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Chapter 27
Magnetism
Copyright © 2009 Pearson Education, Inc.
27-3 Force on an Electric Current in
a Magnetic Field; Definition of B
The force on the wire depends on the
current, the length of the wire, the magnetic
field, and its orientation:
This equation defines the magnetic field B
B.
In vector notation:
Copyright © 2009 Pearson Education, Inc.
27-3 Force on an Electric Current in a
Magnetic Field; Definition of B
Unit of B: the tesla, T:
1 T = 1 N/A·m.
Another unit sometimes used: the gauss (G):
1 G = 10-4 T.
Copyright © 2009 Pearson Education, Inc.
27-3 Force on an Electric Current in
a Magnetic Field; Definition of B
Example 27-1: Magnetic Force
on a current-carrying wire.
A wire carrying a 30-A
current has a length l = 12
cm between the pole
faces of a magnet at an
angle θ = 60°, as shown.
The magnetic field is
approximately uniform at
0.90 T. We ignore the field
beyond the pole pieces.
What is the magnitude of
the force on the wire?
Copyright © 2009 Pearson Education, Inc.
27-3 Force on an Electric Current in
a Magnetic Field; Definition of B
Example 27-3: Magnetic Force
on a semicircular wire.
A rigid wire, carrying a
current I, consists of a
semicircle of radius R and two
straight portions as shown.
The wire lies in a plane
perpendicular to a uniform
magnetic field B
B0. Note choice
of x and y axis. The straight
portions each have length l
within the field. Determine the
net force on the wire due to
the magnetic field B
B0.
Copyright © 2009 Pearson Education, Inc.
27-4 Force on an Electric Charge
Moving in a Magnetic Field
The force on a moving charge is related to
the force on a current since a current is
just a bunch of moving charges:
Once again, the
direction is given by
a right-hand rule.
Copyright © 2009 Pearson Education, Inc.
27-4 Force on an Electric Charge
Moving in a Magnetic Field
Conceptual Example 27-4: Negative
charge near a magnet.
A negative charge -Q is placed at rest
near a magnet. Will the charge begin
to move? Will it feel a force? What if
the charge were positive, +Q?
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27-4 Force on an Electric Charge
Moving in a Magnetic Field
Example 27-5: Magnetic force on a proton.
A magnetic field exerts a force of 8.0 x 10-14 N toward the
west on a proton moving vertically upward at a speed of
5.0 x 106 m/s. When moving horizontally in a northerly
direction, the force on the proton is zero.
Determine the magnitude and direction of the magnetic
field in this region. (The charge on a proton is q = +e =
1.6 x 10-19 C.)
Copyright © 2009 Pearson Education, Inc.
27-4 Force on an Electric Charge
Moving in a Magnetic Field
If a charged particle is
moving perpendicular
to a uniform magnetic
field, its path will be a
circle.
Copyright © 2009 Pearson Education, Inc.
27-4 Force on an Electric Charge
Moving in a Magnetic Field
Example 27-7: Electron’s path in a
uniform magnetic field.
An electron travels at 2.0 x 107 m/s in a
plane perpendicular to a uniform
0.010-T magnetic field. Describe its
path quantitatively.
Copyright © 2009 Pearson Education, Inc.
27-4 Force on an Electric Charge
Moving in a Magnetic Field
Problem solving: Magnetic fields – things to
remember:
1. The magnetic force is perpendicular to the
magnetic field direction.
2. The right-hand rule is useful for determining
directions.
3. Equations in this chapter give magnitudes
only. The right-hand rule gives the direction.
Copyright © 2009 Pearson Education, Inc.
ConcepTest 27.1c Magnetic Force III
A positive charge enters a
uniform magnetic field as
shown. What is the direction of
the magnetic force?
1) out of the page
2) into the page
3) zero
4) to the right
5) to the left


v

q

ConcepTest 27.1c Magnetic Force III
A positive charge enters a
uniform magnetic field as
shown. What is the direction of
the magnetic force?
1) out of the page
2) into the page
3) zero
4) to the right
5) to the left
Using the right-hand rule, you can
see that the magnetic force is
directed into the page. Remember
that the magnetic force must be
perpendicular to BOTH the B field
and the velocity.


