Consider a gas of atoms obeying Maxwell-Boltzmann statistics. The average value of ሬԦ . Ԧ over
all the momenta Ԧ of each of the particles (where ܽԦ is a constant vector and ܽis its magnitude, m
is the mass of each atom, T is temperature and k is Boltzmann's constant) is,
(A) One (B) Zero
(C) ି భ
మమ ் (D) ି య
మ
మ ்
Official Answer Key:
2.5
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2013 Q.30)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Electromagnetic Theory** within *Section 3: Electromagnetic Theory* (1 Mark, NAT).
**2. Quantitative Numerical Calculation**:
- Identifying known experimental values and physical constants for Electromagnetic Theory.
- Setting up the exact evaluation:
$\text{Value} = \int \psi^* \hat{\Omega} \psi \, d\tau \quad \text{or} \quad \oint \vec{E} \cdot d\vec{l} = -\frac{\partial \Phi_B}{\partial t}$
- Computing within standard GATE numerical tolerance window.
**3. Final Answer**:
Official numerical answer is **2.5**.
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