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Question:

The electric field of a plane electromagnetic wave is given by y = E₀icos(kz)(ωt). The corresponding magnetic field B is then given by:

B = E₀c⁻¹sin(kz)cos(ωt)

B = E₀c⁻¹jcos(kz)sin(ωt)

B = E₀c⁻¹jsin(kz)cos(ωt)

B = E₀c⁻¹ksin(kz)cos(ωt)

Solution:

∇ × E = -∂B/∂t
Given that wave is propagating along positive z-axis and E along positive x-axis. Hence B along y-axis.
From Maxwell equation
∇ × E = -∂B/∂t
i.e., ∂E/∂z = -∂B/∂t
and B₀ = E₀/c
so, B = -E₀c⁻¹jsin(kz)cos(ωt)