# Problem based on Laplace and Poisson's Equations. How to find the charge from electric field and potential?

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?

• Use the fact that across a charged surface, the discontinuity of the normal component of the electric field is equal to $\sigma/\varepsilon_0$. – Christophe Mar 28 at 19:25

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.