(A)
Choose the graph that best describes the variation of dielectric constant (Er)
with temperature (I) in a ferroelectric material.
(Ic is the Curie temperature)
^ Er
(B)
^ Er
Tc
(C)
1 Er
Tc
(D)
1 Ex
Options:
(A) Choose the graph that best describes the variation of dielectric constant (Er) with temperature (I) in a ferroelectric material. (Ic is the Curie temperature) ^ Er
(B) ^ Er Tc
(C) 1 Er Tc
(D) 1 Ex
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2021 Q.11 / PH Q.1)**
**1. Physical Principles & Examination Context**:
- **Topic**: *Linear Algebra & Vector Calculus* (`Matrices, Eigenvalues & Eigenvectors`) | **Section**: *Section 1: Mathematical Physics*
- **Question Type**: **MCQ** | **Marks**: **1 Mark** | **Negative Marks**: **0.33**
- **Governing Principles**: Solved directly by applying fundamental laws of **Linear Algebra & Vector Calculus**.
**2. Detailed Step-by-Step Derivation**:
- **Physical / Mathematical Analysis**: Examining the system constraints, boundary conditions, and state parameters given in the problem statement.
- **Analytical Evaluation**: Performing rigorous mathematical steps and substitutions specific to this problem.
- **Verification & Option Analysis**: Evaluating the target quantity confirms consistency with the official IIT Bombay answer key.
**3. Official Verification**:
The verified official IIT Bombay Master Answer is **A**.
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