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The electric field of a plane electromagnetic wave is given by E⃗ = E₀ ı̂ cos(kz) cos(ω t). The corresponding magnetic field B⃗ is then given by

Asked in JEE Main 10th April 1st Shift 2019 · Direction of travel and standing waves

• (1) B⃗ = (E₀)/c ȷ̂ sin(kz) sin(ω t)
• (2) B⃗ = (E₀)/c k̂ sin(kz) cos(ω t)
• (3) B⃗ = (E₀)/c ȷ̂ cos(kz) sin(ω t)
• (4) B⃗ = (E₀)/c ȷ̂ sin(kz) cos(ω t)

Step-by-step solution

Why the other options are wrong

• (2) B along k̂ — for E along ı̂ with a z-dependence, abla × E⃗ lies along ȷ̂
• (3) comes from the space factor must become sin(kz): differentiating cos(kz) with respect to z gives - k sin(kz)
• (4) sin(kz)cos(ω t) keeps B in phase with E; integrating ∂ B/∂ t ∝ cos(ω t) gives sin(ω t), so B lags E by a quarter period

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