GATE PH 2014 • Q14
NAT • 1 Mark
Section 3: Electromagnetic Theory
Electromagnetic Theory
Subtopic: Maxwell's Equations, Waveguides & Radiation
Question Statement:
If the vector potential
,ˆ3ˆ2ˆ z z y y x x A- + =α
satisfies the Coulomb gauge, the value of the constant α is ___________________ .
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2014 Q.14)**
**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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