Magnets

PH 203

Professor Lee Carkner

Lecture 26

Magnetic Materials

The moving charges in a magnet are

spinning or orbiting electrons

Problem: The most common and well-known examples of

magnetism result from extremely complex physics

Dipolar Field

No Magnetic Monopoles

Like Repel, Opposites Attract

Dipoles

= B sin U = -B cos

When aligned with the field the energy is –B, at right angles to the field the energy is 0, when opposite the field the energy is +B Dipoles that are not aligned with the

field will turn until they are

Spin Magnetic Dipole

We can write this as

s=B = (eh/4m) = 9.27X10-24 J/T

The electron can feel a torque and has magnetic potential energy just like a normal magnetic dipole

Orbital Magnetic Dipole

The orbital angular momentum is quantized

We can write the orbital magnetic dipole moment as

orb = -mlB

where B is again the Bohr magneton and ml is the orbital magnetic quantum number (0, 1, 2, 3 …)

Magnetic Energy

Like any magnetic dipole (e.g., a loop of current)

U = -Bext

where potential energy is minimum

Note that the total energy between parallel and anti-parallel spins is 2 Bext

Diamagnetism

Net orbital magnetic dipole moment is zero Like a bunch of loops with half with clockwise and half

with counterclockwise currents

Speeds up electrons one way, slows down electrons other way

Almost all materials are diamagnetic, but the net

effect is usually very weak

Paramagnetism

But they are usually randomly aligned and so there is no net magnetic field

An external magnetic field will cause the

atomic dipole moments to try to align Thermal motions of the material try to

randomize the atoms

Curie’s Law

For low temperatures M can be found from Curie’s Law

M = C(Bext/T) Where C is the Curie constant

Strong magnetic fields and low temperatures

produce more paramagnetism

Ferromagnetism

Due to an effect called exchange coupling, the electron spins of nearby atoms align with each other

Appling an external magnetic field can cause these domains to permanently align

The Earth’s Magnetic Field The Earth has a magnetic field produced by the

dynamo effect

We can find the direction of the Earth’s magnetic field with a small bar magnet called a compass

The Earth’s “north magnetic pole” is really a the south pole of a magnet!

Earth as a Magnet

Jupiter’s Magnetosphere

Planets and Magnetism A planet will have a magnetic field if:

It has a conducting liquid interior It has a fast enough rotation

This interaction region is known as the magnetosphere

Next Time

Final exam, Thursday, 9am

To step down 120 household current to 12 volts, we would need a transformer with a ratio of turns between the primary and secondary transformer of,

A) 1 to 1

B) 10 to 1

C) 12 to 1

D) 100 to 1

E) 120 to 1

What is the direction of the magnetic field in the PAL at a point due east of the center of the region?

A) North

B) South

C) East

D) West

E) Up

Consider a standard 6-sided die. Suppose the magnetic flux through each side 1-5 is equal to the number of spots on the side (in Wb) and points outward for even sides and inward for odd. What is the flux magnitude through the side with 6 spots?

A) 1 Wb

B) 2 Wb

C) 3 Wb

D) 6 Wb

E) 9 Wb

Consider 3 Gaussian surfaces. (1) encloses the north pole of a bar magnet, (2) encloses the south pole of a bar magnet, and (3) encloses the entire bar magnet. Rank the surfaces according to the total magnetic flux through them, greatest first.

A) 1, 2, 3

B) 3, 2, 1

C) 2, 1, 3

D) 1, 3, 2

E) All tie