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

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 The angular momentum This is a current loop; should have magnetic moment

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

22-3 Diamagnetism and Paramagnetism Molecular magnetic dipole moment the vector sum of magnetic dipole moment of all the electrons in the molecular 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 In the external magnetic field it experiences a torque 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 Orientation magnetization

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

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. Solution the induced electric field clockwise

clockwise From Newton’s 2nd law

22-4 The Magnetization of Bulk Matter 1 Definition of magnetization the net magnetic dipole moment per unit volume of the material Discussion (1) (2) Diamagnetic material Paramagnetic material

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

Consider a cylinder of magnetized homogeneous material. 2 Magnetizing current PM Consider a cylinder of magnetized homogeneous material. 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. 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’ q

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

Permeability of vacuum in the homogeneous medium magnetic susceptibilities Permeability of the material When

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

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 , (1) Find the magnetic field inside the paramagnetic material (2) Find the magnitudes and directions of the magnetizing currents on the surfaces of the paramagnetic material. Solution

On inside surface of the paramagnetic material: On outside surface of the paramagnetic material:

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

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. Heat can decrease magnetization. Above critical temperature “Curie point” (770˚ for iron), magnetization cannot be maintained Magnetization can be removed by sudden physical shock.

2 Magnetic domain The magnetic dipole moments are aligned in some regions due to strong interactions between neighboring dipoles. This region of space is called a magnetic domain. volume contain 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.

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 remains even when the applied field is reduced to zero, this effect is called hysteresis.

initial magnetization curve 3 Hysteresis curve (loop) saturation remanence coercivity initial magnetization curve B measured

Discussion Ferromagnets have no fixed relationship between magnetization and external field. It depends on prior magnetization. (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. 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 ACT Which kind of material would you use in a video tape? in a computer read/write head? (a) diamagnetic (c) “soft” ferromagnetic (b) paramagnetic (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

- The effect vanishes with no applied B field 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 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? Solution The 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

22-6 Magnetism and Superconductivity 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 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. Protons and neutrons have intrinsic magnetic moments ( but are 2000times smaller than that of the electron) The component of intrinsic angular momentum is quantized

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” mpz The potential energy parallel 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 the energy of the absorbed photon Resonance: magnetic field has exact energy to flip the spin of the proton 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 l 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 in the homogeneous medium