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Question #42765

Difficulty: 8/10 | 🟢 Free

The Question

A point charge $+q$ is initially at the center of a fixed, uncharged, perfectly conducting spherical shell of inner radius $R$ and outer radius $2R$ . An external agent moves the point charge radially outwards at a constant velocity $v$ (where $v \ll c$ , ensuring quasistatic conditions). The charge is moved from the center ( $r=0$ ) to a distance $r = R/2$ from the center. Calculate the magnitude of the impulse delivered to the point charge by the electric field of the induced surface charges during this time interval.

Options

A.
$\frac{q^2}{24\pi\epsilon_0 R v}$
B.
0
C.
$\frac{q^2}{9\pi\epsilon_0 R v}$
D.
$\frac{q^2}{12\pi\epsilon_0 R v}$

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

Cavity Field Shielding|Electric Field Symmetry|Variable Force Integration

Why This Question Is Tricky

Common Mistakes

This question tests the limits of electrostatic shielding and the Shell Theorem.

A common trap is assuming that the electric field inside any conducting shell is always zero (Option B).

While external charges cannot penetrate a perfect conductor, a charge placed inside a cavity induces a non-uniform surface charge on the inner wall if it is off-center.

As the charge moves, this induced distribution becomes time-dependent.

Students must correctly apply the method of images to find the instantaneous force and integrate this variable force over time to find the impulse, avoiding the mistake of using an average force or final force multiplied by time.

Quick Facts About This Question

Question Information

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