Question

A plane electromagnetic wave varies sinusoidally at 90.0 MHz as it travels along the x direction. The peak value of the electric field is 200 V/m, and it is directed along the y direction. Find the wavelength, the period and the maximum value of the magnetic field. Write expressions in SI units for the space and time variations of the electric field and of the magnetic field. Include numerical values, and include subscripts to indicate coordinate directions. Find the average power per unit area that this wave propagates through space.

Answer 1

Answer:

Explanation:

frequency n = 90 x 10⁶ Hz .

time period T = 1 / n

= 1 / 90 x 10⁶

= 1.11 x 10⁻⁸ S.

wavelength = velocity of light / frequency

= 3 x 10⁸ / 90 x 10⁶

= 3.33 m

maximum value of the magnetic field. ( B₀ )

E₀ / B₀ = c where E₀ and  B₀ are maximum electric and magnetic field .

E₀ / c=  B₀

200/ 3 x 10⁸

= 66.67 x 10⁻⁸ T .

expressions in SI units for the space and time variations of the electric field

$E=E_{0y}sin(2\pi nt - \frac{2\pi x}{\lambda} )$

$E=200sin(180\times 10^6\pi t - \frac{2\pi x}{\lambda} )$ N/C

$B=B_{0z}sin(2\pi nt - \frac{2\pi x}{\lambda} )$

$B=66.67\times 10^{-8}sin(180\times 10^6\pi t - \frac{2\pi x}{\lambda} )$ T