Question

Figure shows a charge q placed at the centre of a hemisphere. A second charge Q is placed at one of the positions A, B, C and D. In which position(s) of this second charge, the flux of the electric field through the hemisphere remains unchanged?

• A. A
• B. B
• C. D
• D. None of these

Answer 1

Answer: (A), (C)

By Gauss's law, flux $\varphi =\oint \vec{E}\cdot \hat{n}dS$
For charge at $A$ and $C$, the flux through the flat circular base will be zero
because $\vec{E}$ and $\hat{n}$ are perpendicular to each other.
Thus the flux through the hemisphere will be unchanged when charge $Q$ at $A$ and $C$.