Chapter 22 Magnetism and Matter

Main Points

• Magnetic Properties of Bulk Matter

• Atomic Magnetic Dipole Moments

• Diamagnetism and Paramagnetism

• The Magnetization of Bulk Matter

magnetic field in materials

• Ferromagnetism

• Magnetism and Superconductivity

• Nuclear Magnetic Resonance

22-1 The Magnetic Properties of Bulk Matter

• An insulator in an electric field

Dielectric constant

• A magnetic material in an magnetic field

—— Relative Permeability

Experiment result

ro

I

N ro

I

N

Materials can be classified by how they respond to an applied magnetic field B0

(slightly less than 1)

• Diamagnetic material (gold, copper, water,…)

(slightly greater than 1)

• Paramagnetic material (aluminum, tungsten, oxygen,…)

• Ferromagnetic material (iron, cobalt, nickel,…)

• Superconductor

22-2 Atoms as Magnets

• Classical view of the atom: electron in orbit around nucleus

This is a current loop; should have magnetic moment

The angular momentum

Gyromagnetic ratio• Quantum mechanics shows the atomic angular momentum is quantized. Its component in a particular direction is always an integer multiple of h/2.

Bohr magneton

• An electron has an intrinsic angular momentum called its spin angular momentum (or just spin)   ; associated with this spin is an intrinsic spin magnetic dipole moment

The component of intrinsic angular momentum is quantized

the vector sum of magnetic dipole moment of all the electrons in the molecular

iimm

Molecular magnetic dipole moment

22-3 Diamagnetism and Paramagnetism

Diamagnetic material : Their atoms have no permanent magnetic dipole moments, either orbital or intrinsic

Paramagnetic material : These materials contain molecules with permanent magnetic dipole moments due to the intrinsic magnetic moments of unpaired electrons.

1 Diamagnetism

We can provide a classical explanation

A diamagnetic material placed in an external magnetic field develops a magnetic dipole moment directed opposite ,so producing an additional field which is opposite to the external field. Induced magnetization

2 Paramagnetism

These dipoles are randomly oriented due to thermal motion

The permanent atomic magnetic moments tend to line up , producing a field that is parallel to the direction of the external field. But thermal motion randomizes their directions, so only a small effect persists 0B

'B

In the external magnetic field

it experiences a torque

Orientation magnetization

• Diamagnetism is present in all materials, although it is masked for materials whose atoms have permanent magnetic dipole moments.

• Two effects determine the extent to which the permanent magnetic dipole s become aligned.

The external field and the temperature

The average alignment will be strong

The average alignment will be weak

Example An electron under the influence of some central force moves at speed vi in a counterclockwise circular orbit of radius R. A uniform magnetic field perpendicular to the plane of the orbit is turned on. Suppose that the magnitude of the field changes at a given rate dB/dt. Show that the change in the magnetic moment of the electron’s orbit is opposite the direction of change in the external field.

the induced electric field

clockwise

Solution

clockwise

From Newton’s 2nd law

22-4 The Magnetization of Bulk Matter

1 Definition of magnetization

V

mM

the net magnetic dipole moment p

er unit volume of the material

Discussion

(1)

(2) Diamagnetic material

Paramagnetic material

Diamagnetic substances are repelled by one pole of a nearby bar magnet.

Paramagnetic substances are attracted to one pole of a nearby bar magnet.

Liquid oxygen is suspended between the two pole faces of a magnet because the liquid is paramagnetic and is magnetically attracted to the magnet

ACT The figure shows two diamagnetic spheres located near the south pole of a bar magnet. Are (a) the magnetic forces on the spheres and (b) the magnetic dipole moments of the spheres directed toward or away from the bar magnet? (c) Is the magnetic force on sphere 1 greater than, less than, or equal to that on sphere 2?

(a) away

(b) away

(c) less

0B

Consider a cylinder of magnetized homogeneous material.

PM

0I

0I

I'

Because of cancellation of neighboring current loops, the net current at any point inside the material is zero, leaving a net current on the surface of the material.

2 Magnetizing current

This surface current I’, called a magnetizing current, is similar to the real current in the windings of the solenoid.

3 The relationship between and i’ SS

M

ne

M

magnetic material

vacuum

4 Gauss’ law in magnetic materials

In magnetic materials, the magnetic field lines also form closed curves. For a closed surface,

5 Ampere’s law in magnetic materials

Magnetic Intensity

magnetic susceptibilities

Permeability of the material

When

in the homogeneous medium

Permeability of vacuum

Small, negative

Small, positive

Large, positive

Using Ampere’s law to find the magnetic field

Ampere's Law can simplify the calculation if there is symmetry of the current! (and the magnetic material )

in the homogeneous medium

Example Find the magnetic field of a long ideal solenoid carrying a current i (per length) with a core of some material.

Solution

check

(2) Find the magnitudes and directions of the magnetizing currents on the surfaces of the paramagnetic material.

Solution

(1) Find the magnetic field inside the paramagnetic material

r

2R

1R

I

r

H

Example A long, straight wire with a radius of and carrying a current of I is coated with paramagnetic material that has a radius of ,

1R

2R

On inside surface of the paramagnetic material:

On outside surface of the paramagnetic material:

r

2R

1R

I

H

'1i

'2i

Example Find the magnetic field of an infinite sheet of current inside the diamagnetic material. The current per unit length (along the direction which is perpendicular to the current) is i .

