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G L Pollack and D R Stump Electromagnetism 1 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 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?)

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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.

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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.

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