v

 q
F

ConcepTest 27.3 Magnetic Field
A proton beam enters a
magnetic field region as shown
below. What is the direction of
the magnetic field B?
1) + y
2) – y
3) + x
4) + z (out of page)
5) – z (into page)
y
x
ConcepTest 27.3 Magnetic Field
A proton beam enters a
magnetic field region as shown
below. What is the direction of
the magnetic field B?
1) + y
2) – y
3) + x
4) + z (out of page)
5) – z (into page)
The picture shows the force acting
in the +y direction. Applying the
y
right-hand rule leads to a B field
that points into the page. The B
field must be out of the plane
because B  v and B  F.
Follow-up: What would happen to a beam of atoms?
x
27-4 Force on an Electric Charge
Moving in a Magnetic Field
Conceptual Example 27-9: A helical path.
What is the path of a charged particle in a
uniform magnetic field if its velocity is not
perpendicular to the magnetic field?
Copyright © 2009 Pearson Education, Inc.
27-4 Force on an Electric Charge
Moving in a Magnetic Field
The aurora borealis (northern lights) is caused
by charged particles from the solar wind
spiraling along the Earth’s magnetic field, and
colliding with air molecules.
Copyright © 2009 Pearson Education, Inc.
27-5 Torque on a Current Loop;
Magnetic Dipole Moment
The forces on opposite
sides of a current loop
will be equal and
opposite (if the field is
uniform and the loop is
symmetric), but there
may be a torque.
The magnitude of the
torque is given by
Copyright © 2009 Pearson Education, Inc.
27-5 Torque on a Current Loop;
Magnetic Dipole Moment
The quantity NIA is called the magnetic
dipole moment, μ:
The potential energy of the loop
depends on its orientation in the field:
Copyright © 2009 Pearson Education, Inc.
27-5 Torque on a Current Loop;
Magnetic Dipole Moment
Example 27-12: Magnetic moment of a
hydrogen atom.
Determine the magnetic dipole moment of
the electron orbiting the proton of a
hydrogen atom at a given instant,
assuming (in the Bohr model) it is in its
ground state with a circular orbit of
radius r = 0.529 x 10-10 m. [This is a very
rough picture of atomic structure, but
nonetheless gives an accurate result.]
Copyright © 2009 Pearson Education, Inc.
27-5 Torque on a Current Loop;
Magnetic Dipole Moment
Example: A rectangular coil 5.40 cm X 8.50 cm
consists of 25 turns of wire and carries a current
of 15.0 mA. A 0.350-T magnetic field is applied
parallel to the plane of the coil.
a) Calculate the magnitude of the magnetic
dipole moment of the coil.
b) What is the magnitude of the torque acting on
the loop?
Copyright © 2009 Pearson Education, Inc.
27-5 Torque on a Current Loop;
Magnetic Dipole Moment
3


