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.


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

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