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A plane electromagnetic wave is propagating along the direction (ı̂ + ȷ̂)/(√2), with its polarization along the direction k̂. The correct form of the magnetic field of the wave would be (Here B₀ is an appropriate constant.)

Asked in JEE Main 9th Jan 2nd Shift 2020 · Writing B from E, and E from B

• (1) B₀ (ı̂ + ȷ̂)/(√2) cos(ω t - k (ı̂ + ȷ̂)/(√2))
• (2) B₀ k̂ cos(ω t - k (ı̂ + ȷ̂)/(√2))
• (3) B₀ (ı̂ - ȷ̂)/(√2) cos(ω t - k (ı̂ + ȷ̂)/(√2))
• (4) B₀ (ȷ̂ - ı̂)/(√2) cos(ω t + k (ı̂ + ȷ̂)/(√2))

Step-by-step solution

Why the other options are wrong

• (1) B is placed along n̂, the propagation direction — B must be perpendicular to it
• (2) B along k̂ is E's own direction; that is the polarisation, not B
• (4) (ȷ̂ - ı̂)/√2 is the reverse of B̂, and the phase (ω t + k n̂·r⃗) reverses the direction of travel

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