A charge q is located at the centre of a cube. The electric flux through any face is

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This question was previously asked in

BPSC AE Paper 5 (Electrical) 25 Mar 2022 Official Paper

Answer 1

Concept:

Gauss Law:

The flux of electric field passing through a closed surface is given by:

\(ϕ = \int \vec D.ds=q\)

∵ \(\vec D=\epsilon_{o}\vec E\)

\(ϕ = \int \epsilon_{o}\vec E.ds=q\)

\(ϕ = \int \vec E.ds={q\over \epsilon_{o}}\)

where ϕ = Electric flux

\(\vec E\) = Electric field

q = Charge enclosed

Explanation:

A cube has six faces. For all its six faces the electric flux will pass in a symmetrical manner giving equal flux through all faces.
The flux through each face is given by:

\(ϕ_{new} = {\phi\over 6} ={q\over 6 \epsilon_{o}}\)

Multiplying and dividing by 4π on numerator and denominator respectively, we get:

\(\phi_{new}=\frac{{4\pi q}}{{6(4\pi {\varepsilon _0})}}\)