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)

NS

Magnetic poles come in two types, “N” and “S”.

Due to the Earth’s magnetism, a magnet will tend to rotate until the “N” end points North. (the earth’s 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.

N N

SS

S N

like poles repel

N N

unlike poles attract

The force gets smaller as distance increases.

N

N

S

Magnetic Field B

Magnetic poles produce a field B(think of S as a – charge and of N as a + charge)

S

The external field exerts forces on poles

B

B

F

F

NS

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

S N

N

S

compass

Lines point out from N pole

BB

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

v

BvqF

(vector product)

+ q

B

v

F

1)

2) NO work done!

3)

4) For a negative charge, the force is in the opposite direction.

UNITS:

B F

v F

sin B v qF

22 mWb

m

weber)( tesla

smC

N

Also… 1 Gauss (G) = 10-4 T

BvqF

Typical Fields

Earth’s 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

X into the page (tail feathers of arrow) out of the page (point of arrow)

For vectors perpendicular to the page, we use:

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.

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 xv

BB

v

v

B

v Bx

+ + + + + + +

B

current I

Current I flows from left to right. In what direction is the force on the wire?

L

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 Bor, (straight wire, uniform B)

The vector length L points along the wire in the direction of the current.

L

ExampleAssume the earth’s 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

0.5 x 10-4 T

A) if the current is flowing NorthB) if the current is flowing East

up

north

Solution