Question

A charge 6Q is placed on one face of a cube of side L. The net electric flux through the cube is.....

Answer 1

Answer:

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Consider a sphere enclosing the cube and touching all the eight corners of the cube. It's possible because cube is a symmetrical object. Now, according to Gauss’s theorem, the total flux coming out of sphere will be equal to “q” coulombs where “q” is the charge at the centre of the sphere (or at the centre of the cube). Due to symmetry, the amount of flux coming out of one cube face will be the same as the flux coming out of 1/6 surface of the sphere, and hence equal to q/6 coulombs.

Therefore, electric flux (in coulombs) coming out of one cube face will be equal to 1/6 of the charge (in coulombs) placed at the centre of the cube.

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Answer 2

Total flux passing through the cube

ϕ= ϵo / q

Due to symmetry of electric field around the charge, and all the six faces of cube being equivalent, the electric flux through any face is

1 / 6 × ϵo / q

6/6 = 1

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