In a parallel plate capacitor, the plate at x = 0 is grounded and the plate at x = d is
maintained at a potential V0. The space between the two plates is filled with a linear
dielectric of permittivity š = š0 (1 +
x
d), where š0 is the permittivity of free space.
Neglecting the edge effects, the electric field (Eā ) inside the capacitor is
Options:
(A) - V0
(d + x) ln 2 xĢ
(B) - V0
d xĢ
(C) - V0
(d + x) xĢ
(D) - V0d
(d + x)x xĢ
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2024 Q.40)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Electromagnetic Theory** within *Section 3: Electromagnetic Theory* (2 Marks, MCQ).
**2. Analytical Derivation & Formalism**:
- Formulating the fundamental physics relations governing Electromagnetic Theory:
- 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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