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An electromagnetic wave travels in the negative z-direction. Its electric field is given by E = 480 * cos(2 * 10⁷ * z + 6 * 10¹⁵ * t) * (-i_hat + 2 * j_hat) V/m. What is the associated magnetic field B?

1. B = 1.6 * 10⁻⁶ * cos(2 * 10⁷ * z + 6 * 10¹⁵ * t) * (-2 * i_hat - j_hat) Wb/m²
2. B = 1.6 * 10⁻⁶ * cos(2 * 10⁷ * z + 6 * 10¹⁵ * t) * (-i_hat + 2 * j_hat) Wb/m²
3. B = 1.6 * 10⁻⁶ * cos(2 * 10⁷ * z + 6 * 10¹⁵ * t) * (2 * i_hat + j_hat) Wb/m²
4. B = 1.6 * 10⁻⁶ * cos(2 * 10⁷ * z + 6 * 10¹⁵ * t) * (2 * i_hat - j_hat) Wb/m²

Correct answer: B = 1.6 * 10⁻⁶ * cos(2 * 10⁷ * z + 6 * 10¹⁵ * t) * (2 * i_hat + j_hat) Wb/m²

Solution

The wave propagates in the -z direction. Using B = (k_hat x E)/c with k_hat = -z_hat and E direction vector (-i+2j), the cross product gives (2i+j), and the magnitude becomes 480/(3*10⁸) = 1.6*10⁻⁶.

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