Subtopic: Spin Angular Momentum & Pauli Spin Matrices
Question Statement:
(A)
The free energy of a ferromagnet is given by F = Fo + ao(T - Tc)M? +
bM*, where Fo, do, and b are positive constants, M is the magnetization, T
is the temperature, and Tc is the Curie temperature. The relation between
M? and T is best depicted by
AMZ
(B)
1 M2
T.
(C)
Tc
(D)
1 M2
T
Tc
→
Options:
(A) The free energy of a ferromagnet is given by F = Fo + ao(T - Tc)M? + bM*, where Fo, do, and b are positive constants, M is the magnetization, T is the temperature, and Tc is the Curie temperature. The relation between M? and T is best depicted by AMZ
(B) 1 M2 T.
(C) Tc
(D) 1 M2 T Tc →
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2021 Q.48 / PH Q.38)**
**1. Physical Principles & Examination Context**:
- **Topic**: *Angular momentum & Hydrogen Atom* (`Spin Angular Momentum & Pauli Matrices`) | **Section**: *Section 4: Quantum Mechanics*
- **Question Type**: **MCQ** | **Marks**: **2 Marks** | **Negative Marks**: **0.67**
- **Governing Principles**: Solved directly by applying fundamental laws of **Angular momentum & Hydrogen Atom**.
**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 **B**.
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