The direction of ∇ሬሬ݂⃗for a scalar field ݂(ݔ,ݕ ,ݖ )=
ଵ
ଶݔଶ -ݕݔ+
ଵ
ଶݖଶ at the point ܲ(1, 1, 2) is
(A)
5
ˆ2ˆ k j (B)
5
ˆ2ˆ k j (C)
5
ˆ2ˆ k j (D)
5
ˆ2ˆ k j
Official Answer Key:
2.5
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2016 Q.33)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Nuclear & Particle Physics** within *Section 9: Nuclear and Particle Physics* (1 Mark, NAT).
**2. Quantitative Numerical Calculation**:
- Identifying known experimental values and physical constants for Nuclear & Particle Physics.
- 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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