Question: A half-space filled with uniform isotropic dielectric with permittivity e has the conducting boundary plane. Inside the dielectric, at a distance l from this plane,

A half-space filled with uniform isotropic dielectric with permittivity e 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.

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