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# ind - Physics 54 Inductance and Oscillations Everything is...

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Physics 54 Inductance and Oscillations Everything is moving ahead on schedule, right over the cliff. — Henry Kissinger Magnetic energy and inductance In the same way that a capacitor stores energy in the E-field, a device that creates a B- field when a current passes through it can store energy in the B-field. Such a device is usually called an inductor . A solenoid provides a simple example. We consider a solenoid of cross-section area A and n turns per unit length carrying current I . We are interested in the work done as the current builds up to its final value. This work represents the energy put into (and stored in) the magnetic field of the solenoid. At any instant, the magnetic flux through one turn of the solenoid is Φ m = BA . The emf induced in this turn is, by the flux rule, E 1 = A dB / dt . A length d of the solenoid contains nd turns in series, which act like batteries in series, so their emf’s add. The total emf induced in this length is E = nAd dB / dt . Since the B-field magnitude is given by B = μ 0 nI it follows that the total emf in length d of the solenoid is E = μ 0 n 2 Ad dI dt . This formula shows that the emf is (minus) a geometric constant times the rate of change of the current. The geometric constant is called the self-inductance: Self inductance The induced emf in an element due to a changing current through the element is given by E = L dI dt , where L is the self inductance of the element.

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ind - Physics 54 Inductance and Oscillations Everything is...

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