Question

An EM wave propagating in $x$-direction has a wavelength of $8\, mm$. The electric field vibrating $y -$ direction has maximum magnitude of $60\, Vm ^{-1}$. Choose the correct equations for electric and magnetic fields if the EM wave is propagating in vacuum :

• A. $E _{ y }=60 \sin \left[\frac{\pi}{4} \times 10^{3}\left( x -3 \times 10^{8} t \right)\right] \hat{ j} Vm ^{-1}$
  $B _{ z }=2 \sin \left[\frac{\pi}{4} \times 10^{3}\left( x -3 \times 10^{8} t \right)\right] \hat{ k } T$
• B. $E _{ y }=60 \sin \left[\frac{\pi}{4} \times 10^{3}\left( x -3 \times 10^{8} t \right)\right] \hat{ j} Vm ^{-1}$
  $B _{ z }=2 \times 10^{-7} \sin \left[\frac{\pi}{4} \times 10^{3}\left( x -3 \times 10^{8} t \right)\right] \hat{ k } T$
• C. $E _{ y }= 2 \times 10^{-7}\sin \left[\frac{\pi}{4} \times 10^{3}\left( x -3 \times 10^{8} t \right)\right] \hat{ j} Vm ^{-1}$
  $B _{ z }=60 \sin \left[\frac{\pi}{4} \times 10^{3}\left( x -3 \times 10^{8} t \right)\right] \hat{ k } T$
• D. $E _{ y }= 2 \times 10^{-7}\sin \left[\frac{\pi}{4} \times 10^{4}\left( x -4 \times 10^{8} t \right)\right] \hat{ j} Vm ^{-1}$
  $B _{ z }=60 \sin \left[\frac{\pi}{4} \times 10^{4}\left( x -4 \times 10^{8} t \right)\right] \hat{ k } T$

Answer 1

Answer: (B)

$B _{0}=\frac{ E _{0}}{ c }=\frac{60}{3 \times 10^{8}}=2 \times 10^{-7} T$
$E \times B$ must be direction of propagation.
So, B $\rightarrow$ z-axis
$ k =\frac{2 \pi}{\lambda}=\frac{\pi}{4} \times 10^{3} m ^{-1} $
$ E _{ y }=60 \sin \left[\frac{\pi}{4} \times 10^{3}\left( x -3 \times 10^{8} t \right)\right] \hat{ j } Vm ^{-1} $
$B _{ z }=2 \times 10^{-7} \sin \left[\frac{\pi}{4} \times 10^{3}\left( x -3 \times 10^{8} t \right)\right] k T$