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Question #42691

Difficulty: 8/10 | 🟢 Free

The Question

A solid conducting sphere $A$ of radius $R$ is initially uncharged. A separate conducting spherical shell $B$ has an outer radius of $3R$ and contains an off-center spherical cavity. A point charge $+Q$ is fixed inside this cavity. The shell $B$ is initially given a net charge of $+2Q$ . Sphere $A$ is placed at a large distance from shell $B$ . The two conductors are then connected by a long, thin conducting wire. After electrostatic equilibrium is reached, what is the final charge on sphere $A$ and the total electric flux passing through a spherical Gaussian surface of radius $4R$ concentric with shell $B$ ?

Options

A.
$\frac{3Q}{4}$ and $\frac{9Q}{4\varepsilon_0}$
B.
$\frac{Q}{2}$ and $\frac{5Q}{2\varepsilon_0}$
C.
$\frac{3Q}{4}$ and $\frac{5Q}{4\varepsilon_0}$
D.
$\frac{Q}{2}$ and $\frac{3Q}{2\varepsilon_0}$

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

Common Potential Redistribution|Cavity Field Shielding|Gauss Law|Integration

Why This Question Is Tricky

Common Mistakes

This question tests the distinction between a conductor's net charge and its outer surface charge, which dictates its potential.

Students often fall into the trap of equating the potential of shell B to V = k(2Q)/(3R), ignoring that the internal point charge induces a -Q charge on the cavity wall, forcing an additional +Q to the outer surface.

Consequently, they misapply the conservation of charge during the redistribution phase.

Furthermore, when calculating the final flux, students frequently forget to sum all enclosed charges (including the internal point charge), mistakenly using only the net charge of the shell.

Quick Facts About This Question

Question Information

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