I I

Magnetic field similar to a bar magnet For a very long solenoid, the magnetic field can be considered to be confined to the region inside the coils.

2a2a z x 2a2a

x z a z r  x components cancel z >> a  a r

i At a point along the axis z >> a current loop in xy-plane magnetic dipole moment right hand screw rule

H B Diamagnetic material  m < 0 (small) B =  o (1+  m ) H Permeability  =  o (1+  m ) =slope of B-H line

Ideal magnetic material or paramagnetic material  m > 0 (small) B =  o  r H =  H  = constant = slope of B-H curve B H

L11.5 : Magnetization If H is large or substance strongly magnetic (e.g. ferromagnetic), as H increases, the magnetization M (and hence B) may increase nonlinearly: Measure from the graph So  r varies with H. Could also use “differential permeability” High field region where slope decreases is called "saturation" region.

L11.6 : Magnetization Hysteresis Ferromagnetic materials also show a “hysteresis” effect, where decreasing the applied magnetic field, or H, doesn’t produce the reverse effect of increasing the field: B r = “remanence” or “residual magnetism” H c = “coercivity”

L11.7 Magnetization “hard” magnetic materials: H c is high, area of the loop is large, used for permanent magnets. “soft” magnetic materials: H c is small, area of loop is small, used for transformer cores & electromagnets. Material can be demagnetized by striking or heating it, or go round the hysteresis loop, gradually reducing its size. "Degaussing"

L9.1 : Magnetic fields due to currents Magnetic fields are produced by currents. Biot-Savart law Ampere’s law Example: so

L9.2 : Magnetic fields due to currents A solenoid: (n is number of turns/length) Therefore(inside)

L9.3 : Magnetic fields due to currents Use the Biot-Savart law to derive the magnetic field on the axis of a current loop: and Therefore

L9.4 : Magnetic fields due to currents Magnetic field of the Earth

L9.5 Magnetic fields due to currents The magnetic field of a magnetic dipole: This magnetic field has the same shape as the electric field of an electric dipole: do the exercise in the Exercise Set. (I  , A  0)

w t I B charge carriers are electrons for copper Right hand rule  electrons are deflected down  bottom of probe is negative Z X Y

w t I B Z X Y

M  HM  H Saturation of M coercivity retentivity (remanence) Saturation of M Area enclosed = energy dissipated in a cycle in reversing the magnetic domains

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