§5.2: Formulations of Magnetostatics Christopher Crawford PHY 417 2014-01-23

Outline Ampère’s law Pseudo-derivation / application – straight wire Example – current sheet septum Example – infinite solenoid 5 formulations of Magnetostatics Review – electrostatics FLUX FLOW Vector potential A Divergence and curl of B Integrals – flux and flow

Ampère’s law on a straight wire Andre Marie Ampère shows that parallel currents attract and antiparallel currents repel Integral field equation – Ampère’s law Differential field equation – also Ampère’s law

Example 5.8: current septum Similar to Ch. 2: plane charge

Example 5.9: infinite solenoid

5 Formulations of Magnetostatics Electrostatics Magnetostatics

Magnetic vector potential A Derivation A from Biot-Savart law Divergence of A

Div. and curl of B Divergence – Gauss-like law Curl – vector Poisson equation –> Ampère’s law