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Conductors and Dielectrics in an Electric Field

Problem 3.92

A small conducting ball carrying a charge \(q\) is located in a uniform isotropic dielectric with permittivity \(\varepsilon\) at a distance \(l\) from an infinite boundary plane between the dielectric and vacuum. Find the surface density of the bound charges on the boundary plane as a function of distance \(r\) from the ball. Analyse the obtained result for \(l \rightarrow 0\).

Reveal Answer
 3.92. σ′=ql(ε−1)/2πr3ε(ε+1); for l→0 and σ′→0\text { 3.92. } \sigma^{\prime}=q l(\varepsilon-1) / 2 \pi r^{3} \varepsilon(\varepsilon+1) ; \text { for } l \rightarrow 0 \text { and } \sigma^{\prime} \rightarrow 0
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