Magnetic Fields

AP Physics Rapid Learning Series - 17

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M ti Fi ldMagnetic Fields

Physics Rapid Learning Series

Rapid Learning Centerwww.RapidLearningCenter.com/© 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 MapPhysics

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 MagnetThe 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 MagnetismA 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 RuleTo visualize magnetic fields and current, use the right hand rule, RHR.

Bf

Thumb = direction of conventional current

f

i e

ld

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 xx x xx x x

To represent a field going into the page:



Visualization TipTo 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 LoopsA loop carrying a current can be described using the right hand rule.

CurrentX 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 XThis gives a field going through and around the hoop as shown.

. . .



Force, current and B fieldsIf 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) = 1F = 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 5B

−=

5 8NF

00m)sin75)(1200A)(1AmN(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 AgainFingers = 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 pageX 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

Force

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 EquationThis 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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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-

FBFB

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 ExampleThe 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.

o19B 0)(.5T)sin9C)(1000m/s(1.6x10F −=

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Nx10 8F 17B

−=

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:

rmvF

2

c =

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rThis force is magnetic in origin:

BF q v B sinθ=

Calculation of RadiusSet these two equations equal:

mvi θB2

rsinθBv q =

Since the v and B are perpendicular, sin θ=1

rmvB v q

2

=

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qvBmvr

2

=

qBmvr =



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 WireOne would imagine that the B field from a current carrying wire is inversely proportional to the distance away from the wire.

πriμB o

2=

Current in wire, A

Constant,4∏x10-7Tm/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

ATm10 x 4πμ 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 I1I

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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10cmB=?

B Field Away from Wire Solution

πriμB o

2=

ATm10 x 4πμ 7

o−=

First, the distance given in centimeters must be changed into meters. This is necessary to match the meter unit in µo.

.10m100cm

1m x 10cm =

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(.10m) 2π

)(15A)A

Tmx10 (4πB

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 SpeakersA 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 SpeakersIn 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:

iMagnetic force

on a moving Magnetic force

on a moving

Magnets contain

domains that

Magnets contain

domains that

Learning Summary

πriμB o

2=

Right Hand Rule RHRRight Hand Rule RHR

gcharged particle

FB=qvBsinθ

gcharged particle

FB=qvBsinθalign

themselves to create

magnetism

align themselves

to create magnetism

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Right Hand Rule, RHRFingers = B field

Thumb = moving chargePalm = force

Right Hand Rule, RHRFingers = B field

Thumb = moving chargePalm = 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

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