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Statement of a problem № 734

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

Solution:
A point charge q is located in vacuum at a distance l from the plane surface of

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