Question

A charge q is kept at the corner of a cube. Electric flux passing through one of those faces not touching that charge is

Answer 1

The total flux from a charge q is q/ε₀ (Gauss's law). If the charge is on the corner of a cube, some of the flux enters the cube and leaves through some of its faces. But some of the flux doesn't enter the cube.

Suppose the charge is at the very centre of this hypothetical cube - it is on a corner of each of the 8 cubes. An equal amount of flux will spread outwards through each of the cubes (symmetry)

Since the flux is shared between 8 cubes, the flux through each is (1/8)q/ε₀

Now flux(1/8th) will pass through three of the faces of (smaller)cube and three faces wont have any effect(the ones from which the cube passes)

This 1/8th will be divided into 3 parts again.

so the total will be (1/24)q/ε₀ from each side

Answer 2

Electric flux passing will be Q/24.

• As per the Gauss's Law, the total or net electric flux due to the charge passing through large cube is defined as - Φ = Q/ε0 Therefore,  

• By the application of a symmetrical argument, the electric flux due to the charge passing through each surface of large cube will be -

        Φ' = Φ/6 = Q/60

• Since, each face of the larger side is made of four faces of four small cubes, being one face each, then  the electric flux that will pass through each face of the smaller cube will be - Φ'' = Φ'/4 = Q/240

• Hence, electric flux passing through the cube side to the charge placed at its vertex will be Q/24