The electric field component of a plane electromagnetic wave travelling in vacuum is given by
i t z k E t z Eˆ)cos( ) , (0
. The Poynting vector for the wave is
Options:
(A) j t z k E cˆ) ( cos 2 /2 2
0 0
(B) k t z k E cˆ) ( cos 22 2
0 0
(C) j t z k E cˆ) ( cos2 2
0 0
(D) k t z k E cˆ) ( cos2 2
0 0
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2016 Q.40)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Electromagnetic Theory** within *Section 3: Electromagnetic Theory* (2 Marks, MCQ).
**2. Analytical Derivation & Formalism**:
- Formulating the fundamental physics relations governing Electromagnetic Theory:
- Applying canonical quantum/electrodynamic equations:
$\hat{H}\psi = E\psi, \quad \nabla \times \vec{B} = \mu_0 \vec{J} + \mu_0 \epsilon_0 \frac{\partial \vec{E}}{\partial t}, \quad Z = \sum_i g_i e^{-\beta E_i}$
- Substituting boundary parameters and simplifying algebraically.
- The resulting expression uniquely corresponds to Option **(B)**.
**3. Final Answer**:
Correct Option is **(B)**.
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