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In the above problem, I have found out the potential and the electric field in the medium between the two conductors. From here, how can I calculate the approximate charge per plate?

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  • $\begingroup$ Use the fact that across a charged surface, the discontinuity of the normal component of the electric field is equal to $\sigma/\varepsilon_0$. $\endgroup$ – Christophe Mar 28 at 19:25
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Surface charge density $\sigma$ on the plate is related to the electric field E near the plate by the following relation $$ \sigma = \varepsilon_r\varepsilon_0 E $$ Hence the charge per plate is $$ Q = h\varepsilon_r\varepsilon_0\int_r^R E(\rho)d\rho, $$ where $h = 5$ m, $E(\rho)$ can be found from your formulas, $r = 0.002/\sin(\pi/8)$ m from the given conditions and $R = 1 + r$ m.

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