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Transcript
10. 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 B E t which is called Faraday’s Law. In integral form, d CE d l dt 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 1 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 selfinductance, 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 L dI dt . G L Pollack and D R Stump Electromagnetism 2 Exercises • Show that an LC circuit is an oscillator. • Show that the energy in an inductor is U 12 LI 2 . • Show that the energy density of the magnetic field is umag B 2 20 . G L Pollack and D R Stump Electromagnetism 3
