1

Chapter 19: MagnetismThe nature of magnetism

Iron ore found near Magnesia

Compass needles align N-S: magnetic Poles

North (South) Poles attracted to geographic North (South)

Like Poles repel, Opposites Attract

No Magnetic Monopoles

Define magnetic field lines = direction of compass deflection.

Electric Currents produce deflections in compass direction.

Electric Currents interact magneticallyI I

I

I

F F F F

2

Magnetic Fields in analogy with Electric Fields

Electric Field:

– Distribution of charge creates an electric field E in the surrounding space.

– Field at charges location exerts a force F=q E on a charge q

Magnetic Field:

– Moving charge or current creates a magnetic field B in the surrounding space.

– Field exerts a force F on a charge moving q

F = qvB sin is angle between B and v.

– F is perpendicular to B an v

3

F = |q| v B sin = |q| v B (v B) v

B

F

+

F = |q| v B sin F = |q| v B

v

B

F

+

v

F = |q| v B sinF = |q| v B

vB

F

+ B

Right Hand Rule (1-2-3) : v, B, F

4

Units of Magnetic Field Strength:

[B] = [F]/([q][v])

= N/(C m s-1)

= Tesla

actually defined in terms of force on standard current

CGS Unit 1 Gauss = 10-4 Tesla

Earth's field strength ~ 1 Gauss

Direction = direction of velocity which generates no force

5

J. J. Thomson’s Measurement of e/m

Electron Gun

E

V

Example 19.2: Electrons are accelerated through a potential difference of 1000 V. The electrons then enter a region where there is a magnetic field and a “crossed” electric field (E and B are perpendicular), both of which are perpendicular to the beam. What magnitude magnetic field must be applied to exactly cancel the effect of the Electric field of 104 V/m?

6

Field of a long straight wire

s

I

B

BI

s

T m A

o

o

2

4 1 10 7

Magnetic field circulates around the wire; use Right hand rule for direction

Thumb in direction of the current, fingers curl around in direction of B

Example 19.2: Find the magnetic field 10 mm from a wire that carries a current of 1.0 A.

7

centerat 2

wireof turnsN using

centerat 2

r

NIB

r

IB

ox

ox

8

Fields tend to cancel in region right between wires.

Field Lines continue down center of cylinder

Field is negligible directly outside of the cylinder

I

B

Magnetic Field in a Solenoid Close packed stacks of coils form cylinder

B

I

solenoid) finitefor (

length)unit per turns(

ILN

B

nnIB

o

o

9

Example 19.3: A solenoid 20 cm long and 40 mm in diameter with an air core is wound with a total of 200 turns of wire. The solenoid is to be used to exactly cancel the Earth's magnetic field where it is 3.0x10-5 T in magnitude. What should the current in the solenoid be for its field to exactly cancel the earth’s field inside the solenoid?

10

Magnetic Materials

Microscopic current loops:

electron “orbits”

electron “spin”

L

Quantum Effects: quantized angular momentum L, Pauli Exclusion Principle, etc. are important in macroscopic magnetic behavior.

11

Magnetic Materials: Microscopic magnetic moments interact with an external (applied) magnetic field and each other, producing additional contributions to the net magnetic field B.

Types of MaterialsDiamagnetic: Magnetic field decreases in

strength.

Paramagnetic: Magnetic field increases in strength.

Ferromagnetic: Magnetic field increases in strength!

Diamagnetic and Paramagnetic are often approximately linear with a relative permeability KM, = KM 0

12

Ferromagnetism:

Greatly increases field

Highly nonlinear, with Hysteresis:

Hysteresis= magnetic record

Magnetization forms in Magnetic Domains

Saturation

Permanent Magnetization

Bnet

Bo

13

More on the magnetic force on a moving charge

For a charged particle moving perpendicular to the Magnetic Field

+

+

vF

F

v– Circular Motion!

Bqmv

R

Rmv

vBqF

||

||2

14

Example 19.5 A mass spectrometer:

velocity selector + circular trajectory

E

R1

R2

E = 40.0 kV/mB = .0800 TVelocity Selector: uses crossed E and B, so that Electric and Magnetic Forces cancel for a particular velocity.

(a)What is the speed of the ions pass through the velocity selector?(b) If the radius of the path of the ions is 390 mm, what is the mass of the ions?

15

In a non-uniform field: Magnetic Mirror

Net component of force away from concentration of

field lines.

B

v

F

Magnetic Bottle Van Allen Radiation Belts

16

Magnetic Force on a Current Carrying Wire

vd

I

L

B

Fi

A

F F

F qvB F QvB

L vt IQ

tF I LB

i

i

sin sin

sin

17

Example 19.6 (almost) A wire carries 100 A due west, suspended between two poles 50 m apart. The Earth’s field is 5.0 x 10-5 T, directed north. What is the magnitude and direction of the magnetic force on the wire.

18

Force between two long parallel current carrying wires

(consider, for this example, currents in the same direction)I1 I2

Bdue to I2

Fdue to I2

F12 = I1 Bdue to I2 L

= I1 (oI2/(2r)) L

F/L = oI1 I2 /(2r)

force on I1 is towards I2

force is attractive (force is repulsive for currents in opposite directions!)

Example: Two 1m wires separated by 1cm each carry 10 A in the same direction. What is the force one wire exerts on the other

19

Torque on a Current Loop (from force on wire segments)Rectangular loop in a magnetic field (directed along z axis) short side length a, long side length b, tilted with short sides at an angle with respect to B, long sides still perpendicular to B.

B

Fa

Fa

Fb

Fb

Forces on short sides cancel: no net force or torque.

Forces on long sides cancel for no net force but there is a net torque.

20

Torque calculation: Side view

Fb = IBb

Fb

moment arm

a/2 cos

= Fb a/2 cos Fb a/2 cos Iab B cos = I A B cos I N A B cos with N loopsMagnetic Dipole ~ Electric Dipole

Switch current direction every 1/2 rotation => DC motorTorque for armature of Galvanometer

magnetic moment

B

21

Magnetic Poles:

Magnetic “dipoles” from electric current

No isolate magnetic poles, they are always present in pairs!

No magnetic monopoles!