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2/14/07 184 Lecture 21 1

PHY 184PHY 184PHY 184PHY 184

Spring 2007

Lecture 21

Title: Magnetism

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2/14/07 184 Lecture 21 2

Permanent MagnetsPermanent MagnetsPermanent MagnetsPermanent Magnets

Examples of permanent magnets include

refrigerator magnets and magnetic door latches. They are all made of compounds of iron, nickel, or

cobalt. If you touch an iron needle to a piece of magnetic

lodestone, the iron needle will be magnetized. If you then float this iron needle in water, the

needle will point toward the north pole of the Earth(approximately!)

We call the end of the magnet that points norththe north pole of the magnet and the other end thesouth pole of the magnet.

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2/14/07 184 Lecture 21 3

Permanent MagnetsPermanent Magnets -- PolesPolesPermanent MagnetsPermanent Magnets -- PolesPoles

Magnets exert forces on one

another --- attractive orrepulsive depending onorientation.

If we bring together twopermanent magnets such thatthe two north poles aretogether or two south poles aretogether, the magnets will repeleach other.

If we bring together a northpole and a south pole, the

magnets will attract each other.

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2/14/07 184 Lecture 21 4

Magnetic Field LinesMagnetic Field LinesMagnetic Field LinesMagnetic Field Lines

Permanent magnets interact with each other at adistance, without touching.

In analogy with the electric field, we define amagnetic field to describe the magnetic force.

As we did for the electric field, we may representthe magnetic field using magnetic field lines.

The magnetic field direction is always tangent tothe magnetic field lines.

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2/14/07 184 Lecture 21 5

Magnetic Field Lines (2)Magnetic Field Lines (2)Magnetic Field Lines (2)Magnetic Field Lines (2)

The magnetic field lines froma permanent bar magnet are

shown below

Two dimensional computer calculation Three dimensional real-life

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2/14/07 184 Lecture 21 6

Break a Permanent Magnet in TwoBreak a Permanent Magnet in TwoBreak a Permanent Magnet in TwoBreak a Permanent Magnet in Two

If we break a permanent

magnet in half, what do we get?

S

SN

N

S

N

SN

A: A north and a south pole each?

B: A piece that is just a north pole and the corresponding south-pole piece?

What do you think?

A?

OR

B?

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2/14/07 184 Lecture 21 7

Broken Permanent MagnetBroken Permanent MagnetBroken Permanent MagnetBroken Permanent Magnet

If we break a permanent

magnet in half, we do notget a separate north poleand south pole.

When we break a barmagnet in half, we always

get two new magnets, eachwith its own north and south pole. Unlike electric charge that exists as positive (proton) and

negative (electron) separately, there are no separate magneticmonopoles (an isolated north pole or an isolated south pole).

Scientists have carried out extensive searches for magneticmonopoles; all results are negative. Magnetism is not caused by magnetic particles! Magnetism is

caused by electric currents.

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2/14/07 184 Lecture 21 8

Magnetic Field LinesMagnetic Field LinesMagnetic Field LinesMagnetic Field Lines

For the electric field, the electric force points in the same

direction as the electric field and the electric force wasdefined in terms of a positive test particle. However, because there is no magnetic monopole, we must

employ other means to define the magnetic force. We can define the direction of the magnetic field in terms

of the direction a compass needle would point. A compass needle, with a north pole and a south pole, will

orient itself in equilibrium such that its north pole points inthe direction of the magnetic field.

Thus the direction of the field can be

measured

atany pointby moving a compass needle around in amagnetic field and

noting the direction that the compass needle points.

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2/14/07 184 Lecture 21 9

The Earths Magnetic FieldThe Earths Magnetic FieldThe Earths Magnetic FieldThe Earths Magnetic Field

The Earth itself is amagnet.

It has amagnetic field sort of like a barmagnet (but not really like a bar magnet).

The poles of the Earthsmagnetic field are not alignedwith the Earths geographic

poles definedas the endpointsof the axis of the Earths rotation.

The Earths magnetic field is not as simpleas drawn here because it is distorted bythe solar wind

Protons fro

mthe Sun

moving

at 400km/s

The field inside the Earthis verycomplex.

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2/14/07 184 Lecture 21 10

Here is the real reason

The Earths Magnetic FieldThe Earths Magnetic FieldThe Earths Magnetic FieldThe Earths Magnetic Field

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2/14/07 184 Lecture 21 11

Earths Magnetic Field StrengthEarths Magnetic Field StrengthEarths Magnetic Field StrengthEarths Magnetic Field Strength

The strength of the Earths magnetic field at the

surface of Earth is on the order of 1 G The strength varies between 0.25 G and 0.65 G

Geomagnetic field strength(National Geophysical Data Center)

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2/14/07 184 Lecture 21 12

Earths Magnetic PolesEarths Magnetic PolesEarths Magnetic PolesEarths Magnetic Poles

The north and south magnetic poles are not located at

the north and south geographic poles The magnetic north pole is located in Canada

The magnetic south pole is located on the edge ofAntarctica

The magnetic poles move around, at a rate of 40 km peryear

By the year 2500 the magnetic north pole will belocated in Siberia

There are indications that the Earths magnetic fieldreverses (N mS) on the time scale of 1 million yearsor so.

