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 $c = 3 \times 10^{8}\, ms^{-1})$

• 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