We know from Gauss Law that the closed surface integral of electric flux () is equal to the charge enclosed () by that closed surface. This is mathematically given by

The electric flux is given by

(a) Charge q is placed at point A corner of the cube of the given cube. To determine the flux through the faces of the given cube, we have to first consider a Gaussian surface. This surface must be a closed surface (here a large cube made up of 8 equivalent cubes) around the charge q at point A as shown in the figure below.

Using equation (2) above, the electric flux through the Gaussian surface is

But, we have to determine the flux through one cube (bolded in the figure below). Since the flux is contributed by 8 cubes (or large cube), the flux contributed by 1 cube will be

(b) Charge q is placed at point B which is at the midpoint of an edge of cube. To determine the flux through the faces of the given cube, we have to first consider a Gaussian surface. This surface must be a closed surface (here a large cube made up of 4 equivalent cubes) around the charge q at point B as shown in the figure below.

Using equation (2) above, the electric flux through the Gaussian surface is

But, we have to determine the flux through one cube (bolded in the figure above). Since the flux is contributed by 4 cubes (or large cube), the flux contributed by 1 cube will be

(c) Charge q is at point C which is at the centre of the face of a cube. To determine the flux through the faces of the given cube, we have to first consider a Gaussian surface. This surface must be a closed surface (here a large cube made up of 2 equivalent cubes) around the charge q at point C as shown in the figure below.

Using equation (2) above, the electric flux through the Gaussian surface is

But, we have to determine the flux through one cube (bolded in the figure below). Since the flux is contributed by 2 cubes (or large cube), the flux contributed by 1 cube will be

(d) Charge q is at point D which is at the centre of the line joining B and C on the face of a cube. To determine the flux through the faces of the given cube, we have to first consider a Gaussian surface. This surface must be a closed surface (here a large cube made up of 2 equivalent cubes) around the charge q at point D as shown in the figure below.

Using equation (2) above, the electric flux through the Gaussian surface is

But, we have to determine the flux through one cube (bolded in the figure below). Since the flux is contributed by 2 cubes (or large cube), the flux contributed by 1 cube will be