Question

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

• A. \(\frac {2\pi q}{6(4πε_0)}\)
• B. \(\frac {4\pi q}{6(4πε_0)}\)
• C. \(\frac {\pi q}{6(4πε_0)}\)
• D. \(\frac {q}{6(4πε_0)}\)

Answer 1

The Correct Option is B

Total flux passing through the close cube \(ϕ = \frac {q}{ε_0}\)
All six surfaces exhibit symmetry with respect to the charge, resulting in an equal contribution to the flux. Consequently, the flux through any single face is:
\(ϕ = \frac ϕ 6 = \frac {q}{6ε_0}\)
\(φ_{face} = \frac {q}{6ε_0} = \frac {4\pi q}{6(4\piε_0)}\)

So, the correct option is (B): \(\frac {4\pi q}{6(4πε_0)}\)