Question

# Consider an antenna which releases an electromagnetic wave of 3cm wavelength traveling in air(of index of...

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?

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)

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