Consider a non-interacting gas of spin 1 particles, each with magnetic moment 𝜇,
placed in a weak magnetic field B, such that
ఓ
ಳ் ≪ 1. The average magnetic
moment of a particle is
Options:
(A) 2𝜇
3 ൬ 𝜇 B
kT൰
(B) 𝜇
2 ൬𝜇 B
kT൰
(C) 𝜇
3 ൬𝜇 B
kT൰
(D) 3𝜇
4 ൬𝜇 B
kT൰
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2022 Q.36)**
**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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