Solution i

B

P ab

c d B

How about that the material up and under the sheet are different? Find

Pab

c d

B

B

Opposite to i

6 Curie’s Law

For Paramagnetic material

22-5 Ferromagnetism

1 Magnetic properties

• Ferromagnetic material can produce a very strong contribution to the magnetic field.

• The magnetization can persist even when the external field is removed, thus leading to permanent magnetism.

• Magnetization can be removed by sudden physical shock.

• Heat can decrease magnetization. Above critical temperature “Curie point” (770˚ for iron), magnetization cannot be maintained

2 Magnetic domain

The magnetic dipole moments

are aligned in some regions due

to strong interactions between

neighboring dipoles.

When the material is un-magnetized, the direction of alignment in one domain is independent of that in another so that no net magnetic field is produced.

This region of space is called a magnetic domain.

containvolume

When an external magnetic field is applied, the boundaries of the domains may shift or the direction of alignment within a domain may change so that there is a net macroscopic magnetic moment in the direction of the applied field.

Some magnetization remain

s even when the applied field

is reduced to zero, this effect

is called hysteresis.

3 Hysteresis curve (loop)

ab

c

d e

f H

B

o

B measured

saturation

remanence

coercivity

initial magnetization curve

Discussion

(2) At temperatures above a critical temperature,

called the Curie temperature, thermal agitation

is great enough to break up the alignment, and

ferromagnetic materials become paramagnetic.

(1) Ferromagnets have no fixed relationship between magnetization and external field. It depends on prior magnetization.

Demo: Curie temperature for Ni

(3) Applications of ferromagnetic materials.

Soft magnetic materials (e.g. iron) have a low coercivity

Easy to be magnetized and demagnetized

Used for transformer cores

Hard magnetic materials (e.g. steel) have a high coercivity

Difficult to be demagnetized

Used for permanent magnets, magnetic tapes or memory disks

ACT Which kind of material would you use in a video tape? in a computer read/write head?

(a) diamagnetic

(b) paramagnetic

(c) “soft” ferromagnetic

(d) “hard” ferromagnetic

A video tape requires a stable permanent magnetic field

A computer read/write head needs a variable magnetic field that can be quickly adjusted

ACT How does a magnet attract screws, paper clips, refrigerators, etc., when they are not “magnetic”?

The materials are all “soft” ferromagnets. The external field temporarily aligns the domains so there is a net dipole, which is then attracted to the bar magnet.

- The effect vanishes with no applied B field- It does not matter which pole is used.

S N

Example A current of 0.5 A flows through a solenoid with 400 turns/m. An iron bar, with is placed along the solenoid axis. (a) What is the magnetic field inside the iron bar? (b) Outside the iron bar, but still within the solenoid?

SolutionThe magnetic intensity inside the solenoid

(a) the magnetic field inside the iron bar

(b) the magnetic field outside the iron bar, but still within the solenoid

Superconductors were invented in 1911 by Dutch physicist, H. Kammerlingh Onnes. When superconductors are cooled at a critical temperature, they act as a perfect conductors with no resistance.

By 1933, W. Meissner and R. Ochsenfeld discovered that superconductors are perfect diamagnets – internal magnetic field exactly cancels external one– Meissner effect

22-6 Magnetism and Superconductivity

Above critical field, superconductivity is destroyed

A Type I superconductor expels magnetic field from its interior by acting as a perfect diamagnet

A Type II superconductor. the magnetic field is confined to filamentary structure.

22-7 Nuclear Magnetic Resonance

Atomic nuclei consist of protons and neutrons.

The component of intrinsic angular momentum is quantized

Protons and neutrons have intrinsic magnetic moments ( but are 2000times smaller than that of the electron)

In magnetic field, the proton experiences a torque

The axis of rotation will precess about the direction of the magnetic field---Larmor precession

Derivation of processional motion

Suppose

Quantum mechanics: only two states are allowed One with spin “up” and one with spin “down”

The potential energy mpz

mpz

mpzparallel to mpz

lower energy state

antiparallel to mpz

higher energy state

When the frequency of the oscillating magnetic field exactly matches the frequency of the precession, the resonance occurs

Resonance: magnetic field has exact energy to flip the spin of the proton

the energy of the absorbed photon

Once a proton is spin-flipped to the higher energy state, it can drop back to the lower energy state by emitting a photon of the same energy hf

NMR (Nuclear Magnetic Resonance)

to measure the Gyromagnetic ratio

to study the material because of the frequency of resonance varying with material

MRI (Magnetic Resonance imaging)

Example A drop of water is suspended in a magnetic field of magnitude 1.80 T and an alternating electromagnetic field is applied, its frequency adjusted to produce spin flips of the protons in the water. The component mz of

the magnetic dipole moment of a proton, measured along the direction of   . What are the frequency f and wavelength of the alternating field?

Solution

Summary

•Diamagnets have reduced internal fields (zero, in the case of superconductors)

• Paramagnets have slightly increased magnetic fields

•Ferromagnets can have permanent magnetic fields

• Magnetic field in material comes from external field and from magnetization

V

mM

in the homogeneous medium