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Question #42314

Difficulty: 8/10 | 🟢 Free

The Question

A parallel plate capacitor has square plates of side length $L$ and separation $d$ . It is kept connected to a battery of constant electromotive force $V$ . A dielectric slab of dielectric constant $K$ and dimensions $L \times L \times d$ is slowly and completely inserted between the plates by an external agent. What is the work done by the external agent, $W_{\text{ext}}$ ? (Assume $\epsilon_0$ is the permittivity of free space and neglect edge effects).

Options

A.
$-\frac{\epsilon_0 L^2 V^2}{2d}(K-1)$
B.
$+\frac{\epsilon_0 L^2 V^2}{2d}(K-1)$
C.
$-\frac{\epsilon_0 L^2 V^2}{2d}\left(1-\frac{1}{K}\right)$
D.
$+\frac{\epsilon_0 L^2 V^2}{d}(K-1)$

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Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Variable_Constraint

Develop pure symbolic logic skills by mastering algebraic constraints without relying on numerical data.

Concepts Behind This Question

Work-Energy Theorem Validity|Dielectric Polarization Logic|Potential vs Field Relationship

Why This Question Is Tricky

Common Mistakes

This question tests the application of the Work-Energy Theorem in electrostatics for a system connected to a constant voltage source.

The primary trap is equating the external work done directly to the change in potential energy ( $W_{\text{ext}} = \Delta U$ ), which is only valid for isolated systems where charge is constant.

When connected to a battery, students must account for the work done by the battery ( $W_{\text{batt}} = \Delta Q \cdot V$ ) as charge redistributes due to the changing capacitance.

Failing to include $W_{\text{batt}}$ leads to a sign and magnitude error, missing the physical reality that the electric field actively pulls the dielectric into the capacitor, requiring the external agent to do negative work to insert it slowly.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Work, Energy, and Power - Class 11 Part 1
Concept	Work-Energy Theorem Validity
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free