Q. A plane Electromagnetic Waves travelling along the $X$-direction has a wavelength of 3 mm. The variation in the electric field occurs in the $Y$-direction with an amplitude 66 Vm$^{-1}$. The equations for the electric and magnetic fields as a function of $x$ and $t$ are respectively
A) $E_{y} = 33\cos{\pi\ \times \ 10^{11}}\left( t - \ \frac{x}{c} \right),$
$B_{z} = 1.1 \times \ 10^{- 7}\cos{\pi \times 10^{11}}\left( t - \frac{x}{c} \right)$
B) $E_{y} = 11\cos{2\pi\ \times 10^{11}}\left( t - \ \frac{x}{c} \right),$
$B_{y} = 11 \times \ 10^{- 7}\cos{2\pi \times 10^{11}}\left( t - \frac{x}{c} \right)$
C) $E_{x} = 33\cos{\pi\ \times \ 10^{11}}\left( t - \ \frac{x}{c} \right),$
$B_{x} = 11 \times \ 10^{- 7}\cos{\pi \times 10^{11}}\left( t - \frac{x}{c} \right)$
D) $E_{y} = 66\cos{2\pi\ \times \ 10^{11}}\left( t - \ \frac{x}{c} \right),$
$B_{z} = 2.2 \times \ 10^{- 7}\cos{2\pi \times 10^{11}}\left( t - \frac{x}{c} \right)$
Explanation
(d) The equation of electric field occurring in $Y$-direction
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ E_{y} = 66\cos{2\pi} \times 10^{11}\left( t - \frac{x}{c} \right)$
Therefore, for the magnetic field in $Z$-direction
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ B_{z} = \frac{E_{y}}{c}$
$= \left( \frac{66}{3\ \times \ 10^{8}} \right)\cos{2\pi\ \times \ 10^{11}}\left( t - \ \frac{x}{c} \right)$
$= 22\ \times \ 10^{- 8}\cos{2\pi\ \times \ 10^{11}}\left( t - \ \frac{x}{c} \right)$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 22\ \times \ 10^{- 7}\cos{2\pi\ \times \ 10^{11}}\left( t - \ \frac{x}{c} \right)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.