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Question

# An electric charge q is placed at the centre of a cube of side α. The electric flux on one of its faces will be

A
q6ϵ0
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B
qϵ0a2
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C
q4πϵ0a2
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D
qϵ0
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Solution

## Step 1: Given that:The charge placed at the centre of the cube= q side of the cube= a Step 2: Formula used:According to Gauss theorem, " the electric flux linked with a closed surface due a charged enclosed by the surface is equal to 1ε0 times the charge enclosed by the surface. That is Φ=qenclosedε0 , where Φ is the electric flux.​Step 3: Calculation of the electric flux linked with one face of the cube:The electric flux linked with the whole surface of the cube which encloses the charge q is given byΦt=qε0 As there are 6 faces in a cube and each havce same surface area.The electric flux linked with each face of the cube will beΦf=16×ΦtΦf=16×qε0Φf=q6ε0 Thus,The electric flux linked with one of the surfaces of the cube will be q6ε0 .Hence,Option C) q6ε0 is the correct option.

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