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Let's say that I have two identical glass spheres with $\kappa_{\text{body}}=5$ charged negatively with a charge $-q$ on both of them. I then place them in glycerin which has $\kappa_\text{medium}=40$. So $\kappa_{\text{medium}}>\kappa_{\text{body}}$.

Will the two spheres attract or repel? What happens when $\kappa_{\text{medium}}<\kappa_{\text{body}}$?

Table of Dielectric Contants

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Will the two spheres attract or repel?

The two spheres will always repel, since they both are negatively charged. The repulsion force will decrease as the dielectric constant of the medium increases.

If the distance between the glass spheres was much greater than their size, we could treat the spheres as point charges and determine the repulsion force between them by applying the Coulomb's law for dielectric medium: $F=\frac 1 {4\pi \epsilon_0\epsilon_r} \frac {q^2} {r^2}$. The formula clearly shows that the force is inversely proportional to the dielectric constant of the medium, $\epsilon_r$.

If the distance between the spheres is not much greater than their size, the force calculated by this formula would not be accurate, but it still would decrease with the introduction of a dielectric material, since dielectric materials, due to their polarization, weaken the electric field.

What happens when κmedium<κbody?

The dielectric constant of the glass will weaken the field inside each sphere, including the field generated by the other sphere, and, to that extent, it will also weaken the repulsion force between the spheres. But that would not qualitatively change the effect of the medium on the repulsion force, regardless of the relationship between the dielectric constant of the glass and the medium: the force will monotonously decrease as the dielectric constant of the medium increases.

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