Question Statement:
In spherical polar coordinates (r, ð, ð), the unit vector ðĖ at (10, ð/4, ð/2) is
(A) kĖ (B)
1
â2 (jĖ + kĖ) (C)
1
â2 (-jĖ + kĖ) (D)
1
â2 (jĖ - kĖ)
2/12
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2018 Q.4)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Quantitative & Analytical Aptitude** within *General Aptitude* (1 Mark, NAT).
**2. Quantitative Numerical Calculation**:
- Identifying known experimental values and physical constants for Quantitative & Analytical Aptitude.
- 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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