Magnetic Fields

AP Physics Rapid Learning Series - 17
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M ti Fi ldMagnetic Fields
Physics Rapid Learning Series
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© Rapid Learning Inc. All rights reserved.
Wayne Huang, Ph.D.
Keith Duda, M.Ed.
Peddi Prasad, Ph.D.
Gary Zhou, Ph.D.
Michelle Wedemeyer, Ph.D.
Sarah Hedges, Ph.D.

Learning Objectives
By completing this tutorial, you will:
Understand the nature of
magnetism.
Examine the relationship
between magnetism,
force and moving charge.
S l f
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See examples of
magnetism in nature and
technology.
Concept Map
Physics
Studies
Previous content
New content
Electrical
Forces
Electric Charge
Magnetic
Forces
When moving
Created from
and
Atoms
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Magnetic
Fields
When moving
in
Magnetic
Domains
Arranged in
Described
by
Right
Hand
Rule

The Nature of
Magnetism
This section will describe the basic
nature of magnetism
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nature of magnetism.
Magnetic Domains
The motion of electrons may produce unusual
forces. These often cancel out and don’t
amount to anything interesting.
In certain materials, groups of atoms have their
electrons aligned into small areas called magnetic
domains that behave as small magnets
themselves.
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Magnetic Elements
Iron, cobalt, and nickel are common magnetic
materials.
These materials are called ferromagnetic.
All materials are magnetic, but most are only VERY
slightly magnetic.
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Polarization
The poles of a magnet cannot be separated. There
are no magnetic monopoles, unlike electric
chargescharges.
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A North pole will always be accompanied by a
South pole.

Attraction and Repulsion
Just like electric charges (poles): likes repel,
opposites attract.
S N
S N
N S
N S
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N S N S
Breaking Magnets
If you break a magnet, you don’t get an isolated N
and S pole. Each segment becomes its own
complete mini magnet.complete mini magnet.
N S
N S One magnet
Two complete
magnetsNS
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N SNS
Four
complete
magnetsNS NS

Earth as a Magnet
The Earth is a large magnet. Magnetic north and
geographic north are not in the same location. The
difference between these is called magnetic
declinationdeclination.
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Note that what we call the North pole is actually
the magnetic south pole of our Earth!
Magnetic Fields
Magnetic fields, B fields, may be drawn similarly
to E fields. Go from N to S. E field was + to -.
N S
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Where the lines are more concentrated is an area
of higher magnetic flux/strength.

Field Lines
N S
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A small compass could be used to “trace” the
magnetic field lines in simple situations.
N S
Repeatedly moving the compass creates the same
field lines as seen before.
Electricity and Magnetism
A wire carrying an electric current produces
magnetism.
In fact, any moving charge creates magnetism.
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Earth’s Magnetic Field
This is why the Earth has a magnetic field.
( )The molten metal (charge) in its center is
continually rotating.
Thus, a magnetic field is formed around the Earth.
This is called the dynamo effect.
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Curious fact: Every few million years, the earth’s
magnetic field reverses itself!!!
Other Magnetic Fields
Jupiter spins very fast, this may explain why it has
a very large magnetic field.
Most moons in the solar system have no molten core.
Thus they have no magnetic field.
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y g

Moving ChargeMoving Charge,
Magnetism, and
Force
This section will describe the relationship
between magnetic fields moving charge
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between magnetic fields, moving charge,
and force.
Right Hand Rule
To visualize magnetic fields and current, use the
right hand rule, RHR.
B
f
Thumb = direction of
conventional current
f
i
e
l
d
Fingers = point or curl
in direction of
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current
in direction of
magnetic, B, field

Right Hand Rule for a Wire
Current
The thumb
points in the
direction of the
current.
The fingers wrap
around in the
direction of a
circular
magnetic field
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magnetic field.
Fields Into and Out of Page
Often it is necessary to symbolize fields that go
into or out of the 2 dimensional page.
To represent a field coming directly out of the page:
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x x x
x x x
x x x
To represent a field going into the page:

Visualization Tip
To remember the notation for B fields going into
and out of the page, think of an arrow.
When the B field is coming at you, out of the page,
ld th ti A d t i d
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you would see the arrow tip. A dot is used.
When the B field is going away from you, into the
page, you would see the arrow feathers. An X is used.
Right Hand Rule for Loops
A loop carrying a current can be described using
the right hand rule.
Current
X X X X X X
X X X X
X X X X
. . .
. . .
. . .
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X X X X
X X X X X X X
This gives a field going through and around the
hoop as shown.
. . .

