Consider an electromagnetic wave propagating in the z-direction in vacuum, with
the magnetic field given by B⃗ = B⃗ 0ei(kz-𝜔t). If B0 = 10-8 T, the average
power passing through a circle of radius 1.0 m placed in the xy plane is P (in
Watts). Using 𝜖0 = 10-11
C2
N m2 , what is the value of
103P
𝜋 (rounded off to
one decimal place)?
Official Answer Key:
2.5
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2023 Q.61)**
**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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