Figure shows a ch

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=0^o 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.