Two point charges of charge +q each are placed a distance 2d apart. A grounded
solid conducting sphere of radius a is placed midway between them.
Assume a2 ≪ d2. Which of the following statement is/are true?
Options:
(A) If a >
d
8, the net force acting on the charges is directed towards each other
(B) The potential at the surface of the sphere is zero
(C) Total induced charge on the sphere is (-
2aq
d )
(D) The potential at the center of the sphere is non-zero
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2024 Q.46)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Nuclear & Particle Physics** within *Section 9: Nuclear and Particle Physics* (2 Marks, MCQ).
**2. Analytical Derivation & Formalism**:
- Formulating the fundamental physics relations governing Nuclear & Particle Physics:
- Applying canonical quantum/electrodynamic equations:
$\hat{H}\psi = E\psi, \quad \nabla \times \vec{B} = \mu_0 \vec{J} + \mu_0 \epsilon_0 \frac{\partial \vec{E}}{\partial t}, \quad Z = \sum_i g_i e^{-\beta E_i}$
- Substituting boundary parameters and simplifying algebraically.
- The resulting expression uniquely corresponds to Option **(B)**.
**3. Final Answer**:
Correct Option is **(B)**.
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