Question

For a plane electromagnetic wave, the magnetic field at a point $x$ and time $t$ is $\vec{B}(x,t)=\left[1.2\times 10^{-7}\sin \left(0.5\times 10^{3}x+1.5\times 10^{11}t\right)\hat{k}\right]T$ The instantaneous electric field $\vec{E}$ corresponding to $\vec{B}$ is :
(speed of light $c=3\times 10^{8}m{s}^{-1})$

• A. $\vec{E}(x,t)=\left[36\sin \left(0.5\times 10^{3}x+1.5\times 10^{11}t\right)\hat{k}\right]\frac{v}{m}$
• B. $\vec{E}(x,t)=\left[-36\sin \left(0.5\times 10^{3}x+1.5\times 10^{11}t\right)\hat{j}\right]\frac{v}{m}$
• C. $\vec{E}(x,t)=\left[36\sin \left(1\times 10^{3}x+0.5\times 10^{11}t\right)\hat{j}\right]\frac{v}{m}$
• D. $\vec{E}(x,t)=\left[36\sin \left(1\times 10^{3}x+1.5\times 10^{11}t\right)\hat{j}\right]\frac{v}{m}$

Answer 1

Answer: (B)

$\vec{E}$ and $\vec{B}$ are perpendicular for EM wave
$E_0=C{B}_0$
$=3\times 10^8\times 1.2\times 10^{-7}=36$
Having same phase
Propagation is along $-x$ -axis, $\vec{B}$ is along $z$ -axis
hence $\vec{E}$ must be along $y$ -axis