Consider a solenoid of length L and radius R, where R « L. A steady-current
flows through the solenoid. The magnetic field is uniform inside the solenoid
and zero outside.
0
Among the given options, choose the one that best represents the variation
in the magnitude of the vector potential, (0, Aq, 0) at z = L/2, as a function
of the radial distance (r) in cylindrical coordinates.
Useful information: The curl of a vector F, in cylindrical coordinates is
(A)
^ Аф
(B)
1 Аф
→
(C)
^ Аф
(D)
1 Аф
Options:
(A) ^ Аф
(B) 1 Аф →
(C) ^ Аф
(D) 1 Аф
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2021 Q.16 / PH Q.6)**
**1. Physical Principles & Examination Context**:
- **Topic**: *Central force problem* (`Kepler's Laws & Planetary Orbits`) | **Section**: *Section 2: Classical Mechanics*
- **Question Type**: **MCQ** | **Marks**: **1 Mark** | **Negative Marks**: **0.33**
- **Governing Principles**: Solved directly by applying fundamental laws of **Central force problem**.
**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 **C**.
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