Force, current and B fields
If an electric current is passed through a wire that is
already in a B (magnetic) field, it will experience a
force.
A l
BiLsinθFB =
Force due
to
magnetic
field, N
Angle
between i
and B field
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B field, T
Length of
wire, m
Current in
wire, A
Effect of Angle
When using the formula FB=BILsinθ, the
directions must be carefully considered.
Thus, if the current and B field are parallel,
θ = 0o, sin (0o) = 0
F = 0, minimum force
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If the current and B field are perpendicular,
θ = 90o, sin(90o) = 1
F = BiL, maximum force

B Units
If you examine the previous formula, you will
notice that B has units of N/(Am).
One Newton per Amp Meter is 1 Tesla, T.
1 Gauss = 1 x 10 -4 T
Obviously a Gauss is a small unit
of magnetic field and a Tesla is a
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of magnetic field, and a Tesla is a
large one. The earth’s magnetic
field is .5 G, or .5 x 10 -4 T .
Current Carrying Wire Example
Calculate the magnetic
force on a high tension
po er ire carr ing 1200 Apower wire carrying 1200 A
of current.
Assume the wire is 100m
long and situated at a 75°
angle to the Earth’s
magnetic field of 5x10-5 T.
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Current Carrying Wire Solution
BiLsinθFB =
5
100m)sin75T)(1200A)((5x10F 5
B
−
=
5 8NF
00m)sin75)(1200A)(1
Am
N
(5x10F 5
B
−
=
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5.8NFB =
Notice that even with this very high current, the
force is relatively small. Also, see how the units
cancel out to yield Newton as the answer unit.
Right Hand Rule Again
Fingers = direction of B field
Thumb = direction of conventional current
Line perpendicular to Palm = direction of forcep p
N S
FB
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current

Force on a charge in B field
Sometimes there aren’t wires to carry current or
charge. A lone electron may be flying through the
air and encounter a B field. A similar effect
happens, a force is exerted on the particle.
The RHR can be used again. Since the thumb
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shows direction of conventional current, or +
charge movement, if a negative particle is moving,
then the thumb direction must be reversed.
Charge Moving in Field
B field into the page
X X X X X X
X X X X X X
+velocity
V is to the leftX X X X X X
X X X X X X
X X X X X X
F
o
r
c
e
V is to the left
F is downward
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X X X X X X
This situation results in a centripetal force that
keeps the particle moving in a circle.
At any point in time, v and F are perpendicular.

Another Force Equation
This formula calculates the force that acts on a
charged particle moving in a B field.
Force due to A l
qvBsinθFB =
Force due to
magnetic
field, N
Angle
between v
and B field
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Force is a maximum when v is perpendicular to B
B field, TCharge, C
Velocity,
m/s
Movement of Electron
An electron is fired into a magnetic field that is going
into the page as shown. How will it behave?
X X X X
e-
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X X X X
X X X X
e

Direction of Negative Particle
Use the RHR, remember that conventional current
flows opposite electron flow.
X X X X
X X X X
e-
FB
FB
F
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Initially, the force exerted on the particle is down.
This makes it begin to curve. As it continues, the
force is always pointing inward causing the electron
to move in a clockwise circle.
FB
Calculation of Force Example
The magnitude of the force on this sample electron
could be calculated. Assume the single electron
moves at 1000 m/s through the B field of 0.5 T.
B i θF qvBsinθFB =
The charge on a single electron could easily be
calculated or found in a reference text.
o19
B 0)(.5T)sin9C)(1000m/s(1.6x10F −
=
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Nx108F 17
B
−
=
This small magnitude is the force exerted on the
single electron moving through our example B field.

Size of Curve
The charged particle will travel in a circle. What factors
do you think will affect the size, radius, of this circle?
The force causing the particle to turn acts as a
centripetal force:
r
mv
F
2
c =
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r
This force is magnetic in origin:
BF q v B sinθ=
Calculation of Radius
Set these two equations equal:
mv
i θB
2
r
sinθBvq =
Since the v and B are perpendicular, sin θ=1
r
mv
Bvq
2
=
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qvB
mv
r
2
=
qB
mv
r =

Mass Spectrometer
A mass spectrometer can separate/identify various
isotopes. They can also help identify various
unknown chemical reactants.
Ions are accelerated by an electric potential. They are
then flung into a magnetic field. Their paths help
describe their properties.
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A heavier object will curve less in the magnetic field, a
lighter one will curve more.
Mass Spectrometer Diagram
. . . . . .
B field out
of paper
-
Detector
. . . . . .
. . . . . .
of paper
m1 m2
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Atoms with varying masses will travel different arcs.
This “separates” or identifies isotopes with varying
masses.
+ions
+

B Field Due to a Straight Wire
One would imagine that the B field from a current
carrying wire is inversely proportional to the
distance away from the wire.
πr
iμ
B o
2
=
Current in
wire, A
Constant,
4∏x10-7
Tm/A
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πr2
B field, T
Perpendicular
distance to
wire, m
μo
μo is known as the permeability of free space.
It is a constant that is similar to the one used in
coulomb’s law εcoulomb s law, εo
A
Tm
10x4πμ 7
o
−
=
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Don’t confuse μo with the coefficient of friction, they
are not the same.

