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Question #87598

Difficulty: 5/10 | 🟢 Free

The Question

An infinite non-conducting sheet with a uniform surface charge density $+\sigma$ is placed in the $y-z$ plane at $x = 0$ . An infinitely long straight wire with a uniform linear charge density $+\lambda$ is placed parallel to the $z$ -axis, passing through the point $x = -d, y = 0$ . A point charge $+Q$ is moved slowly by an external agent from point $A(d, 0, 0)$ to point $B(0, d, 0)$ . What is the work done by the external agent? (Assume the medium is vacuum with permittivity $\epsilon_0$ )

Options

A.
$Q \left( \frac{\sigma d}{2\epsilon_0} + \frac{\lambda \ln 2}{4\pi\epsilon_0} \right)$
B.
$Q \left( -\frac{\sigma d}{2\epsilon_0} + \frac{\lambda \ln 2}{4\pi\epsilon_0} \right)$
C.
$Q \left( \frac{\sigma d}{2\epsilon_0} + \frac{\lambda \ln 2}{2\pi\epsilon_0} \right)$
D.
$-Q \left( \frac{\sigma d}{2\epsilon_0} + \frac{\lambda \ln 2}{4\pi\epsilon_0} \right)$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Multi-Concept_Bridge

Master problems that require linking physics and math concepts to solve complex competitive questions.

Concepts Behind This Question

Conservative Field Path Independence|Potential Energy Reference|Field due to Infinite Sheet

Why This Question Is Tricky

Examiner Levers

Dimensional Analysis

Tests if the student verifies units/dimensions before selecting.

Difficulty Boost : +2

Common Mistakes

This question tests the student's ability to handle potential differences for infinite charge distributions where the standard $V(\infty) = 0$ reference fails due to divergent integrals.

Students who blindly memorize potential formulas often attempt to assign absolute potentials using infinity as a reference, leading to undefined values.

Furthermore, it tests the application of path independence in conservative fields by requiring the calculation of radial distances from the line charge rather than integrating along a specific Cartesian path.

Finally, it traps students who confuse the work done by the electric field with the work done by an external agent (Option D) or miscalculate the geometric distance to the line charge (Option C).

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Electrostatic Potential and Capacitance - Class 12
Concept	Conservative Field Path Independence
Difficulty	5
Cognitive Load	6
Target Solve Time	140 sec
Access	Free