##### Induced Charges
ems.es.c.ic

Charge in hollow conductor. Induced surface charges on inside and outside surfaces.

Field outside spherical conductor with irregular cavity

Consider a spherical conductor centered at the origin, and having an irregularly-shaped cavity containing a point charge \(q\) somewhere inside. What is the field outside the sphere?

Answer:

\[ {\bf E} = \frac{1}{4\pi\varepsilon_0} q \frac{\hat{\bf r}}{r^2}. \]

Namely, the internal surface completely screens the point charge, leaving the field to be exactly zero (as it should) within the conductor (that's the idea behind a Faraday cage). By charge conservation, the conductor remains neutral, so a charge \(q\) distributes itself uniformly over its external surface.

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Author: Jean-Sébastien Caux

Created: 2022-03-24 Thu 08:42