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Question #42759

Difficulty: 8/10 | 🟢 Free

The Question

An uncharged solid conductor of arbitrary, non-spherical shape contains a perfectly spherical cavity of radius $R$ . A point charge $+q$ is initially held at the center of the cavity. The charge is then moved slowly to a point at a distance $R/2$ from the center. What is the work done by the external agent in this process?

Options

A.
$-\frac{q^2}{24\pi\epsilon_0 R}$
B.
$0$
C.
$-\frac{q^2}{12\pi\epsilon_0 R}$
D.
$+\frac{q^2}{24\pi\epsilon_0 R}$

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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

Conductor Interior Potential|Symmetry and Virtual Work|Integration

Why This Question Is Tricky

Common Mistakes

This question tests the student's understanding of cavity dynamics and the energy of induced charge distributions.

A common trap is assuming that because the cavity is inside a conductor, the electric field is zero everywhere inside, leading to $W=0$ .

Another lethal trap is calculating the work done as $W = q\Delta V_{ind}$ without the $1/2$ factor, forgetting that the induced charge distribution changes as the point charge moves, which requires the use of self-energy formulas ( $U = \frac{1}{2}qV_{ind}$ ).

Furthermore, students may incorrectly assume the arbitrary outer shape of the conductor affects the internal work done, failing to apply the principle of electrostatic shielding.

Quick Facts About This Question

Question Information

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