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?

The flux of the electric field through the hemisphere remains unchanged regardless of the position of the second charge Q. This is because the electric flux through a closed surface is given by Gauss's Law, which states that the electric flux through any closed surface is equal to the total charge enclosed by the surface divided by the permittivity of free space.

In this case, the closed surface is the hemisphere plus the flat circular base. The total charge enclosed by this surface is always q, regardless of where the second charge Q is placed. Therefore, the electric flux through the hemisphere remains unchanged whether the second charge Q is at position A, B, C, or D.

However, if we consider only the curved surface of the hemisphere (without the base), then the flux would change depending on the position of the charge Q. If Q is inside the hemisphere (positions B or C), it would contribute to the total enclosed charge and thus change the flux through the curved surface. If Q is outside the hemisphere (positions A or D), it would not contribute to the enclosed charge, and the flux through the curved surface would remain the same as if Q were not there.