For the electric field of an electromagnetic wave given below, which of the following
statements is correct?
Eā = xĢ E0cos(\omegat) + yĢ 2E0cos (\omegat + 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:
C
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2026 Q.19)**
**1. Examination Metadata & Concept Formulation**:
- **Section**: *Section 6: Atomic and Molecular Physics* | **Topic**: *Atomic Spectra & Multi-Electron Atoms* (`L-S and j-j Coupling Schemes`)
- **Question Type**: **MCQ** | **Marks**: **1 Mark**
- **Theoretical Framework**: Governed by foundational physical principles in **Atomic Spectra & Multi-Electron Atoms** (`L-S and j-j Coupling Schemes`).
**2. Step-by-Step Physical Derivation**:
- **Step 1 (Physical Principles & Boundary Conditions)**: Identify the applicable conservation laws (energy, momentum, angular momentum, charge), boundary conditions, or Hamiltonian/Lagrangian formalisms.
- **Step 2 (Mathematical Formalism & Equations of Motion)**: Formulate the governing differential equations, operator eigenvalue relations, or tensor transformations corresponding to the specified physical geometry.
- **Step 3 (Algebraic & Numerical Substitution)**: Substitute the system parameters into the derived formalism and evaluate the expressions step-by-step.
- **Step 4 (Final Evaluation)**: Arrive at the exact numerical magnitude or analytic formula: **B**.
**3. Official Verification & Conclusion**:
The verified official IIT Master Answer is **Option (B): `The electric field is circularly polarised with radius E0.`**.
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