As depicted in the figure, a charge q is situated at the centre of a hemisphere. A second charge Q is positioned at one of the locations A , B , C , and D . For which location(s) of this second charge does the flux of the electric field through the hemisphere remain unchanged?

Step-by-step solution

The initial electric flux through the curved surface of the hemisphere due to the charge q at the centre is _ q = q 2 ₀ . When a second charge Q is placed at any external point, the total flux through the hemisphere becomes _ total = _ q + _ Q , where _ Q is the flux due to the charge Q . For the total flux to remain unchanged, the flux through the curved surface due to Q must be zero, i.e., _ Q = 0 . Consider a closed surface formed by the curved hemispherical surface and its flat circular base. By Gauss's law, th