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Magnetic field in a plane electromagnetic wave is given by B⃗ = B₀ sin(kx + ω t) ȷ̂ T. Expression for corresponding electric field will be (where c is speed of light.)

Asked in JEE Main Online 2017 · Writing B from E, and E from B

• (1) E⃗ = - B₀c sin(kx + ω t) k̂ V/m
• (2) E⃗ = B₀c sin(kx - ω t) k̂ V/m
• (3) E⃗ = (B₀)/c sin(kx + ω t) k̂ V/m
• (4) E⃗ = B₀c sin(kx + ω t) k̂ V/m

Step-by-step solution

Why the other options are wrong

• (1) comes from with -k̂, (-k̂) × ȷ̂ = +ı̂, so the wave would travel along +x, not - x
• (2) comes from the phase (kx - ω t) is a wave along +x, contradicting the given B
• (3) B₀/c instead of B₀c — E₀ = cB₀

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