The electric field in a plane electromagnetic wave is given by : $E_y=69 \sin \left[0.6 imes 10^3

Question

The electric field in a plane electromagnetic wave is given by : $E_y=69 \sin \left[0.6 	imes 10^3 x-1.8 	imes 10^{11} tight] \mathrm{V} / \mathrm{m}$. The expression for magnetic field associated with this electromagnetic wave is $\_\_\_\_$ T.

Professor PC Thomas Classes · Answer

The amplitude of the magnetic field is $B_0 = \frac{E_0}{c}$, where $c = \frac{\omega}{k} = \frac{1.8 	imes 10^{11}}{0.6 	imes 10^3} = 3 	imes 10^8 	ext{ m/s}$. Thus, $B_0 = \frac{69}{3 	imes 10^8} = 2.3 	imes 10^{-7} 	ext{ T}$. The direction of wave propagation is $+\hat{i}$ and electric field is along $+\hat{j}$. Since direction of propagation is along $\vec{E} 	imes \vec{B}$, the magnetic field must be along $+\hat{k}$ direction (z-axis). Therefore, $B_z = 2.3 	imes 10^{-7} \sin\left[0.6 	imes 10^3 x - 1.8 	imes 10^{11} tight]$.