Faraday’s Law: Generalized A loop moving in a field has a current induced (Think F=qvB) If the loop is stationary, and the magnet moves, a current is still created! Why? Charges in the loop “see” a changing magnetic field, and this creates an electric field. This electric field moves the charges and causes the current.

Alternate View of Faraday’s Law Changes in magnetic flux induce an e-field in the conductor. This e-field exerts a force on the free electrons, pushing the charges around. F=qE Recall –emf is the work per unit charge  =W/q=d  /dt –and that work = Fl where l is some arbitrary path length Therefore, around any closed path of length l

Exercise: A loop of wire surrounds an ideal solenoid Solenoid has 15,000 turns/meter and a radius of 2cm. The wire loop has a radius of 4cm. The current in the solenoid is increased at a rate of 10A/s What is the magnitude of the induced e-field at each position along the wire?

From Faraday’s Law (Absolute values b/c only care about magnitude) Since solenoid is ideal, B-field exists only inside it. Therefore, flux through the wire is

Therefore,