Question

Consider an antenna which releases an electromagnetic wave of 3cm wavelength traveling in air(of index of refraction 1) and amplitude of the B-field component of 3mT. what is the resonant frequency of the antenna? write the equation for the E-field component as it propagates in the x direction. How does the equation change if the elctromagnetic wave enters a medium of index of refraction 1.52?

Answer 1

f= c/ lmada = 3 * 10^8/0.03 m = 100 * 10^8 Hz

E = Emax cos ( kx- wt)

Emax = Bmax c = 3* 10^-3 ( 3 * 10^8) =9* 10^5 N/C

E = 9* 10^5 N/C (cos ( 2pi/0.03 * x- 2pi( 100 * 10^8 ) t)

= 9 * 10^5 N/C cos ( 209.33 x - 6.28 * 10^10 t)

when wave enters to new medium new wavlenght is

lamda' = lamda/n = 0.03/1.52 = 0.0197 m

k = 2pi/ lamda'=318.18

f = c/ lamda' = 3 * 10^8/0.0197 = 5.91 * 10^6

w = 2pi f = 2pi ( 5.91 * 10^6) = 37.11 * 10^6

E = 9 * 10^5 N/C cos ( 318.18x - 5.91 * 10^6t)