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Question #42797

Difficulty: 8/10 | 🟢 Free

The Question

Two fixed concentric thin conducting spherical shells have radii $R$ and $3R$ , and carry uniformly distributed charges $+Q$ and $+2Q$ respectively. A particle of mass $m$ and charge $-q$ (where $q > 0$ ) is moving in a stable circular orbit of radius $2R$ , concentric with the shells. What is the total mechanical energy of the particle? (Assume the reference for zero potential energy is at infinity, and $\epsilon_0$ is the permittivity of free space)

Options

A.
$-\frac{11qQ}{48\pi\epsilon_0 R}$
B.
$-\frac{qQ}{16\pi\epsilon_0 R}$
C.
$-\frac{7qQ}{48\pi\epsilon_0 R}$
D.
$-\frac{5qQ}{16\pi\epsilon_0 R}$

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

Potential of Concentric Shells|Orbital Velocity Energy Balance

Why This Question Is Tricky

Common Mistakes

This question tests the critical distinction between dynamic force balance and path-independent potential energy in a conservative field.

A common trap is the misapplication of the Virial Theorem ( $E = -K = U/2$ ), which is only valid for a pure $1/r$ potential without constant offsets.

Students often incorrectly assume the total energy is simply $-K$ (yielding $-\frac{qQ}{16\pi\epsilon_0 R}$ ) by ignoring the outer shell's potential, or they assume $E = U/2$ (yielding $-\frac{7qQ}{48\pi\epsilon_0 R}$ ) by using the total potential to dictate kinetic energy.

Another trap is calculating the potential by assuming all charge is concentrated at the center.

The correct approach requires independently evaluating the local electric field (which dictates kinetic energy via centripetal force) and the global electric potential (which dictates potential energy).

Quick Facts About This Question

Question Information

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