GATE PH 2026 • Q11 MCQ • 1 Mark

Section 3: Electromagnetic Theory

Electromagnetic Theory

Subtopic: Maxwell's Equations, Waveguides & Radiation

Question Statement:

In free space, an electromagnetic wave is travelling whose wavevector is k⃗ = 10(x̂ + √3ŷ) m-1 . The electric field component of this electromagnetic wave is given by E⃗ (r , t) = ẑ 600 cos(k⃗ ⋅ r - 𝜔t) V.m-1 . The speed of light in free space is c = 3.0 × 108 m.s-1. The corresponding magnetic field B⃗ (r , t) is

Options:

  • (A) B⃗ (r , t) = 2 × 10-6(√3x̂ - ŷ) cos(k⃗ ⋅ r - 𝜔t) V.m-2.s
  • (B) B⃗ (r , t) = 10-6(√3x̂ - ŷ) cos(k⃗ ⋅ r - 𝜔t) V.m-2.s
  • (C) B⃗ (r , t) = 2 × 10-5(-√3x̂ + ŷ) cos(k⃗ ⋅ r - 𝜔t) V.m-2.s
  • (D) B⃗ (r , t) = 10-5(√3x̂ - ŷ) cos(k⃗ ⋅ r - 𝜔t) V.m-2.s

Official Answer Key:

B

Step-by-Step Solution & Explanation

### **Official Solution & Step-by-Step Derivation (GATE PH 2026 Q.11)** **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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