A point charge q is placed at the origin, inside a linear dielectric medium of infinite
extent, having relative permittivity 𝜖r. Which o f the following option (s) is/are
correct?
Options:
(A) The magnitude of the polarization varies as
1
r2
(B) The magnitude of the polarization varies as
1
r3
(C) The magnitude of the screened charge due to the dielectric medium is less than the
magnitude of the point charge q for 𝜖r > 1
(D) The magnitude of the screened charge due to the dielectric medium is more than the
magnitude of the point charge q for 𝜖r = 1
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2025 Q.57)**
**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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