A line charge of length frac a ' 2 is kept at the center of an edge BC of a cube ABCDEFGH having edge length ' a ' as shown in the figure. If the density of line is λ C per unit length, then the total electric flux through all the faces of the cube will be \ . (Take, ε 0 as the free space permittivity)

Physics · Electrostatics

JEE Main 2025 — 22 January, Morning Shift — Question 47

A line charge of length $\frac{\mathrm{a} \text { ' }}{2}$ is kept at the center

of an edge BC of a cube ABCDEFGH having edge length ' $a$ ' as shown in the figure.

If the density of line is $\lambda \mathrm{C}$ per unit length, then the total electric

flux through all the faces of the cube will be $\qquad$ _. (Take, $\epsilon_{0}$ as the free space permittivity)

Option A:
$\frac{\lambda a}{8 \epsilon_{0}}$
Correct
Option B:
$\frac{\lambda a}{16 \epsilon_{0}}$
Option C:
$\frac{\lambda a}{2 \epsilon_{0}}$
Option D:
$\frac{\lambda a}{4 \epsilon_{0}}$

Answer: A

Step-by-step solution

Total charge inside the cube $=\frac{\lambda \frac{\mathrm{a}}{2}}{4}=\frac{\lambda \mathrm{a}}{8}$ $\therefore \phi=\frac{\mathrm{q}_{\text {in }}}{\varepsilon_{0}}=\frac{\lambda \mathrm{a}}{8 \varepsilon_{0}}$

Answer key and solution verified before publishing.

Practise Electrostatics

Start with this question, then two more from the same chapter — with a tutor that explains every step. Free.

Solve a similar one free

Exam: JEE Main 2025
Paper: 22 January, Morning Shift
Subject: Physics
Chapter: Electrostatics
Topic: Electric flux and Gauss's Law