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13.4 Inductance

Part of Electromagnetic Induction in AP® Physics C: Electricity and Magnetism. Read the opening section, then create a free account for the full interactive lesson, practice, and progress tracking.

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A changing current in a circuit produces a changing magnetic field, and that changing magnetic field can induce an emf in the same circuit. This is called self-induction. The constant that relates the induced emf to the rate of change of current is the inductance L:

\mathcal{E}_L = -L\frac{dI}{dt}

The minus sign again reflects Lenz’s law. An inductor resists changes in current, not current itself. A large inductance means even a modest rate of current change can produce a significant induced emf.

An inductor also stores energy in its magnetic field. The energy stored is

U_B = \frac{1}{2}LI^2

This can be derived from power. The instantaneous power into the inductor is

P = I\mathcal{E} = IL\frac{dI}{dt}

P = \frac{dU}{dt} = LI\frac{dI}{dt}

which gives

dU = LI\,dI

Integrating from 0 to I:

U = \int_0^I LI' \, dI' = \frac{1}{2}LI^2

So an inductor is the magnetic analogue of a capacitor, which stores electric-field energy.

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