G L Pollack and D R Stump Electromagnetism Electromagnetic Induction Faraday’s law If a magnetic field changes in time there is an induced electric field. In differential form, the field equation is which is called Faraday’s Law. In integral form, where  is the magnetic flux through any surface with boundary curve C. (Why are the two equations equivalent?)

G L Pollack and D R Stump Electromagnetism 2 Lenz’s law The direction of the induced electric field in electromagnetic induction opposes the change of magnetic flux; i.e., if a conductor is present then the induced current produces a magnetic field in the direction tending to maintain the flux. Self-inductance A current I in a conducting loop creates a magnetic field. The flux through the loop is proportional to the current,  = LI. The constant of proportionality L is the self- inductance, which depends on the geometry of the loop. If I changes in time there is an induced emf around the loop, which is by Faraday’s law. 

G L Pollack and D R Stump Electromagnetism 3 Exercises Show that an LC circuit is an oscillator. Show that the energy in an inductor is. Show that the energy density of the magnetic field is.