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An electromagnetic wave travels along the z-axis: E = E0*cos(kz - omega*t). Which of the following are correct? (A) B = (1/c)*(k_hat cross E) = (1/omega)*(k_vec cross E) (B) E = c*(B cross k_hat) (C) k_hat dot E = 0, k_hat dot B = 0 (D) k_hat cross E = 0, k_hat cross B = 0

1. B = (1/c)*(k_hat cross E) = (1/omega)*(k_vec cross E)
2. E = c*(B cross k_hat)
3. k_hat dot E = 0, k_hat dot B = 0
4. k_hat cross E = 0, k_hat cross B = 0

Correct answer: B = (1/c)*(k_hat cross E) = (1/omega)*(k_vec cross E)

Solution

For a plane EM wave along z: (A) B = (1/c)(k_hat cross E); since k_vec = k*k_hat and k/omega = 1/c, also B = (1/omega)(k_vec cross E). Correct. (B) From B = (1/c)(k_hat cross E), using vector identity: E = c(B cross k_hat). Correct. (C) k_hat perpendicular to both E and B (transverse wave) => dot products are zero. Correct. (D) k_hat cross E = 0 and k_hat cross B = 0 would mean E, B parallel to k_hat — INCORRECT for transverse EM waves. Correct options: A, B, C.

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