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Question

The length of each side of a cubical closed surface is a. If charge q is situated on one of the vertices of the cube then the flux passing through each face of the cube will be :

A
q6ε0
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B
q24ε0
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C
q8ε0
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D
zero
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Solution

The correct option is D q24ε0

Think of this cube as one of 8 surrounding the charge.Every face has 4 squares and there are 6 faces, hence total no. of squares are 24. Each of 24 squares which make up the surface of this larger cube gets the same flux as every other one. So,

onefaceE.da=124largecubeE.da=124.qϵ0 (using Gauss's law)


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