The x-y plane is the boundary between free space and a magnetic material with relative
permeability r . The magnetic field in the free space is k B i Bz x
ˆˆ . The magnetic field in the
magnetic material is
(A) k B i Bz x
ˆˆ (B) k B i Bz r x
ˆˆ
(C) k B i Bz x
r
ˆˆ1
(D) k B i Bz x r
ˆˆ
Official Answer Key:
2.5
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2016 Q.49)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Electromagnetic Theory** within *Section 3: Electromagnetic Theory* (2 Marks, 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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