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Question #43640

Difficulty: 8/10 | 🟢 Free

The Question

Two fixed concentric thin spherical shells of radii $R$ and $3R$ carry uniformly distributed positive charges $Q$ and $2Q$ respectively. A particle of mass $m$ and positive charge $q$ is projected from infinity directly towards the common center of the shells with an initial kinetic energy $K_0 = \frac{qQ}{3\pi\epsilon_0 R}$ . What is the distance of closest approach of the particle to the center of the shells?

Options

A.
$\frac{3R}{2}$
B.
$\frac{9R}{4}$
C.
$\frac{3R}{4}$
D.
$\frac{5R}{4}$

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

Distance of Closest Approach|Gauss Law Applicability|Potential of Concentric Shells

Why This Question Is Tricky

Common Mistakes

This question tests the application of the Shell Theorem and the superposition principle for electrostatic potential.

A common trap is assuming that the entire charge of the system ( $3Q$ ) acts as a point charge at the center for all distances, which leads to the incorrect energy equation $K_0 = \frac{1}{4\pi\epsilon_0}\frac{3qQ}{r_{min}}$ and the trap answer $9R/4$ .

Another trap is ignoring the constant potential contribution of the outer shell once the particle penetrates it, leading to $3R/4$ .

Students must recognize that inside a uniformly charged spherical shell, the electric field is zero, meaning the potential is constant and equal to its value at the surface, which must be added to the point-charge-like potential of the inner shell.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Atoms - Class 12
Concept	Distance of Closest Approach
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free