Field inside a conductor

Problem

Conceptual: field lines inside a conductor. Explain in five lines why, under static conditions, the electric field inside a conductor is zero. What would happen if, for an instant, it were not?

Solution

Why the internal field is zero. A conductor contains free charges (conduction electrons) that can move without friction. If at an interior point an electric field $\vec E \neq 0$ existed, it would exert a force $\vec F = q\vec E$ on the free charges, setting them in motion. But under static conditions, by definition, nothing is moving. The only situation compatible with equilibrium is therefore $\ev{\vec E_\text{int} = 0}.$

The self-cancellation mechanism. Suppose that for an instant the internal field is not zero. The free charges react immediately: they move under the action of the force, accumulating on the surface of the conductor (positive on one side, negative on the other). This redistribution creates an induced field that opposes the applied one. The process continues — on timescales of order $10^{-19}$ s for a good conductor — until the induced field exactly cancels the external one at every interior point, restoring $\vec E_\text{int} = 0$.

Consequences. At equilibrium all the net charge sits on the outer surface; the field just outside is perpendicular to the surface; and the entire volume of the conductor is a single equipotential region. This is the same principle that makes a car or a metal cage an electrostatic shield.

Connections

Topics: Electric field and potential Concepts: Conductors in electrostatic equilibrium · Electric field Skills: Applying Gauss’s theorem Methods: Gauss’s theorem Objects: Charged sphere