A charge Q is placed at the centre of an imaginary hemispherical surface. Using symmetry arguments and the Gauss\'s law, find the flux of the electric field due to this charge through the surface of the hemisphere (figure ).

Explanation

a. and b.: Since the point charge Q is located just above
the centre of the flate face, then almost half the lines
emitting from Q will pass through the flate surface.
Any line passing through the flat surface will also
pass through the curved surface below it. Hence the
required flux is `phi = Q//2epsilon_0`. Here flux through curved
surface will be positive and through flat surface will
be negative having same magnitude.
c. If the charge is placed exactly is placed exactly at the centre, then any
line emitting from the charge will be parallel to the flat
surface. Hence, there is no flux through the flat surface.
But the flux through the curved surface will remain the
same as `phi = Q//2epsilon_0`.