Electromagnetism PHYS20141

Paul.Campbell-3@manchester.ac.uk

Schuster 4-11

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Week 8

- Inductance

- Relative permeability

- Magnetization & magnetic susceptibility

- Mechanisms for magnetization

- diamagnetism

Inductance

- Consider a solenoid

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Magnetic dipoles

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Magnetic susceptibility

� χB < 0 – Diamagnetism - equivalent to induced polarization

� χB > 0 – Paramagnetism- equivalent to intrinsic polarization

NB we will also consider the possibility of a non linear

response M(B) in ferromagnets

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Magnetic susceptibilities

� Glass -1.1 x 10-4

� Gold -3.6 x 10-5

� Copper -9.8 x 10-6

� Water -9.1 x 10-6

� Magnesium 1.2 x 10-3

� Aluminium 2.3 x 10-3

� Tungsten 6.8 x 10-3

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Diamagnetic

Paramagnetic

Electron in orbit = current

Consider an electron orbiting around a nucleus –

motion of electrons = current in opposite direction

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e-

v

L

m

Area, A = πr2 r

Switch on an external field

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e-

v

L

m

Bext

FORCE = -ev x B

FORCE = qE

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As per dielectrics…

- Mechanisms for magnetization- Paramagnetism

- Bound current & surface current

- Magnetostatic equations in magnet

- Interfaces between magnets

Paramagnetism

� Consider a material with intrinsic

magnetic dipoles

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Paramagnetism

� Alignment of intrinsic magnetic dipoles

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Diamagnetism &

paramagnetism

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Increases field

inside the magnet

Decreases field

inside the magnet

Magnetostatics in a magnet

In dielectrics there is a bound charge density ρbound and a surface charge σP.

In a magnet there is a equivalent bound current density

and surface current (see Grant and Phillips for

derivation Pgs 181-187)

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Bound & surface current

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Return to the solenoid

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B⊥ is continuous

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H// is continuous

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