Electromagnetism II

Cristina Lazzeronic.lazzeroni@bham.ac.uk

Lecture 5

Maxwell’s equations for free space

They apply simultaneously at any given point in free space.How do they change in presence of material ?

Lecture 4:

Atomic/molecular dipoles

Macroscopic polarization P

Equivalent charge/current

Re-expression of M1 in dielectrics: electric displacement D

LIH:

Relative permittivity Electric susceptibility

Lecture 5: Magnetism (I)

Atomic / molecular magnetic dipoles Macroscopic magnetization MTypes of magnetism and their microscopic origin: diamagnetism paramagnetism ferromagnetism

Why useful ?

TransformersMotorsGenerators

Iron cores

Magnetic recording tapes

Computer disks

All depend directly on magnetic properties of materials

Magnetism

Magnetism is linked to the behaviour of electrons in materials:moving charges, orbital motion and intrinsic spin.

Net magnetic moment of atom is obtained by combining orbital and spin moments of all the electrons, taking into account their direction.

Why isn’t everything magnetic ?

In a sense, everything is magnetic !But material only exhibit “familiar” magnetic effects when: - atoms contain unpaired electrons and- large scale alignment of the dipole moments occur

Orbital motion

Spin :

Magnetic and electric dipoles :

Paramagnetism : Atoms of a paramagnetic material have permanent magneticdipoles. These dipoles are randomly oriented - magnetic fields averageto zero.

In external field B0, dipoles tends to align with B0.Result in an additional magnetic field Bm

N atoms, maximum dipole moment = µNThermal collisions randomize dipole orientation and reducetotal dipole moment.

Paramagnetism :

Relative permeability = ratio between field in material and applied field.If material doesn’t respond to B0, km =1

Magnetic moment per unit volume M (magnetization):

Magnetic susceptibility

Magnetic susceptibility: small, dimensionless number;value depends on temperature, pressure.

Paramagnetic: B > B0 , km > 1 , χB > 0Example: for Oxygen (atmospheric pressure, 20oC)

LIH material Linear : M is proportional to B Isotropic : M is in the same direction as B Homogeneous : same throughout the material

Paramagnetism : very temperature dependent

Glass km = 1 - 1.5 x10-5 Water χB / 10-6 = - 9.0

km<1

Superconductors are an exception χB = -1

Diamagnetism :

Ferromagnetism : Materials with atoms having unpaired electron spins.Electron spins become coupled to form a domain (~1010 atoms, scale of 10-7 m) Large electromagnetic moment

When domains are randomly arranged, material as a wholeis un-magnetised

Ferromagnetism :

km becomes very large: ~103 - 105

Domains which are magnetized in the direction of an appliedexternal field grow at the expenses of those which are not aligned to the magnetic field

Ferromagnetism :

Magnetization curve: M versus B0

Ferromagnetism : Hysteresis loop: BM versus B0

Ferromagnetism :

Ferromagnetism :

Magnetization is different when theexternal field is increasing fromwhen it is decreasing: hysteresis

Cause: reorientations of domaindirections are not totally reversible

Use: magnetic storage of information

Review : Materials can be grouped into para-, dia-, and ferro-magnetic

Diamagnetics: atoms don’t have intrinsic magnetic dipole moment. A dipole moment may be induced by an external field,its direction being opposite to that of the field (Lenz’s law).χB is negative and usually small.

Paramagnetics: atoms have a magnetic dipole moment due tounpaired electrons. Intrinsic magnetic dipole moments tend to line up with external magnetic field thus enhancing (slightly) the field. This tendency is interfered by thermal agitation whichrandomizes the alignment. χB is positive and small and very temperature dependent.

Review : Ferromagnetics: quantum interaction between neighbouringatoms locks atomic dipoles in rigid parallelism despite disordering tendency of thermal agitation (magnetic domains).Due to alignment of spin magnetic moments of electrons(quantum effect).M is no longer proportional to B.Hence χB not well defined, but generally positive and large.

Hysteresis: ferromagnetic magnetization curves do not retracethemselves. Some alignment of dipoles remain even whenthe external field if removed. Familiar “permanent” magnets.

Summary :

Effect χB km Origin

Recommended readings:Grant+Phillips: 4.3, 5.1, 5.2

Next Lecture: Magnetism (II)

Maxwell’s equations for magnetic materials