What will be the total flux through the faces of the cube as in figure with side of length a if a charge q is placed at ?
(a) A: a corner of the cube.
(b) B : midpoint of an edge of the cube.
(c) C: centre of a face of the cube.
(d) D : midpoint of B and C.

Explanation

(a) Cube has 8 corners. Charge on each corner:
`=q/(8 xx 1) = q/8`
`therefore` Electric flux at A.
`phi = q/(8epsilon_(0))`
(b) If the charge q is placed at B, middle point of an edge of the cube, it is being shared equally by 4 cubes.
Flux through each cube,
`phi = phi^(.)/4 = q/(4epsilon_(0))`
(c) If the charge q is placed at C, the centre of a face of the cube, it is being shared equally by 2 cubes.
`therefore` Flux through each cube,
`phi = phi^(.)/epsilon_(0) = q/(2epsilon_(0))`
(d) Finally, if charge q is placed at D, the midpoint of B and C, it is being shared equally by 2 cubes.
`therefore` Flux through each cube,
`phi = phi^(.)/epsilon_(0) = q/(2epsilon_(0))`