A plane EM wave is propagating along the $x$ direction. It has a wavelength of $4\ \text{mm}$. If the electric field is in the $y$ direction with the maximum magnitude of $60\ \text{V m}^{-1}$, the equation for magnetic field is:
Answer: (A) $B_z = 2\times10^{-7}\sin\left[\dfrac\pi2\times10^3\left(x - 3\times10^8t\right)\right]\hat k\ \text{T}$
$B_0 = \dfrac{E_0}{c} = \dfrac{60}{3\times10^8} = 2\times10^{-7}\ \text{T}$ and $k = \dfrac{2\pi}{\lambda} = \dfrac{2\pi}{4\times10^{-3}} = \dfrac\pi2\times10^3\ \text{m}^{-1}$.
With $\vec E$ along $y$ and propagation along $x$, $\vec B$ is along $z$ ($\hat j\times\hat k = \hat i$):
$$B_z = 2\times10^{-7}\sin\left[\frac\pi2\times10^3(x - 3\times10^8t)\right]\hat k\ \text{T}$$
Solution by Sreeraj P, M.Sc Physics