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An electromagnetic wave with frequency ω and wavelength λ travels in the +y direction. Its magnetic field is along +x axis. The vector equation for the associated electric field (of amplitude E₀) is

Asked in JEE Main Online 2012 · Writing B from E, and E from B

• (1) E⃗ = - E₀ cos(ω t + (2π)/λ y) x̂
• (2) E⃗ = E₀ cos(ω t - (2π)/λ y) x̂
• (3) E⃗ = E₀ cos(ω t - (2π)/λ y) ẑ
• (4) E⃗ = - E₀ cos(ω t + (2π)/λ y) ẑ

Step-by-step solution

Why the other options are wrong

• (1) E along x̂ is B's own direction, and (ω t + (2π/λ)y) is a wave travelling along - y
• (2) comes from phase right, but E along x̂ is parallel to B
• (4) comes from direction ẑ is right, but the phase (ω t + (2π/λ)y) describes propagation along - y

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