Calculate the dielectric constant of the material

[DODGEVIPER13]

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 couldn't find it?

 

[rude man]

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 ε_r = 1.73.

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

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

Also never mind computing forces numerically. All you need is F_vacuum/F_dielectric = 1.73.

 

[DODGEVIPER13]

Cool so my answer was good for once