B Field Diagram
In a simple one wire situation the
magnetic field can be found atCurrent magnetic field can be found at
any point using the RHR.
Consider how two parallel wires
near each other might behave.
The currents could be moving
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either way also.
Two Current Carrying Wires
I1 I2 I1
I
Use the RHR, current flowing in one wire, and the B
field created from the other...
1 2 I1 2
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Notice that if the current is in the same direction, the
forces are attractive.
Also see how they are repulsive if the currents oppose
each other.

B Field Away from Wire Example
In a typical household circuit, a wire usually
carries no more than 15A of current. How strong is
the magnetic field at point a distance of 10cm from
this wire?
Current
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10cm
B=?
B Field Away from Wire Solution
πr
iμ
B o
2
=
A
Tm
10x4πμ 7
o
−
=
First, the distance given in centimeters must be
changed into meters. This is necessary to match
the meter unit in µo.
.10m
100cm
1m
x10cm =
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(.10m)2π
)(15A)
A
Tm
x10(4π
B
7-
= T3x10 5−
=

Magnetism inMagnetism in
Nature and
Technology
This section will explain several
examples of magnetism in action You
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examples of magnetism in action. You
may be familiar with some of these.
Solar Magnetism
Because of the churning/dynamic nature of the
sun, magnetic fields are abundant there.
Even a small telescope, equipped with the proper
filter, can see magnetic eruptions on the surface.
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This type of observation also shows that the sun is
rotating.

Charged Projectiles
From solar
eruptions like
this, charged
particles are
thrown at the
Earth.
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These particles may become trapped in the Earth’s
magnetic field and be seen as the northern or
southern lights.
Audio Speakers
A speaker contains a permanent magnet, along with
a coil of wire. When current runs through the coil, a
magnetic field is formed.
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The attraction or repulsion from the two fields moves
a stiff paper cone that creates sound waves.

Large Speakers
In general, larger magnets provide more force, thus
moving more air and creating more sound. This means
that larger/heavier speakers are usually better.
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However, there are some more recent models that
provide excellent performance in a compact
package.
MRI
A relatively new type of biological imaging is
Magnetic Resonance Imaging.
In this procedure, a patient is exposed to a very
strong magnetic field. The protons in water atoms
line up in this magnetic field.
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Next, a radio pulse is sent in that tips the protons
over a bit. When they right themselves, a faint
signal is emitted.

MRI Images
MRI’s create rather detailed views even of soft
structures that X rays often miss.
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Unlike X rays, no ionizing radiation is used in an MRI
scan.
Magnetic Media
Audio cassettes, VCR tapes and floppy disks all
store information magnetically.
In each case, information is encoded onto a
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substance that can be magnetized.
This information originates as an electric current
that may come from a microphone, computer, etc.

More on Magnetic Media
This electric current is amplified, then sent to a
recording head magnet that is near the audio, video,
or computer tape.
As the current is varied the signal is etched or
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As the current is varied, the signal is etched or
imprinted onto the tape as a magnetic code.
This code persists even after it leaves the
recording head magnet and is stored for later
use.
B field caused
by current:
B field caused
by current:
i
Magnetic force
on a moving
Magnetic force
on a moving
Magnets
contain
domains that
Magnets
contain
domains that
Learning Summary
πr
iμ
B o
2
=
Right Hand Rule RHRRight Hand Rule RHR
g
charged particle
FB=qvBsinθ
g
charged particle
FB=qvBsinθ
align
themselves
to create
magnetism
align
themselves
to create
magnetism
54/56
Right Hand Rule, RHR
Fingers = B field
Thumb = moving charge
Palm = force
Right Hand Rule, RHR
Fingers = B field
Thumb = moving charge
Palm = force
Magnetic force on a
current carrying wire:
FB=BiLsinθ
Magnetic force on a
current carrying wire:
FB=BiLsinθ

Congratulations
You have successfully completed
the tutorial
Magnetic Fields
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Magnetic Fields

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