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Question #42778

Difficulty: 8/10 | 🟢 Free

The Question

A parallel plate capacitor is formed by a fixed rigid conducting plate and the flat front face of an elastic conducting block. The block has a natural length $L$ , cross-sectional area $A$ , and Young's modulus $Y$ . Its back face is attached to a fixed rigid wall. Initially, the block is held unstretched such that the gap between the fixed plate and the front face of the block is $d$ . A battery of constant voltage $V$ is connected across the fixed plate and the block, and the system is allowed to fully charge. The block is then released. Due to electrostatic attraction, it stretches and eventually settles at a stable equilibrium where the gap is $\frac{3d}{4}$ . What is the total heat dissipated in the system after the block is released? (Assume the electric field is uniform in the gap, zero inside the block, and neglect fringing effects).

Options

A.
$\frac{1}{18} \frac{\epsilon_0 A V^2}{d}$
B.
$\frac{5}{9} \frac{\epsilon_0 A V^2}{d}$
C.
$\frac{5}{18} \frac{\epsilon_0 A V^2}{d}$
D.
$\frac{1}{6} \frac{\epsilon_0 A V^2}{d}$

Check Your Answer

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

Energy Density Locality|Work Done in Stretching|Integration

Why This Question Is Tricky

Common Mistakes

This question tests the rigorous application of energy conservation in deformable electrostatic systems.

A common trap is neglecting the work done by the battery during the mechanical deformation ( $W_{batt} = \Delta Q \cdot V$ ), leading students to incorrectly assume $H = -\Delta U_{elec} - \Delta U_{mech}$ .

Another trap is assuming the electric field remains constant at $V/d$ rather than updating to the local equilibrium value $V/x$ , which causes errors in calculating the mechanical strain energy.

Furthermore, students might erroneously include the heat of initial charging if they fail to separate the static charging phase from the dynamic mechanical release phase.

Quick Facts About This Question

Question Information

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