What will be the total flux through the faces of the cube, with side of length a if a charge q is placed at (a) A : a corner of the cube (b) B : mid-point of an edge of the cube (c ) C : center of a face of the cube (d) D : mid-point of B and C.

Explanation

(a) A charge is kept at the corner of a cube. Let us visualise a total of eight identical cubes with a sharing point A (at which charge is placed), forming a bigger cube. So, the charge will be at the centre of the bigger cube thus formed. The total flux `q/epsilon_0` will then be equally divided among eight cubes, hence the flux through the faces of the given cube will be `q/(8epsilon_0)`
(b)If the charge is kept at the midpoint of the edge then we can visualise a total of four such cubes is such a way that they all share that edge to surround the charge symmetrically. The total flux `q/epsilon_0` will be divided among the four cubes equally. Hence, the flux for each cube will be `q/(4epsilon_0)`
(c )If the charge is kept at the centre of a face then the identical cube sharing that face will enclose the charge completely to apply Gauss theorem. The total flux `q/epsilon_0` will be equally divided between the two. Hence, the flux associated with one cube will be `q/(2epsilon_0)`
(d)In this case too, the two cubes can enclose the charge completely and symmetrically between them to get the equal share from the total flux of `q/epsilon_0`. Hence, the flux through each cube will be `q/(2epsilon_0)`