Consider a tiny current loop driven by a sinusoidal alternating current. If
the surface integral of its time-averaged Poynting vector is constant, then the
magnitude of the time-averaged magnetic field intensity, at any arbitrary
position, F, is proportional to
1
(A)
(B)
(C)
(D)
1
r
GY DOME
Options:
(A)
(B)
(C)
(D) 1 r GY DOME
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2021 Q.15 / PH Q.5)**
**1. Physical Principles & Examination Context**:
- **Topic**: *Lagrangian & Hamiltonian Dynamics* (`Euler-Lagrange Equations of Motion`) | **Section**: *Section 2: Classical Mechanics*
- **Question Type**: **MCQ** | **Marks**: **1 Mark** | **Negative Marks**: **0.33**
- **Governing Principles**: Solved directly by applying fundamental laws of **Lagrangian & Hamiltonian Dynamics**.
**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**.
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.