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Question #42756

Difficulty: 8/10 | 🟢 Free

The Question

A solid conducting sphere of radius $3R$ contains an eccentric spherical cavity of radius $R$ . The center of the cavity is located at a distance $R$ from the center of the conducting sphere. An ideal electric dipole of dipole moment $p$ is placed exactly at the center of this cavity. The conductor is given a net positive charge $Q$ , and the entire system is placed in a uniform external electric field of magnitude $E_0$ . What is the minimum work done by an external agent to slowly rotate the dipole by an angle of $180^\circ$ about its center?

Options

A.
$0$
B.
$2 p E_0$
C.
$\frac{p^2}{4\pi\epsilon_0 R^3}$
D.
$\frac{p Q}{4\pi\epsilon_0 R^2}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Intuition_Breaker

Train your brain to resist "obvious" answers that are designed to deceive your intuition.

Concepts Behind This Question

Work Done in Rotating Dipole|Flux and Surface Geometry|Cavity Field Shielding

Why This Question Is Tricky

Common Mistakes

This question tests the 'Cavity Field Shielding' theorem and the Uniqueness Theorem.

Students commonly fall into two traps: (1) They assume the external field $E_0$ penetrates the cavity, leading to a standard work calculation of $2pE_0$ . (2) They recognize shielding but incorrectly assume that the eccentric position of the cavity causes an asymmetric induced charge distribution on the inner wall, creating a non-zero torque.

The trap forces students to realize that the inner cavity wall is a perfect sphere centered on the dipole.

Therefore, the induced field is always parallel to the dipole, making the torque and the work done exactly zero, regardless of the outer boundary's shape or external charges.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Electrostatic Potential and Capacitance - Class 12
Concept	Work Done in Rotating Dipole
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free