B = E₀c⁻¹sin(kz)cos(ωt)
B = E₀c⁻¹jcos(kz)sin(ωt)
B = E₀c⁻¹jsin(kz)cos(ωt)
B = E₀c⁻¹ksin(kz)cos(ωt)
∇ × 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)