Calculate the dielectric constant of the material

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SUMMARY

The dielectric constant of a material can be calculated using the forces exerted by point charges in free space compared to a dielectric medium. In this discussion, the force between two point charges in free space is 2.6 nN, which reduces to 1.5 nN in a dielectric material. The relative dielectric constant (εr) is determined to be 1.73, indicating that the dielectric constant (ε) of the material is 1.73 times that of free space (ε0 = 8.855e-13 F/m). The calculations confirm that the approach used was correct, focusing on the ratio of forces rather than numerical force computations.

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  • Basic knowledge of electrostatics and charge interactions
  • Ability to manipulate equations involving constants such as ε0
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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?
 
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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
 

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