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Question #42781

Difficulty: 8/10 | 🟢 Free

The Question

A parallel plate capacitor with plate area $A$ and separation $d$ is connected to a constant DC voltage source $V$ . A dielectric slab of mass $m$ , dielectric constant $K$ , and dimensions identical to the space between the capacitor plates is initially placed just outside the capacitor. An external agent pushes the slab completely into the capacitor such that the slab moves with a constant velocity $v$ . Neglecting friction and edge effects, what is the work done by the external agent, $W_{\text{ext}}$ ?

Options

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

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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

Common Potential Redistribution|Energy Density Locality|Integration

Why This Question Is Tricky

Common Mistakes

This question tests the comprehensive application of the work-energy theorem in electrodynamics.

A common trap for students is to equate the work done by the external agent directly to the change in the capacitor's stored electrostatic energy ( $W_{\text{ext}} = \Delta U$ ), completely ignoring the work done by the connected battery, which leads to a sign and magnitude error.

Another trap is misidentifying the direction of the external force; because the dielectric is naturally pulled into the strong electric field region to minimize the system's potential energy, the external agent must exert a retarding force to maintain constant velocity, resulting in negative work.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Electrostatic Potential and Capacitance - Class 12
Concept	Common Potential Redistribution
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free