A long straight string carrying a charge \( \lambda \) per unit length passes through an imaginary cube of edge a, entering and leaving through the centres of two opposite faces. The electric flux through the cube is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( \frac{\lambda a}{\varepsilon_0} \)
By Gauss’s law, the electric flux through any closed surface is \( q/\varepsilon_0 \), where \( q \) is the total charge enclosed by the surface. Only the charge inside the cube counts, whatever the shape of the surface.
The string enters through the centre of one face and leaves through the centre of the opposite face. So the length of string inside the cube is the edge \( a \). The charge enclosed is:
\( q_{\mathrm{enc}}=\lambda a \)
The flux through the cube is then:
\( \begin{aligned} \Phi &= \frac{q_{\mathrm{enc}}}{\varepsilon_0} \\ &= \frac{\lambda a}{\varepsilon_0} \end{aligned} \)
NCERT (2026-27):
Gauss’s Law – “We state Gauss’s law without proof:
Electric flux through a closed surface S \( =q/\varepsilon_0 \)\( \qquad (1.31) \)
q = total charge enclosed by S.”