ch32 dia para_ferro_magnetism

Rogers: Lectures based on Halliday, Resnick and Walker’s Fundamentals of Physics, Copyright 2005 by Wiley and Sons

Material, including many figures, is used with permission of John Wiley and Sons, Inc.Material is not to be further distributed in any format and is subject to Copyright Protection. 1

Ch32-1/14

Ch 32: Dia_para_ferro Magnetismsections 8-11

Magnetism in materials is essentially a quantum mechanical effect.

Intrinsic quality of electrons: spin angular momentum (or spin) - linked to it’s intrinsic spin dipole moment (intrinsic in same sense as its charge).

In an atom, electrons also have orbital angular momentum - has an associated orbital magnetic dipole moment.

Only component along any axis of both of these angular momentacan be measured - they are quantized (i.e. can only have certain discrete values).

Magnetic properties of materials are understood in terms of these fundamental properties of electrons in materials

Ch32-2/14

Orbital and spin magnetic dipole moments of electrons in an atom add vectorially

-those of atoms add vectorially in a material.

Any resultant magnetic dipole moment for a material => magnetic field and material is magnetic. A magnetic dipole moment produces a magnetic field:

(skipped in section 29-6)

Diamagnetism: weak magnetic dipoles are produced in an external magnetic field -they are aligned but disappear when Bext does.

Paramagnetism: Bext will aligns permanent magnetic dipoles of each atom but disappear when Bext does.

Ferromagnetism: regions of permanent magnetic dipoles are aligned initially - Bext aligns regions -alignment and resultant field partially remain when Bext is removed.

Magnetic materials



Ch32-3/14

DiamagnetismWeak magnetic dipoles are produced in an external magnetic field. They are aligned but disappear when Bext does.

Applies to most common materials.

In absence of Bext each atom has no net dipole moment since number of electrons orbiting in one direction is same as in other direction.

A diverging non-uniform magnetic field -net effect is to produce a magnetic force away from strong part of field.

A diamagnetic material placed in Bext develops a magnetic dipole moment directed opposite Bext . If field is non-uniform, diamagnetic material is repelled from region of greater magnetic field.

One can levitate a frog above a strong solenoid!

Ch32-4/14

Question

Two diamagnetic spheres are near S pole of magnet. Are

(a) magnetic forces on spheres and

(b) magnetic dipole moments of spheres directed towards or away from the bar magnet?

(c) Is magnetic force on 1 >, =, or < force on 2?



Ch32-5/14

Question

Two diamagnetic spheres are near S pole of magnet. Are (a) magnetic forces on spheres and (b) magnetic dipole moments of spheres directed towards or away from the bar magnet? (c) Is magnetic force on 1 >, =, or < force on 2?

Ans (a): force is away since the field is strongest at pole face

Ans (b): the magnetic dipole moment is directed opposite to the external field. The external field goes into the S pole faceso the magnetic dipole is directed to the left.

Ans (c): external field is weaker at 1 => force is weaker there.

Ch32-6/14

Paramagnetism

Common for materials containing transition elements, rare earths and actinides (appendix G). Each atom has a net permanent magnetic dipole moment but they are randomly oriented if no Bext . In a magnetic field they tend to become lined up which leaves the sample with a net magnetic dipole moment and hence generates a magnetic field.

Thermal motion has a much higher energy than the potential gained from alignment => far from perfect alignment.

Magnetization M has direction of net magnetic dipole and magnitude is measured magnetic moment/volume (A m2/ m3 = A/m). Maximum magnetization is Nµ/V where N is # atoms in sample

Paramagnetic material in Bext develops a magnetic dipole moment in direction of Bext and is attracted towards

region of greater Bext if Bext is non-uniform



Ch32-7/14

ParamagnetismCurie’s Law

Pierre Curie (winner of one Nobel Prize, husband of Marie Curie who won two and father of a daughter who also won a Nobel Prize) noted that magnetization increased with Bext and decreased with increasing temperature.

Magnetization curve for potassium chromium sulfate. Curie’s Law is only an approximation

Ch32-8/14

Question

Two paramagnetic spheres near S end of a bar magnet. Are (a) magnetic forces on spheres and (b) magnetic dipole moments of spheres directed towards or away from magnet?

(c) Is magnetic force greater on 1 or 2?



Ch32-9/14

Question

Two paramagnetic spheres near S end of a bar magnet. Are (a) magnetic forces on spheres and (b) magnetic dipole moments of spheres directed towards or away from magnet?

(c) Is magnetic force greater on 1 or 2?

Ans (a): paramagnetic => force towards stronger magnetic field => to rightAns (b): paramagnetic => magnetic dipole aligned with magnetic field. S pole => field into pole => magnetic dipole aligned to right.

Ans (c): Field stronger at 2 => force stronger at 2.

Ch32-10/14

Ferromagnetism

Ferromagnetic materials are what we commonly think of as magnetic.

In these materials there is a coupling between neighbouring atoms to align the magnetic dipoles. This exchange coupling exists even in the absence of Bext .

Above the Curie temperature, exchange coupling breaks down and the materials become paramagnetic in nature. For iron, this temperature is 1043 K (770oC).



Ch32-11/14

Ferromagnetism (cont)Rowland ring

Rowland ring: a circular toroidal core of circular cross section -used to study properties of materials. A primary coil P of n turns/m is wrapped around core and carries current ip.

Coil is essentially a long solenoid bent into a circle.

With no iron core present the magnetic field inside coil would be

However, with iron in place magnetic field is usually larger by a large amount.

BM is magnetic field from iron core.

Ch32-12/14

Ferromagnetism (cont)Rowland ring

The secondary coil can be used to measure magnetic field through it, => BM is measured after subtracting known Bo .

Magnetization curve shows -even fairly weak field induces 60% of maximum possible, -getting to maximum requires a very strong Bo (about 1 T).



Ch32-13/14

Ferromagnetism (cont)Magnetic domains

Why isn’t all iron a strong magnet naturally?

Crystal structure breaks material into individual domains which are aligned internally, but not overall.

Further, `real’ iron is polycrystalline, i.e. many small crystals randomly oriented.

A ferromagnetic material placed in Bext develops a strong magnetic dipole moment in direction of Bext by aligning domains. In a non-uniform field it will be attracted towards region of greatest magnetic field.

Ch32-14/14

Ferromagnetism (cont)Hysteresis

Magnetization curves for ferromagnetic materials do not retrace themselves as the external field is reversed.

Start at (a) with unmagnetized iron. Increase the current and we get to (b) with Bo, BM . As the current and hence Bois reduced to 0, induced magnetization is still present (c).

As Bo is reversed BM eventually becomes 0 and becomes reversed at (d) etc etc.

This lack of retraceability is called hysteresis and bcdebis called a hysteresis loop.

Points e and c => permanent magnetism.

The magnetic domains have a memory.

ch32 dia para_ferro_magnetism

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