A closed hemispherical surface consists of a flat circular base and a curved dome. A point charge q is placed on the axis of symmetry at an infinitesimally small distance just outside the flat base. If the outward normal is taken as positive, what are the values of the electric flux through the curved surface and the flat base, respectively?

Step-by-step solution

Since the charge q is placed strictly outside the closed hemispherical surface, the net enclosed charge is zero. By Gauss's law, the total electric flux through the entire closed surface is zero. The charge is placed at an infinitesimally small distance from the flat circular base. From the perspective of the charge, the flat base subtends a solid angle approaching 2 steradians, effectively acting like an infinite plane. Therefore, exactly half of the total electric field lines originating from the charge will ente