Question

Electric flux through cube when charge placed at center of edge

Answer 1

First of all, I suppose you mean each face, rather than each side. Area of a side is zero, so flux passing through it will be zero. Imagine that the charge is located at origin and the corner of the cube also at origin. We can use Gauss's law and symmetry to solve it. Place 7 more identical cubes around the original one so that the 8 cubes symmetrically cover the origin. Each face of this mega cube contains 4 faces of original. The mega cube has 6 faces symmetrically placed around origin, totally 24 faces. The total flux according to Gauss's law is q/epsilon0. So flux through each face is q/24 epsilon0.