Write the equation for the force between 2 charges when they are placed in any medium other than air
Answers
Answer:
The simplest situation, with both the media having no free charge particles and neutral, will leave out the simplest approach to consider the effective lengths \sqrt{\varepsilon_{1,2}}r_{1,2} in each media, where r_{1,2} is the portion of the straight distance lying in media 1 or 2, and \varepsilon_{1,2} being respective medium permittivities. Then just add them up to have the effective total distance between the two charges, r_{\rm eff}.
The physics behind is that for the Coulomb force, any charge-neutral medium acts effectively as a scaling mechanism to the distance, by introducing the permittivity different from that of the vacuum.
On the other hand, if there are free charges in the medium(s), they will get polarized by getting organized in reaction to the primary charges. Depending that particular composition, the Coulomb force may vary, or can even vanish, if the naive separation r is large enough (example: Debye length in plasma). As a demonstration, if free charges of both kinds are present (neutral mediums), they will try accumulating near the respective attracting one (q_1 or q_2), and away from the opposite, finally being arranged according to the shape/size of the respective media. They will exert respective forces on both q_{1,2}, in addition to the force above. So, the net force (due to q_{1,2} on q_{2,1}) will be different. However, the lower bound of that force is zero as, the medium polarization cannot exceed the energy of the electrostatic fields due to both q_{1,2}.
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