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I I B B 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. Magnetic field from current loop 0.9 2a x 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 z 2a dBz dB cos dBx dB sin z x components cancel dB dB r2 a2 z2 cos r r z z >> a a z r a x B right hand screw rule magnetic dipole moment m miA At a point along the axis i current loop in xy-plane Bz z >> a 0 iA 2 z 3 B Diamagnetic material m < 0 (small) B = o (1+ m ) H H Permeability = o (1+ m ) =slope of B-H line B Ideal magnetic material or paramagnetic material m > 0 (small) B = o r H = H = constant = slope of B-H curve 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: Br = “remanence” or “residual magnetism” Hc = “coercivity” L11.7 Magnetization “hard” magnetic materials: Hc is high, area of the loop is large, used for permanent magnets. “soft” magnetic materials: Hc 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 Example: Ampere’s law 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: (I, A0) This magnetic field has the same shape as the electric field of an electric dipole: do the exercise in the Exercise Set. Y X + Z + + + + + + - - - w I - - - B - - - - t charge carriers are electrons for copper Right hand rule electrons are deflected down bottom of probe is negative Y X Z w I t B Hysteresis Curve for an Iron sample Saturation of M 2.0 1.5 retentivity (remanence) 1.0 MH B (T) 0.5 0.0 coercivity -0.5 -1.0 retentivity (remanence) -1.5 -2.0 of M Saturation -100 -50 0 H 50 100 -1 (A.m ) Area enclosed = energy dissipated in a cycle in reversing the magnetic domains H G I E D A L K I J F C B