What is the electric flux through each face of a cube of edge a when a point charge q is placed at the centre of the cube?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( \frac{q}{6\varepsilon_0} \)
By Gauss’s law, the total electric flux through a closed surface is \( q/\varepsilon_0 \), where \( q \) is the charge enclosed. With the charge at the centre, the six faces of the cube are placed alike about it. So each face gets an equal share of the total flux, whatever the edge \( a \).
The flux through the whole cube is:
\( \displaystyle \Phi_{\mathrm{cube}}=\frac{q}{\varepsilon_0} \)
The flux through each face is:
\( \begin{aligned} \Phi_{\mathrm{face}} &= \frac{\Phi_{\mathrm{cube}}}{6} \\ &= \frac{q}{6\varepsilon_0} \end{aligned} \)
NCERT (2026-27):
Gauss’s Law – “We state Gauss’s law without proof:
\( \text{Electric flux through a closed surface S}=q/\varepsilon_0 \)\( \qquad (1.31) \)
q = total charge enclosed by S.”