Question

a dielectic slab of thickness of t=d/3 and dielectric constant kand the force between them is 9F/25.Find the value of k​

Answer 1

Answer:

A dielectric effectively behaves as if it was thicker than it is. If the dielectric constant is K and the thickness of the dielectric is t, then for calculating the force it behaves as if the thickness was tK−−√.

To see this let's take the example we know about where the dielectric fills the space between the charges:

Force

In (a) the thickness of the dielectric is the same as the distance between the charges, r, so the effective thickness is rK−−√. If we put this in the force law we get:

F=14πϵ0Q1Q2(rK−−√)2=14πϵ01KQ1Q2r2

as we expect. The force is reduced by a factor of K.

Now consider (b). To get the effective distance between the charges we have to add the distance through the air, r−t, plus the effective thickness of the dielectric, tK−−√, so the effective distance between the charges is:

d=(r−t)+tK−−√

and the force is just:

F=14πϵ0Q1Q2d2=14πϵ0Q1Q2(r−t+tK−−√)2

This is how you get the force when the space between the charges is only partially filled by the dielectric