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

Answer: (B)

$\frac {4\pi q}{6(4πε_0)}$

Answer 2

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): $\frac {4\pi q}{6(4πε_0)}$