(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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 [tex]r_{1}[/tex] and the cylinder has inner radius [tex]r_{2}.[/tex] The space between the wires is filled with a dielectric having dielectric constant [tex]\kappa.[/tex]

2. Relevant 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 [tex]E_{no_dielectric}/\kappa[/tex]. So then if my cylindrical capacitor has E field = [tex]\frac{2\lambda}{r}[/tex], then my E field inside the dielectric material would be [tex]\frac{2\lambda}{r\kappa}[/tex]. So then if I am given a value for the dielectric strength of the dielectric (say [tex]A[/tex], which would happen at the inner radius of the cylindrical shell which is [tex]r_{2}[/tex]), would I do

[tex]A = \frac{2\lambda}{r\kappa}[/tex], and then I can find the charge density which is

[tex]\frac{Ar\kappa}{2}[/tex]. And, since the potential between the wire and the shell would be [tex]2\lambda*ln\frac{r_{2}}{r_{1}}[/tex], would I just substitute the new value for lambda I got to get the potential? For some reason this was marked wrong?

Thanks!

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# Dielectric breakdown

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