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Electrostatics

JEE Main level, single correct, medium

273 of 311

Question 273 of 311

A line charge of length $\frac{\text { ' } a \text { ' }}{2}$ is kept at the center of an edge $B C$ of a cube $A B C D E F G H$ having edge length ' $a$ ' as shown in the figure. If the density of line charge is $\lambda$ C per unit length, then the total electric flux through all the faces of the cube will be _______. (Take, $\epsilon_0$ as the free space permittivity)

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Answer: (D) $\frac{\lambda \mathrm{a}}{8 \epsilon_0}$

\begin{aligned} & \text { Charge of the line charge }=\frac{a \lambda}{2} \\ & \text { Portion of wire inside cube }=\frac{1}{4} \\ & \therefore \quad q_{e n}=\frac{1}{4}\left(\frac{a \lambda}{2}\right)=\frac{a \lambda}{8} \\ & \qquad \phi=\frac{q_{e n}}{\varepsilon_0}=\frac{a \lambda}{8 \varepsilon_0}\end{aligned}

JEE Main question paper PDF

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JEE Main 2025 Apr 2 Shift 1 question paper

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