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Question #42901

Difficulty: 8/10 | 🟢 Free

The Question

A solid, uncharged conducting sphere of radius $R = 20 \text{ cm}$ contains an empty, eccentric spherical cavity of radius $r = 5 \text{ cm}$ . The center of the cavity $C_1$ is located at a distance $a = 10 \text{ cm}$ from the center of the sphere $C_2$ . A point charge $Q = +6 \mu\text{C}$ is placed outside the conductor at a distance $d = 30 \text{ cm}$ from $C_2$ . The points $Q$ , $C_1$ , and $C_2$ are collinear, with $C_1$ located between $Q$ and $C_2$ . Assuming the electric potential at infinity is zero, what is the electric potential at the center of the cavity $C_1$ ?

(Take $\frac{1}{4\pi\epsilon_0} = 9 \times 10^9 \text{ N}\cdot\text{m}^2/\text{C}^2$ )

Options

A.
$1.8 \times 10^5 \text{ V}$
B.
$2.7 \times 10^5 \text{ V}$
C.
$1.35 \times 10^5 \text{ V}$
D.
$0 \text{ V}$

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

Electric Field Line Geometry|Cavity Field Shielding|Surface Integration

Why This Question Is Tricky

Common Mistakes

This question tests the student's understanding of electrostatic shielding and the behavior of conductors as equipotential volumes.

A common trap is to assume that the potential inside the cavity can be calculated by simply applying Coulomb's law to the external charge (yielding $2.7 \times 10^5 \text{ V}$ ), completely ignoring the non-uniform induced charge distribution on the conductor's surface.

Students fail to recognize that the induced charges self-adjust to perfectly cancel the external electric field inside the conductor, making the entire volume (including the empty cavity) an equipotential.

By evaluating the potential at the center of the spherical conductor, where the asymmetric induced charges contribute zero net potential, the true potential of the cavity is elegantly revealed.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Electric Charges and Fields - Class 12
Concept	Electric Field Line Geometry
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free