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Two point charges a distance $d$ apart in free space exert a force of $1.4\times10^{-4}N$. When the free space is replaced by a homogeneous dielectric medium, the force becomes $0.9\times10^{-4}N$. What is the dielectric constant $\epsilon_r$ of the medium?

I have been staring at this problem for awhile. I can only think of using $E={F/Q}$. But the problem is this only applies to free space and I do not know $Q$. So I am not sure where to start to compare the free space and medium.

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The charges are still the same. Only the dielectric medium is varied. So, it's easier than you think...

Both the forces differ only by the relative permittivity $\epsilon_r$.

Hence the relation, $$\frac{F}{F_m}=\frac{\epsilon}{\epsilon_0}=\epsilon_r$$

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Oh wow! Thanks, as always I think to hard about it. –  user22740 Apr 5 '13 at 1:56
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