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Here is an interesting problem which I have been trying to solve. For convienience of discussion, I have broken it into parts to show where I get stuck:

Two charges [itex]Q_{1}[/itex] and [itex]Q_{2}[/itex] are kept in space at a distance r from each other in a medium of dielectric constant K. The force between them is given by

[tex]F = \frac{1}{4\pi\epsilon_{0}K}\frac{Q_{1}Q_{2}}{r^2}[/tex]

Problem #1: Now if instead of the original dielectric medium we have a slab of dielectric constant K and width r/2 placed somewhere between the two charges, then find the force betwen the two charges (this is not homework so I guess its in the right place).

Problem #2 (This is what I could not do): The space between the two charges (i.e. r) is filled with two dielectric slabs of thickness [itex]d_{1}[/itex] and [itex]d_{2}[/itex] and dielectric constants [itex]K_{1}[/itex] and [itex]K_{2}[/itex] such that [itex]d_{1}+d_{2} = d[/itex].

My reasoning (so far) for the first problem: If two charges are kept at a distance r in a medium of dielectric constant K then they must be kept in air at a separation = [itex]r\sqrt{K}[/itex] in air to keep the force of interaction constant. This gives the effective distance they must be placed at in air, as [itex]\frac{r}{2} + \frac{r\sqrt{K}}{k}[/itex]. How do I use this for the second problem?

Advice/help is greatly appreciated.

Thanks and cheers

vivek

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# Calculating the Coulomb Force between 2 charges in space

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