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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

 = mB sin q
U = -mB cos q

 When aligned with the field the
energy is –mB, at right angles to the
field the energy is 0, when opposite
the field the energy is +mB
 Dipoles that are not aligned with the
field will turn until they are
Spin Magnetic Dipole

We can write this as
ms = mB = (eh/4pm) = 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
morb = -mlmB
where mB 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 = -mBext

where potential energy is minimum
Note that the total energy between parallel and
anti-parallel spins is 2 mBext
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)
B)
C)
D)
E)
1 to 1
10 to 1
12 to 1
100 to 1
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)
B)
C)
D)
E)
North
South
East
West
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)
B)
C)
D)
E)
1 Wb
2 Wb
3 Wb
6 Wb
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)
B)
C)
D)
E)
1, 2, 3
3, 2, 1
2, 1, 3
1, 3, 2
All tie