The magnetic field in a plane electromagnetic wave is given by: B _...

Recall the standard form of the equation of electromagnetic wave in terms of the magnetic field, ${B}_{y} = {B}_{0}\sin \left(kx + \omegat\right)T$, here ${B}_{0}$ is the magnitude of magnetic field, $k = \dfrac{2\pi}{\lambda} \text{ and } \omega = 2\pif$. The equation is given in the question, ${B}_{y} = 2 \times {10}^{- 7}\sin \left(\pi \times {10}^{3}x + 3\pi \times {10}^{11}t\right)T$

$⇒ \lambda = \dfrac{2\pi}{k} = \dfrac{2\pi}{\pi \times {10}^{3}}$$⇒ \lambda = 2 \times {10}^{- 3}m$.