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Question #43764

Difficulty: 8/10 | 🟢 Free

The Question

A thin, perfectly absorbing spherical shell of radius $R$ is uniformly charged such that its electrostatic self-energy is $U$ . An isotropic point light source emitting a constant electromagnetic power $P$ is located at the center of the shell. The shell is divided into two identical hemispheres by a hypothetical plane. Assuming the system is in gravity-free space and ignoring any thermal re-emission from the shell, what is the minimum total external force required to hold the two hemispheres together?

Options

A.
$\frac{U}{2R} + \frac{P}{2c}$
B.
$\frac{U}{4R} + \frac{P}{4c}$
C.
$\frac{U}{4R} + \frac{P}{2c}$
D.
$\frac{U}{2R} + \frac{P}{4c}$

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

Intensity and Photon Flux|Self-Energy of Charged Sphere|Shell Theorem

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to decouple electromagnetic momentum flux from static electrostatic energy storage, while rigorously applying vector integration.

A very common trap is integrating scalar pressure over the curved hemispherical surface area ( $2\pi R^2$ ) instead of the projected cross-sectional area ( $\pi R^2$ ).

If a student makes this scalar integration error for both fields, they arrive at Option A.

If they correctly project the electrostatic force but mistakenly assume the momentum of the hemispherical photon beam is half the total scalar momentum ( $P/2c$ ), or if they incorrectly assume a reflecting surface ( $2I/c$ ), they arrive at Option C.

The problem forces a deep understanding of how isotropic pressures translate into net directional forces on bounded geometries.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Dual Nature of Radiation and Matter - Class 12
Concept	Intensity and Photon Flux
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free