NIA

25
15.0

10
A   0.054 m  0.085 m 



a) coil
 1.72 103 A  m 2
b) Note: B  coil    coil  B  coil B sin 90o  coil B
 1.72 103 A  m 2   0.350 T 
 6.02 104 N  m
Copyright © 2009 Pearson Education, Inc.
27-6 Applications: Motors
An electric motor uses the torque on a
current loop in a magnetic field to turn
magnetic energy into kinetic energy.
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27-6 Applications:
Galvanometers
A galvanometer
takes advantage of
the torque on a
current loop to
measure current; the
spring constant is
calibrated so the
scale reads in
amperes.
Copyright © 2009 Pearson Education, Inc.
ConcepTest 27.7b Magnetic Force on a Loop II
1) move up
If there is a current in
2) move down
the loop in the direction
3) rotate clockwise
shown, the loop will:
4) rotate counterclockwise
5) both rotate and move
B field out of North
B field into South
N
S
N
S
ConcepTest 27.7b Magnetic Force on a Loop II
1) move up
If there is a current in
2) move down
the loop in the direction
3) rotate clockwise
shown, the loop will:
4) rotate counterclockwise
5) both rotate and move
Look at the north pole: here the
F
magnetic field points to the right and
the current points out of the page.
N
S
The right-hand rule says that the force
must point up. At the south pole, the
same logic leads to a downward force.
Thus the loop rotates clockwise.
F
27-7 Discovery and Properties of the
Electron
Electrons were first observed in cathode ray tubes.
These tubes had a very small amount of gas inside,
and when a high voltage was applied to the cathode,
some “cathode rays” appeared to travel from the
cathode to the anode.
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27-7 Discovery and Properties of the
Electron
The value of e/m for the cathode rays was
measured in 1897 using the apparatus below; it
was then that the rays began to be called
electrons.
Figure 27-30 goes here.
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27-7 Discovery and Properties of the
Electron
Millikan measured the electron charge directly
shortly thereafter, using the oil-drop apparatus
diagrammed below, and showed that the
electron was a constituent of the atom (and not
an atom itself, as its mass is far too small).
The currently accepted
values of the electron
mass and charge are
m = 9.1 x 10-31 kg
e = 1.6 x 10-19 C
Copyright © 2009 Pearson Education, Inc.
27-8 The Hall Effect
When a current-carrying wire
is placed in a magnetic field,
there is a sideways force on
the electrons in the wire. This
tends to push them to one
side and results in a potential
difference from one side of the
wire to the other; this is called
the Hall effect. The emf differs
in sign depending on the sign
of the charge carriers; this is
how it was first determined
that the charge carriers in
ordinary conductors are
negatively charged.
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27-9 Mass Spectrometer
All the atoms
reaching the
second magnetic
field will have the
same speed; their
radius of curvature
will depend on
their mass.
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27-9 Mass Spectrometer
Example 27-14: Mass spectrometry.
Carbon atoms of atomic mass 12.0 u are
found to be mixed with another, unknown,
element. In a mass spectrometer with fixed B′,
the carbon traverses a path of radius 22.4 cm
and the unknown’s path has a 26.2-cm radius.
What is the unknown element? Assume the
ions of both elements have the same charge.
Copyright © 2009 Pearson Education, Inc.
Summary of Chapter 27
• Magnets have north and south poles.
• Like poles repel, unlike attract.
• Unit of magnetic field: tesla.
• Electric currents produce magnetic fields.
• A magnetic field exerts a force on an electric
current:
Copyright © 2009 Pearson Education, Inc.
Summary of Chapter 27
• A magnetic field exerts a force on a moving
charge:
• Torque on a current loop:
• Magnetic dipole moment:
Copyright © 2009 Pearson Education, Inc.
Chapter 28
Sources of Magnetic Field
Copyright © 2009 Pearson Education, Inc.
28-1 Magnetic Field Due to a Straight
Wire
The magnetic field due to a
straight wire is inversely
proportional to the distance
from the wire:
The constant μ0 is called the
permeability of free space,
and has the value
μ0 = 4π x 10-7 T·m/A. (exactly!)
Copyright © 2009 Pearson Education, Inc.
28-1 Magnetic Field Due to a Straight
Wire
Example 28-1: Calculation of B
B
near a wire.
An electric wire in the wall of a
building carries a dc current of
25 A vertically upward. What is
the magnetic field due to this
current at a point P 10 cm due
north of the wire?
Copyright © 2009 Pearson Education, Inc.
28-1 Magnetic Field Due to a Straight
Wire
Example 28-2: Magnetic field midway between two
currents.
Two parallel straight wires 10.0 cm apart carry
currents in opposite directions. Current I1 = 5.0 A is
out of the page, and I2 = 7.0 A is into the page.
Determine the magnitude and direction of the
magnetic field halfway between the two wires.
Copyright © 2009 Pearson Education, Inc.
28-1 Magnetic Field Due to a Straight
Wire
Conceptual Example 28-3: Magnetic field due to
four wires.
This figure shows four long parallel wires which
carry equal currents into or out of the page. In
which configuration, (a) or (b), is the magnetic
field greater at the center of the square?
Copyright © 2009 Pearson Education, Inc.
ConcepTest 28.1b Magnetic Field of a Wire II
Each of the wires in the figures
below carry the same current,
either into or out of the page.
In which case is the magnetic
field at the center of the square
greatest?
1
B=?
2
B=?
1) arrangement 1
2) arrangement 2
3) arrangement 3
4) same for all
3
B=?
ConcepTest 28.1b Magnetic Field of a Wire II
Each of the wires in the figures
below carry the same current,
either into or out of the page.
In which case is the magnetic
field at the center of the square
greatest?
1
2
1) arrangement 1
2) arrangement 2
3) arrangement 3
4) same for all
3
28-2 Force between Two Parallel Wires
The magnetic field produced
at the position of wire 2 due
to the current in wire 1 is
The force this field exerts
on a length l2 of wire 2 is
 0 I1 
F2  I 2 2 B1  I 2 2 

2

d


0 I1I 2

2
2 d
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28-2 Force between Two Parallel Wires
Parallel
currents
attract;
antiparallel
currents repel.
RIGHT HAND
RULE!!
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28-2 Force between Two Parallel Wires
Example 28-5: Suspending a wire with a current.
A horizontal wire carries a current I1 = 80 A dc. A
second parallel wire 20 cm below it must carry
how much current I2 so that it doesn’t fall due to
gravity? The lower wire has a mass of 0.12 g per
meter of length.
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