Consider two solid dielectric spheres of radius a, separated by a distance R(R >>a). One of the spheres has a charge q, and the other is neutral (see figure.) We double the distance between two sphere. How much charge should reside on the first sphere now so that the force between the spheres remains the same?
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Sol. The charged sphere will polarize the neutral one, which acquires a dipole moment p proportional to the electric field created by the charged sphere
p ∝ E ∝ 
The force between the dipole and the charged sphere is given by the product of the dipole moment and the gradient of the electric field at the dipole.
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