# Dielectric breakdown

## Homework Statement

Hello:
I am asked to find the maximum voltage in a cylindrical capacitor. The capacitor consists of an inner wire and an outer cylindrical shell. The wire has radius $$r_{1}$$ and the cylinder has inner radius $$r_{2}.$$ The space between the wires is filled with a dielectric having dielectric constant $$\kappa.$$

## Homework Equations

This is in CGS units (actual calculations have been converted to SI)
So I know that the electric field E in a dielectric is $$E_{no_dielectric}/\kappa$$. So then if my cylindrical capacitor has E field = $$\frac{2\lambda}{r}$$, then my E field inside the dielectric material would be $$\frac{2\lambda}{r\kappa}$$. So then if I am given a value for the dielectric strength of the dielectric (say $$A$$, which would happen at the inner radius of the cylindrical shell which is $$r_{2}$$), would I do
$$A = \frac{2\lambda}{r\kappa}$$, and then I can find the charge density which is
$$\frac{Ar\kappa}{2}$$. And, since the potential between the wire and the shell would be $$2\lambda*ln\frac{r_{2}}{r_{1}}$$, would I just substitute the new value for lambda I got to get the potential? For some reason this was marked wrong?

Thanks!