A parallel plate capacitor with spacing d and area of cross-section A is connected
to a source of voltage V. If the plates are pulled apart quasistatically to a spacing
of 2d, then which of the following statements are correct?
Options:
(A) The force between the plates at spacing 2d is
ଵ
଼ ቀ
ఢబమ
ௗమ ቁ
(B) The work done in moving the plates is
ଵ
଼ ቀ
ఢబ మ
ௗ ቁ
(C) The energy transferred to the voltage source is
ଵ
ଶ ቀ
ఢబ మ
ௗ ቁ
(D) The energy of the capacitor reduces by
ଵ
ସ ቀ
ఢబ మ
ௗ ቁ
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2022 Q.53)**
**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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