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An electromagnetic wave travels along the z-axis: E = E₀ cos(k*z - omega*t). Which of the following options are correct?

1. The associated magnetic field is given as B = (1/c) k_hat x E = (1/omega)(k_vec x E)
2. The electromagnetic field can be written in terms of the associated magnetic field as E = c*(B x k_hat)
3. k_hat dot E = 0, k_hat dot B = 0
4. k_hat x E = 0, k_hat x B = 0

Correct answer: The associated magnetic field is given as B = (1/c) k_hat x E = (1/omega)(k_vec x E)

Solution

For an EM wave propagating in k_hat direction: B = (k_hat x E)/c = (k_vec x E)/omega (since k_vec = k*k_hat and omega = k*c). Also E = c*(B x k_hat). Since E is transverse, k_hat dot E = 0 and k_hat dot B = 0. But k_hat x E != 0. So options 1, 2, 3 are correct; option 4 is wrong.

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