- Home
- Standard 12
- Physics
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 $66\ Vm^{-1}$. The equations for the electric and magnetic fields as a function of $x$ and $t$ are respectively :-
$E_y = 33\ cos\ \pi \times 10^{11} \left( {t - \frac{x}{c}} \right)$
$B_z = 1.1 \times 10^{-7}\ cos \pi \times 10^{11}\left( {t - \frac{x}{c}} \right)$
$E_y = 11\ cos\ 2\pi \times 10^{11} \left( {t - \frac{x}{c}} \right)$
$B_z = 11 \times 10^{-7}\ cos 2\pi \times 10^{11}\left( {t - \frac{x}{c}} \right)$
$E_y = 33\ cos\ \pi \times 10^{11} \left( {t - \frac{x}{c}} \right)$
$B_z = 11 \times 10^{-7}\ cos \pi \times 10^{11}\left( {t - \frac{x}{c}} \right)$
$E_y = 66\ cos\ 2\pi \times 10^{11} \left( {t - \frac{x}{c}} \right)$
$B_z = 2.2 \times 10^{-7}\ cos 2\pi \times 10^{11}\left( {t - \frac{x}{c}} \right)$
Solution
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
$\mathrm{B}_{\mathrm{z}}=\frac{\mathrm{E}_{\mathrm{y}}}{\mathrm{c}}$
$=\left(\frac{66}{3 \times 10^{8}}\right) \cos 2 \pi \times 10^{11}\left(\mathrm{t}-\frac{\mathrm{x}}{\mathrm{c}}\right)$
$=22 \times 10^{-8} \cos 2 \pi \times 10^{11}\left(t-\frac{x}{c}\right)$
$=2.2 \times 10^{-7} \cos 2 \pi \times 10^{11}\left(\mathrm{t}-\frac{\mathrm{x}}{\mathrm{c}}\right)$
