A point charge `Q` is placed at one corner of a cube. Find flux passing through
(a) cube
(b) each face of cube containing the charge
(c ) each face of cube not containing the charge

Explanation

(a) First , make the surface close by placing three identical cubes , at three sides of given cube and four cube above. Now charge comes at the centre of `8` cubes. The flux passing through each cube will be `1//8^(th)` of the flux `Q//in_(0)`. Hence , flux passing through given cube `= Q//8 in_(0)`.
(b) The flux through this cube is `Q//8 in_(0)`. The charge is contained in three faces, `AHEF , ABGF , ABCH`. In these faces , electric field due at `Q` will be in the plane of faces , electric field due to `Q` will be in the plane of face and area is perpendicular to face hence flux `phi' = E S cos 90^(@) = 0`. The flux through these three faces is zero.
(c ) The flux `Q//8 in_(0)` is passing through remaining three faces mamely `DEFG , BCDG` and `CDEH`.
By symmetry , flux through each face not containing the charge `= Q//24 in_(0)`.