M. Fabbrichesi , SISSA

Faraday's law and Conservation laws

Faraday's law of induction is presented in both differential and integral forms. Next, the equation of continuity for the electric charge is discussed as an example of local conservation law. It is then shown how Maxwell had to introduce a new term, the displacement current (∂ E/∂ t) in order to satisfy the charge continuity equation. This term allows Maxwell's equation to produce electromagnetic waves. Next an exercise is proposed: find the current in a rotating circuit in a region of constant magnetic field. The situation of two entangled solenoids is then exploited to introduce the Lenz law ("a manifestation of the energy conservation") and the concept of mutual inductance. The lesson proceeds with conservation of energy and momentum: the Poynting's Theorem [Jackson, sec. 6.7]. The meaining of the Poyinting vector S=E x B is discussed with a few examples (e.g plane capacitor).