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I have the problem given in Irodov stated as follows

  • Two positive charges $q_1$ and $q_2$ are placed a distance $r$ apart in air, now a dielectric slab of thickness $t$ $(t\lt r)$ with relative permittivity $k$. Find the force of electrostatic interaction between the two charges.

My question is what effect does the dielectric have on the field outside the dielectric medium.

The answer which I had been directed to just states the dielectric behaves as though it's thickness was t√k, but there is no mathematical proof for that. Hence, I request for a proper mathematical proof for the effect.

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