General Physics (PHYS )

Chapter 22

Magnetism

Magnetic Force Exerted on a

current

Magnetic Torque

Electric Currents, magnetic Fields,

and Ampere’s Law

Current Loops and Solenoids

Magnetism in Matter

Magnetism • Magnetic effects from natural magnets have been known for a

long time. Recorded observations from the Greeks more than 2500 years ago.

• The word magnetism comes from the Greek word for a certain type of stone (lodestone) containing iron oxide found in Magnesia, a district in northern Greece.

• Properties of lodestones: could exert forces on similar stones and could impart this property (magnetize) to a piece of iron it touched.

• Small sliver of lodestone suspended with a string will always align itself in a north-south direction—it detects the earth’s magnetic field.

The Magnetic Field

Permanent bar magnets have opposite poles on

each end, called north and south. Like poles

repel; opposites attract.

If a magnet is broken in half,

each half has two poles:

Bar Magnet • Bar magnet ... two poles: N and S

Like poles repel; Unlike poles attract.

• Magnetic Field lines: (defined in same way as electric field lines,

direction and density)

• Does this remind you of a similar case in electrostatics?

NS

Magnetic Field Lines of a bar magnet

Electric Field Lines of an Electric Dipole

NS

Chapter 22 Cont.

• http://medschoolodyssey.wordpress.com/2010/03/30/some-statistics-on-the-mcat-and-your-undergraduate-major/

Magnetism

Earth’s Magnetic Field

Magnetic Monopoles? • Perhaps there exist magnetic charges, just like electric charges. Such an entity

would be called a magnetic monopole (having + or - magnetic charge).

• How can you isolate this magnetic charge?

Try cutting a bar magnet in half:

• Many searches for magnetic monopoles—the existence of which would explain (within framework of QM) the quantization of electric charge (argument of Dirac)

• No monopoles have ever been found!

N S N N S S

Even an individual electron has a magnetic “dipole”!

Source of Magnetic Fields? • What is the source of magnetic fields, if not magnetic charge?

• Answer: electric charge in motion!

– e.g., current in wire surrounding cylinder (solenoid) produces very similar field to that of bar magnet.

• Therefore, understanding source of field generated by bar magnet lies in understanding currents at atomic level within bulk matter.

Orbits of electrons about nuclei

Intrinsic “spin” of electrons (more important effect)

Magnetic Fields in analogy with Electric Fields

Electric Field: – Distribution of charge creates an electric field E(r) in

the surrounding space.

– Field exerts a force F=q E(r) on a charge q at r

Magnetic Field: – Moving charge or current creates a magnetic field B(r)

in the surrounding space.

– Field exerts a force F on a charge moving q at r

– (emphasis this chapter is on force law)

11

Applications of magnetic forces

“electric” motor, “electric” car, “electric” generator,

“electric” drill, solenoid actuator.

tape recorder, magnetic hard drive, CRT for oscilloscopes

and TV

magnetic levitation for trains

science (Nmr, mass spectrometer)

medicine (MRI; magnetic navigation systems for catheter)

The Magnetic Force on Moving Charges

This is an

experimental result

– we observe it to

be true.

Force on a Charge Moving in a Magnetic Field

is the magnetic force

is the charge

is the velocity of the charge

is the magnetic field

This equation defines B, just as defines .

vB

BF

q

EqFE

E

B

Magnitude of FB.

• The magnitude of FB = |q| v B sin q

– q is the smaller angle between and

– FB is zero when and are parallel or antiparallel

• q = 0 or 180o

– FB is a maximum when and are perpendicular

• q = 90o

v

v

v

B

B

B

The Magnetic Force on Moving Charges

The magnetic force on a moving charge is

actually used to define the magnetic field:

• Recall

• The SI unit of magnetic field is the tesla (T).

• The gauss (G) is also a commonly used unit: 1 T = 104 G

)sin( so

)sin(

q

q

qv

FB

qvBF

mA

N

smC

NT

)/(

• So, we know how to find the magnitude.

• How do we find the direction of the magnetic force F?

Direction of FB: tricky because of cross product

19

The Magnetic Force on Moving Charges

In order to figure out which

direction the force is on a

moving charge, you can use a

right-hand rule. This gives the

direction of the force on a

positive charge.

Direction of FB: Right-Hand Rule #1

• Your thumb is in the direction of the force if q is positive.

21

Left Hand Rule

• Left hand rule is used for electrons charges.

• Your turn… how would it look like?

Got it 1

1. a

2. b

3. c

4. none

0%

0%

0%

0%

Figure shows a proton in a magnetic field.

For which of the three proton velocities shown will the

magnetic force be greatest?

Got it 2

1. Parallel into the paper

2. Parallel out of the paper

3. Perpendicular into the paper

4. Perpendicular out of the paper

0%

0%

0%

0%

Figure shows a proton in a magnetic field.

What will be the direction of the force in all three cases?

Example 2 Figure shows 3 protons entering a 0.10-T magnetic field.

All three are moving at 2.0 Mm/s.

Find the magnetic force on each.

velocity selector.

Electromagnetic

force

B

1

2

3

q F v B

FB + FE = 0 when v = E/B

The Motion of Charged Particles in a

Magnetic Field

A positively charged particle in an electric field

experiences a force in the direction of the field;

in a magnetic field the force is perpendicular to

the field. This leads to very different motions:

The Motion of Charged Particles in a

Magnetic Field

Because the magnetic force is always

perpendicular to the direction of motion, the path

of a particle is circular.

Also, while an electric field can do work on a

particle, a magnetic field cannot – the particle’s

speed remains constant.

The Motion of Charged Particles in a

Magnetic Field

For a particle of mass

m and charge q,

moving at a speed v

in a magnetic field B,

the radius of the

circle it travels is:

http://www.youtube.com/watch?v=a2

_wUDBl-

g8&list=PLF7A98FE5F5D0B39D

Charged particle in a magnetic field

GOT IT 3

1. Clockwise

2. Counterclockwise

0%

0%

A uniform magnetic field points out of this page.

Will an electron that’s moving in the plane of the

page circle

as viewed from above the page?

The Motion of Charged Particles in a

Magnetic Field

In a mass spectrometer, ions of different mass

and charge move in circles of different radii,

allowing separation of different isotopes of the

same element.

The Motion of Charged Particles in a

Magnetic Field

If a particle’s velocity

makes an angle with the

magnetic field, the

component of the

velocity along the

magnetic field will not

change; a particle with

an initial velocity at an

angle to the field will

move in a helical path.

http://www.youtube.com/

watch?v=lT3J6a9p_o8

Aurora Borealis

The Magnetic Force Exerted on a Current-

Carrying Wire

The force on a segment of a current-carrying

wire in a magnetic field is given by:

RHR and LHR can be used for

other variables.

• http://www.youtube.com/watch?v=tUCtCYty-ns

• Demo

Summary of Chapter 22

• All magnets have two poles, north and south.

• Magnetic fields can be visualized using

magnetic field lines. These lines point away

from north poles and toward south poles.

• The Earth produces its own magnetic field.

• A magnetic field exerts a force on an electric

charge only if it is moving:

• A right-hand rule gives the direction of the

magnetic force on a positive charge.

Summary of Chapter 22

• If a charged particle is moving parallel to a

magnetic field, it experiences no magnetic force.

• If a charged particle is moving perpendicular to a

magnetic field, it moves in a circle:

• If a charged particle is moving at an angle to a

magnetic field, it moves in a helix.