Question

Problem 2 A hemispherical surface with radius R is a region of uniform electric field E has its axis aligned parallel to the direction of the field. Derive an expression for the electric flux through the surface. Final answer not given

Answer 1

Let us consider a closed hemisphere which cosists of curved surface and circle we know that for a closed surface having no charge enclosed in it, the total flux is zero i.e phi_total = 0 (1) Now the flux through the circular base: phi_base = E^rightarrow middot A^rightarrow = E A cos theta = E (pi R^2) cos 180 degree = - pi R^2 E (2) Total flex (phi_total) = phi_base + phi_curved (flex through curved surface) or phi_curved = phi_total - phi_base = 0 - (- pi R^2 E) = pi R^2 E