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2/14/07 184 Lecture 21 13

Magnetic DeclinationMagnetic DeclinationMagnetic DeclinationMagnetic Declination

A compass needle points toward the magnetic north pole ratherthan true north.

The angle between the direction a compass needle points and truenorth is called the magnetic declination.

The magnetic declination is defined to be positive when magnetic north is east of true north

negative when

magnetic north is west of true north

The magnetic north pole currently resides on a line that passesthrough central Missouri, Eastern Illinois, Western Iowa, andEastern Wisconsin

Along this line the magnetic declination is zero.

West of this line thema

gnetic declination is positive

and re

aches18r in Seattle.

East of this line the declination is negative, up to -18r in Maine.

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2/14/07 184 Lecture 21 14

Magnetic Declination (2)Magnetic Declination (2)Magnetic Declination (2)Magnetic Declination (2)

Because the positions of the Earths magnetic poles move with time, the

magnetic declination is not constant. For example, here is the estimated magnetic declination for Lansing,

Michigan for the period 1900 2004.

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2/14/07 184 Lecture 21 15

Definition of the Magnetic Field

Notations

Electric field = E(x)

Magnetic field = B(x)

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2/14/07 184 Lecture 21 16

Magnetic ForceMagnetic ForceMagnetic ForceMagnetic Force

We define the magnetic field in terms of its effect on an

electrically ch

arged p

article (q).

Recall that an electric field exerts a force on a particle withcharge q given by

A magnetic field exerts no force on a stationary charge. But amagnetic field does exert a force on a charge that moves

across the field.

The direction of the force is perpendicular to both the velocityof the moving charged particle and the magnetic field; themagnetic force is sideways.

The Lorentz force

)(xEqFTTT

!

)(xBvqFTTTT

v!

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2/14/07 184 Lecture 21 17

Right Hand RuleRight Hand RuleRight Hand RuleRight Hand Rule

The direction of the cross produce (vxB ) is given by the

right hand rule.

To apply the right hand rule

Use your right hand! Align thumb in the direction of v

Align your index finger with the magnetic field

Your middle finger will point in the direction of the crossproductvxB .

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2/14/07 184 Lecture 21 18

Right Hand Rule (2)Right Hand Rule (2)Right Hand Rule (2)Right Hand Rule (2)

What about the sign of the

charge?

If q is positive, then F is in thesame direction asvx B.

If q is negative, F is in theopposite direction.

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2/14/07 184 Lecture 21 19

Magnitude of Magnetic ForceMagnitude of Magnetic ForceMagnitude of Magnetic ForceMagnitude of Magnetic Force

The magnitude of the magnetic force on amoving charge is

where U is the angle between the velocity of the chargedparticle and the magnetic field.

Do you see that there is no magnetic force on a chargedparticle moving parallel to the magnetic field? (Because U iszero and sin(0)=0)

Do you see when the magnetic forfce is most strong? (Max.

force is for U = 90 degrees; then F = q v B)

FB ! qvBsinU

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2/14/07 184 Lecture 21 20

The magnetic force on a moving charge is sideways.

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2/14/07 184 Lecture 21 21

Clicker Question (1)Clicker Question (1)Clicker Question (1)Clicker Question (1)

The figure shows a charged

particle with velocity v travelsthrough a uniformmagnetic fieldB. What is the direction of themagnetic force F on the particle?

A) negative z direction

B) positive y direction

C) positive z direction

D) negative x direction

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2/14/07 184 Lecture 21 22




A) positive y direction

B) positive z direction

C) the force is 0


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2/14/07 184 Lecture 21 23




A) positive y direction

B) the force is 0

C) negative z direction


F = q v B sin(180) = 0

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2/14/07 184 Lecture 21 24

Units of Magnetic Field StrengthUnits of Magnetic Field StrengthUnits of Magnetic Field StrengthUnits of Magnetic Field Strength

The magnetic field strength has received its own named

unit, the tesla (T), named in honor of the physicist andinventor Nikola Tesla (1856-1943)

A tesla is a rather large unit of the magnetic field strength.

Sometimes you will find magnetic field strength state inunits of gauss (G), (not an official SI unit)

1 T = 1Ns

Cm! 1

N

Am

1 G = 10-4

T 10 kG = 1 T

Check unit consistency:F = q v BN = C (m/s) T

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2/14/07 184 Lecture 21 25

Example: Proton in B FieldExample: Proton in B FieldExample: Proton in B FieldExample: Proton in B Field

Consider a region of uniform

magnetic field (green dots); themagnitude is B=1.2 mTand thedirection is vertical. A protonwith kinetic energy E=8.48 10-13Jenters the field, moving

horizontally fro

msouth tonorth.Calculate the magnetic

deflecting force on the proton.

Answer: 6.1 x 10-15 N

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