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Conductors and Dielectrics in an Electric Field

Problem 3.93

A half-space filled with uniform isotropic dielectric with permittivity \(\varepsilon\) has the conducting boundary plane. Inside the dielectric, at a distance \(l\) from this plane, there is a small metal ball possessing a charge \(q .\) Find the surface density of the bound charges at the boundary plane as a function of distance \(r\) from the ball.

Reveal Answer
 3.93. σ′=ql(ε−1)/2πr3ε . \text { 3.93. } \sigma^{\prime}=q l(\varepsilon-1) / 2 \pi r^{3} \varepsilon \text { . }
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