Question

A plane electromagnetic wave travelling along the $X-$ direction has a wavelength of $3mm$ . The variation in the electric field occurs in the $Y-$ direction with an amplitude $66V{m}^{-1}$ . 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. $E_y=66\cos 2\pi \times {10}^{11}\left(t-\frac{x}{c}\right),$ $B_z=2.2\times {10}^{-7}\cos 2\pi \times {10}^{11}\left(t-\frac{x}{c}\right)$
• E. $E_y=66\cos \pi \times {10}^{11}\left(t-\frac{x}{c}\right),$ $B_y=2.2\times {10}^{-7}\cos \pi \times {10}^{11}\left(t-\frac{x}{c}\right)$

Answer 1

Answer: (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 $B_z=\frac{E_y}{c}\left(\frac{600}{3\times {10}^8}\right)\cos 2\pi \times {10}^{11}\left(t-\frac{x}{c}\right)$
$=22\times {10}^{-8}\cos 2\pi \times {10}^{11}\left(t-\frac{x}{c}\right)$
$=2.2\times {10}^{-7}\cos 2\pi \times {10}^{11}\left(t-\frac{x}{c}\right)$