Self-induction and inductance

A circuit carrying a current generates a magnetic field of its own, and hence a flux through itself. If the current varies, this flux varies too and, by Faraday’s law, an EMF arises that opposes the change. This is the phenomenon of self-induction.

Principle — Inductance of a circuit

For every circuit the linear relation between self-linked flux and current holds: $\ev{\Phi_B^\text{self} = L\cdot i}$ where $L$ is the circuit’s inductance, measured in henries (H).

The crucial point is that $L$ depends only on the geometry of the circuit (number of turns, shape, dimensions, core material), not on the instantaneous value of $i$. It is a characteristic constant of the circuit, exactly as the capacitance $C$ is for a capacitor.

The parallel with the capacitor is illuminating: inductance is to a solenoid what capacitance is to a capacitor. On one hand $C = Q/\Delta V$ links charge and voltage; on the other $L = \Phi_B/i$ links flux and current. These are the two geometric quantities that govern, respectively, the storage of electric energy and of magnetic energy.

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Topics: Electromagnetic induction Concepts: Inductance and self-induction · Magnetic flux

Related exercises: Problem — The electric guitar · Problem — Energy in a solenoid’s field · Problem — Ranking the EMF of four square loops