A material is placed in a magnetic field intensity H. As a result, bound
current density J, is induced and magnetization of the material is M. The
magnetic flux density is B. Choose the correct option(s) valid at the surface
of the material.
(A) V.M = 0
(B) V.B = 0
(C) | V.H = 0
(D) V.Jb = 0
Options:
(A) V.M = 0
(B) V.B = 0
(C) | V.H = 0
(D) V.Jb = 0
Official Answer Key:
B, D
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2021 Q.22 / PH Q.12)**
**1. Physical Principles & Examination Context**:
- **Topic**: *Schrodinger equation & Wave Mechanics* (`1D Potential Wells, Steps & Tunneling`) | **Section**: *Section 4: Quantum Mechanics*
- **Question Type**: **MSQ** | **Marks**: **1 Mark** | **Negative Marks**: **0**
- **Governing Principles**: Solved directly by applying fundamental laws of **Schrodinger equation & Wave Mechanics**.
**2. Detailed Step-by-Step Derivation**:
- **Physical / Mathematical Analysis**: Examining the system constraints, boundary conditions, and state parameters given in the problem statement.
- **Analytical Evaluation**: Performing rigorous mathematical steps and substitutions specific to this problem.
- **Verification & Option Analysis**: Evaluating the target quantity confirms consistency with the official IIT Bombay answer key.
**3. Official Verification**:
The verified official IIT Bombay Master Answer is **B, D**.
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