Q. A plane electromagnetic wave 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 $66\ V\ m^{- 1}$. 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) $E_{0} = 66Vm^{- 1}$
$B_{0} = \frac{E_{0}}{C} = \frac{66}{3 \times 10^{8}} = 2.2 \times 10^{- 7}T$
Since electromagnetic wave is of transverse nature. Hence if electric field is along $y$-axis, then magnetic field must be in $z$-axis. Since propagation is $x$-axis. Hence correct option is (d)
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.