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The electric field of a plane polarized electromagnetic wave in free space at time t = 0 is given by an expression E⃗(x, y) = 10ȷ̂ cos[(6x + 8z)]. The magnetic field B⃗(x,z,t) is given by (c is the velocity of light)

Asked in JEE Main 10th Jan 2nd Shift 2019 · Writing B from E, and E from B

Answer: (1) 1/c(6k̂ - 8ı̂) cos[(6x + 8z - 10ct)]

Step-by-step solution

k⃗ = 6ı̂ + 8k̂, |k⃗| = 10 ⇒ ω = 10c and n̂ = (6ı̂ + 8k̂)/10

so E⃗ = 10ȷ̂ cos(6x + 8z - 10ct)

B⃗ = (1/c) n̂ × E⃗ = (1/c)(1/10)(6ı̂ + 8k̂) × 10ȷ̂ cos[…] = (1/c)(6k̂ - 8ı̂) cos[…], using ı̂ × ȷ̂ = k̂ and k̂ × ȷ̂ = -ı̂

Why the other options are wrong

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