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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:

  1. 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.
  2. 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 by

Φt=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 be

Φf=16×Φt

Φf=16×qε0

Φf=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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