figure a is free to rotate about an axis passing through
opposite sides. There are no net forces or torques on the pivot sides of the loop.
When these sides are parallel to the B field, the force on them is zero. At any other
angle to the field, the forces on them are equal and opposite in the plane of the loop
and so produce no net force or net torque.
• The other two sides of the loop do produce a net torque, which tends to rotate the
loop.
Torque on a Current Carrying Coil
 = NIAB sin 
Where
(not on gold sheet)
 is the torque
N is the number of loops in the coil
I is the current
A is the area of the loop. It can be any shape.
B is the magnetic field
 is the angle between the normal to the plane
of the loop and the B-field.
Example 19.7: A circular loop of wire radius 0.50 m is in a uniform magnetic field of
0.30 T. The current in the loop is 2.0 A. Find the magnitude of the torque when
a) the plane of the loop is parallel to the magnetic field,
b) the plane of the loop is perpendicular to the magnetic field,
c) the plane of the loop is at 30° to the magnetic field.
Example 19.8: Two long, straight wires separated by a distance of 0.30 m carry
currents in the same direction. If the current in one wire is 10 A and the current in
the other 8.0 A, find the magnitude and direction of the forces per unit length (per
meter) between the wires. What if the currents are in opposite directions?
Check for Understanding
1. A long, straight, horizontal wire is located on the equator and carries a current
directed toward the east. What is the direction of the force on it due to the
Earth’s magnetic field?
a)
b)
c)
d)
east
west
south
upward
Answer: d, according to the right hand force rule
Check for Understanding
Check for Understanding
19.6 Applications of
Electromagnetism
electron
is not
moving
no current in
the wire
X
X
The dc Motor
• An electrical motor is a device that converts electrical energy into mechanical
energy.
• A pivoted, current carrying coil with N loops in a magnetic field will rotate freely, but
for only a half-cycle, or through a maximum angle of 180°.
• Recall that  = NAIB sin , and
when the magnetic field is
perpendicular to the plane of the coil
(sin  = 0), the torque is zero and the
coil is in equilibrium.
• To provide for continuous rotation,
the current is reversed every half
turn so that the torque-producing
forces are reversed. This is done by
means of a split-ring commutator.
• Contact brushes provide a path for
current.
• When current is supplied, one half-ring is
electrically positive and the other negative.
The coil and ring rotates.
• When the coil and ring have gone through
half a rotation, the half rings come in contact
with the opposite brushes. Their polarity is
reversed, and the current in the coil is in the
opposite direction. This changes the
directions of the torque. The process repeats
and the spinning continues.
For a real motor, the rotating
shaft is called the armature.
Cathode Ray Tube (CRT)
• The cathode ray tube is a vacuum tube that is used in an oscilloscope, such as
those in some laboratories.
• Electrons, negatively charged, are “boiled off” a hot filament in an electron gun
and accelerated by a voltage applied between the cathode (-) and anode (+).
• The picture tube in older television sets and computer monitors is also a cathode
ray tube.
• Magnetic coils are usually used there to deflect the electron beam.
Open this Cathode Ray Tube Simulation in
Explorer:
http://highered.mcgrawhill.com/olcweb/cgi/pluginpop.cgi?it=swf::100
%::100%::/sites/dl/free/0072512644/117354/
01_Cathode_Ray_Tube.swf::Cathode Ray
Tube
The Mass Spectrometer
• A mass spectrometer is a device used to measure the mass of atoms or
molecules. It is often used to separate isotopes, or atoms of different masses.
• Actually, the masses of ions are measured since electric and magnetic fields
have motional effects only on charged particles. (An ion is an atom or molecule
with a net electric charge.)
• Ions with a known charge (+q) are produced by heating the substance to be
analyzed.
• The resulting beam of ions introduced into the mass spectrometer has a
distribution of speeds. Ions with a particular velocity are selected by means of a
velocity selector, made up of charged plates and a magnetic field that allow
particles traveling at only that velocity to go undeflected.
• The values of the E and B fields between the plates of the velocity selector
determine the velocity.
• For a positively charged ion, the E-field produces a downward force F = qE. The
B-field produces an upward force F = qvB1.
• If the beam is not deflected, the resultant force must be zero, so
qE = qvB1
or
v=E
B1
• If the plates are parallel, E = V/d. Since the voltage
and plate separation are controllable quantities, a
more practical version of the equation is
v=V
ion speed in a velocity selector
B1d
• Beyond the velocity selector, the beam passes through a slit into another magnetic
field (B2), which is perpendicular to the direction of the beam.
• The force due to this magnetic field (F = qvB2) is always perpendicular to the
velocity of the ions, which are therefore deflected along a circular path.
• The magnetic force supplies the centripetal force for this motion, and
mv2 = qvB2
r
so, m =
qdB1B2
V
r
particle mass via
mass spectrometer
Example 19.9: In a mass spectrometer, a single-charged particle has a speed of
1.0 x 106 m/s and enters a uniform magnetic field of 0.20 T. The radius of the
circular orbit is 0.020 m.
a) What is the mass of the particle?
b) What is the kinetic energy of the particle?
Check for Understanding
1. A mass spectrometer
a)
b)
c)
d)
can be used to determine the masses of atoms and molecules
requires charged particles
can be use to determine relative abundances of isotopes
all of these
Answer: d
2. Why can a nearby magnet distort the display of a computer monitor or
television picture tube?
Answer: The magnetic force on the electron beam, which “prints” pictures,
causes the deflection of the electrons.
Homework for Chapter 19
• HW 19.B: p.629-631:52-56,58,61,62,75,76,78,79.
Chapter 19 Formulas
v=
m=
E =
B1
V
B1d
qdB1B2
V
ion speed in a velocity selector
r =
qB2r
v
particle mass via
mass spectrometer