5 - Time-dependent fields: Faraday's law and Maxwell's equations

Summary

Oersted's discovery of the magnetic effect of currents not only stimulated renewed interest in electricity and magnetism, but also led to the development of sensitive instruments which used the deflection of magnets to measure currents; a simple galvanometer was devised by Schweigger in 1820, and the more sensitive astatic galvanometer by Nobili in 1825. Previously, electric currents could only be detected by the observation of sparks, or by their chemical effects in electrolysis. The latter method was quantitative, but not well suited to the detection of small currents. The use of the galvanometer was important in the experimental work of Faraday at the Royal Institution in London, where in 1831–2 he carried out a now famous series of experiments on the induction of electric currents by magnetic fields.

Faraday found that a current was induced to flow round a closed conducting circuit when a nearby magnet was moved, or the current in a nearby circuit was changed, or when the circuit was moved in a fixed magnetic field. In all these cases he established that the induced current was proportional to the rate of change of magnetic flux through the circuit.

Faraday's law of induction

The current flow that Faraday observed when a coil of wire was moving in a static magnetic field B(r) can be understood in terms of effects we have already discussed.