A hemisphere of radius $R$ is placed in a uniform electric field $E$ such that the field lines are p

Question

A hemisphere of radius $R$ is placed in a uniform electric field $E$ such that the field lines are parallel to its axis of symmetry. What is the magnitude of the electric flux through its curved surface?

Professor PC Thomas Classes · Answer

(a) : For a closed surface in a uniform electric field, the net electric flux is zero. The hemisphere consists of a flat circular base and a curved surface. The flux through the flat base is $-E 	imes (\pi R^2)$ (since the field lines enter the base against the area vector). To maintain a net zero flux, the flux through the curved surface must be exactly equal and opposite, i.e., $+E \pi R^2$.