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Magnetism

CHAPTER 29 Magnetic fields exert a force on

moving charges. CHAPTER 30 Moving

charges (currents) create magnetic

fields. CHAPTERS 31, 32 Changing magnetic

fields create electric fields.

(Induction)

Magnetic fields

- Magnetic poles, forces, and fields
- Force on a moving charged particle
- Force on a current-carrying wire

Magnets and Magnetic Forces

Similar model to electrostatics Each magnet has

two poles at its ends.B is the magnetic field

vector (magnetic flux density)

Magnetic poles come in two types, N and S.

Due to the Earths magnetism, a magnet will

tend to rotate until the N end points North.

(the earths north magnetic pole is actually a

south pole)

Forces between magnets are due to the forces

between each pair of poles, similar to the

electrostatic forces between point charges.

unlike poles attract

like poles repel

The force gets smaller as distance increases.

Magnetic Field B

Magnetic poles produce a field B(think of S as a

charge and of N as a charge)

B

F

The external field exerts forces on poles

F

B

Quiz

What is the direction of the force on a magnetic

dipole placed in a uniform magnetic field?

B

Magnetic field lines and Magnetic Dipoles

Compass needle (a magnetic dipole) aligns with

B

B

B

compass

N S

S N

Lines point out from N pole

Electric charge and Magnetic fields

Hans Ørsted discovered (1819) that moving

electric charges create magnetic fields. Also,

external magnetic fields exert forces on moving

electric charges.

A current loop acts like a magnetic dipole.

Define B by the force that an external field

exerts on a moving charge

Charge q moving with velocity , feels a force

(vector product)

F

B

q

v

1) 2) ? NO work done! 3) 4) For a negative

charge, the force is in the opposite

direction.

UNITS

Also 1 Gauss (G) 10-4 T

Typical Fields

Earths Field 1 x 10-4 T (1 Gauss) Strong

fridge magnet 10-2 T (100 G) Big lab

electromagnet 4 T (40,000 G) Superconducting

magnet up to 20 T (200,000 G)

Vector Diagrams

The three vectors F, v, B never lie in a single

plane, so the diagrams are always

three-dimensional. The following convention helps

with drawing the vectors.

For vectors perpendicular to the page, we use

X into the page (tail feathers of arrow)

out of the page (point of arrow)

Examples

For a positive charge q moving with velocity v

draw the force vector.

x x x x x x x x x x

x x x x x x

B

B

v

B

v

x

B

Wire

current I

L

Current I flows from left to right. In what

direction is the force on the wire?

B

The total force on the wire of length L is F

Nqv x B, where N is the number of charges in

length L.

N (number of charges/volume) x (volume) n

x (AL), where A is the cross-sectional area

So, F (nALqv) x B (nqvA)L x B

F I L x B

(straight wire, uniform B)

or,

The vector length L points along the wire in the

direction of the current.

Example

up

0.5 x 10-4 T

north

Assume the earths magnetic field is 0.5 x 10-4

T, and points North, 50o below the

horizontal. What is the force (magnitude and

direction) on a straight horizontal power line

100 m long, carrying 400 A

50o

- if the current is flowing North
- if the current is flowing East

Solution