All Problems

Conductors and Dielectrics in an Electric Field

Problem 3.89

A point charge qq is located in vacuum at a distance ll from the plane surface of a uniform isotropic dielectric filling up all the half-space. The permittivity of the dielectric equals ε\varepsilon. Find: (a) the surface density of the bound charges as a function of distance rr from the point charge qq; analyse the obtained result at l→0l \rightarrow 0; (b) the total bound charge on the surface of the dielectric.

Reveal Answer
3.89 . (a) Since the normal component of the vector DD is continuous at the dielectric interface, we obtain σ′=−ql(ε−1)/2πr3(ε+1),\sigma^{\prime}=-q l(\varepsilon-1) / 2 \pi r^{3}(\varepsilon+1), for l→0l \rightarrow 0 and σ′→0\sigma^{\prime} \rightarrow 0 (b) q′=−q(ε−1)/(ε+1)q^{\prime}=-q(\varepsilon-1) /(\varepsilon+1)
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