# Calculate the dielectric constant of the material

## Homework Statement

two point charges in free space are separated by distance d and exert a force 2.6 nN on each other. The force becomes 1.5 nN when the free space is replaced by a homogeneous dielectric material. Calculate the dielectric constant of the material.

## Homework Equations

I used an equation but i did not write it down so I am not totally sure what I used

## The Attempt at a Solution

2.6=(9E9)Q^2/d^2 then Q=.000016997d then 1.5=(.000016997d)^2(9e9)/(epsilonr) then epsilonr=1.73 now I have a couple of problems with what I did first I believe I have only found for the relative dielectric constant rather than the dielectric constant. An the second problem is that I did not convert nano newtons to Columbs/m^2N^2 as I wasnt sure of the conversion I searched on google and couldnt find it?

rude man
Homework Helper
Gold Member
The two charges aren't necessarily of the same strength (in Coulombs) so don't bother trying to compute them.

Still, what you did was OK. The answer is εr = 1.73.

The force is kq1*q2/d^2 but k = 1/4πε. In vacuo ε = ε0 = 8.855e-13 F/m and er = 1.

In the dielectric er = 1.73 as you have computed, and ε = 1.73ε0.

Also never mind computing forces numerically. All you need is Fvacuum/Fdielectric = 1.73.

Cool so my answer was good for once