For the electric field of an electromagnetic wave given below, which of the following
statements is correct?
Eā = xĢ E0cos(št) + yĢ 2E0cos (št + š
2)
Options:
(A) The electric field is linearly polarised with slope 2.
(B) The electric field is circularly polarised with radius E0.
(C) The electric field is elliptically polarised with a ratio of major to minor axis being 2.
(D) The electric field is unpolarised with the two components being phase shifted by š/2.
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2026 Q.19)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Electromagnetic Theory** within *Section 3: Electromagnetic Theory* (1 Mark, 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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