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?
As we know, the electric flux through a surface element ds is
Where,
is the electric field passing through the area
∆S is the area element
θ is the angle between the area element and electric field
The point A and C lie in the straight line with the charge q,
While the points B and D make an angle θ with the area element,
Thus, Electric flux at point A and C is
(θ=0o for the point in the straight line)
Hence, the flux of the electric field through the hemisphere remains unchanged when second charge is placed at point A and C.