Pre-Quantum Electrodynamics
Induced Chargesems.ca.c.ic
- PM 3.4
- Gr 2.5.2
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.

Created: 2024-02-27 Tue 10:31