Suppose you are listening to the WKAR FM radio station on a car radio. The carri

Question

Suppose you are listening to the WKAR FM radio station on a car radio. The carrier frequency of the transmission is 90.5 MHz. Assume the RMS electric field of the wave at your location is 0.00197 V/m.

(A) Calculate the mean Poynting vector at your location. Include the unit, W/m^2, in your answer. {Note: if the answer is 1.23×10-4 W/m2, then the answer submitted to lon-capa should be written as 1.23e-4 W/m2.}
(B) Calculate the mean energy flux, in W/m2. Include the unit in your answer.
(C) Calculate the amplitude of oscillation of the magnetic field. Include the unit, T, in your answer.
(D) Calculate the amplitude of oscillation of the electric field. Include the unit, V/m, in your answer.
(E) Calculate the wavelength of the carrier wave. Include the unit, m, in your answer.

Explanation / Answer

Given that Frequency f = 90.5 M Hz Rms electric field of the wave is Erms = 0.00197V /m                                                             =197*10^-5 V/m Em =Erms*2      =278.6*10^-5 V/m magnetic field is Bm= Em / c                                  = 278.6*10^-5 V/m / 3.0*10^8 m/s                                   = 92.86*10^-13 T A) Mean poynting vector is S =( 1/ 0 ) (Em*Bm )                                       S = 1/ 4*10^-7 * 278.6*10^-5 V /m * 92.86*10^-13 T                                           = 2059.92*10^11 W / m^2   B ) S mean energy is Smean = Bm * Em / 2                                           = 92.86*10^-13 T *(278.6*10^-5 V/m) / 2                                           = 0.12935*10^-13 W / m^2 C ) Amplitude of oscillation of magnetic field is         magnetic field is Bm = Em / c                                        = 278.6*10^-5V /m / 3.0*10^8 m/s                                       =92.86*10^-13 T D) Amplitude of oscillation of electric field is                           Em = Erms * 2                                  = (197*10^-5V /m)* 2                                   = 278.6*10^-5 V/m E ) wavelength   is = c / f                                      = 3.00*10^8 m/s / 90.5 *10^6 Hz                                      = 3.31m Given that Frequency f = 90.5 M Hz Rms electric field of the wave is Erms = 0.00197V /m                                                             =197*10^-5 V/m Em =Erms*2      =278.6*10^-5 V/m magnetic field is Bm= Em / c                                  = 278.6*10^-5 V/m / 3.0*10^8 m/s                                   = 92.86*10^-13 T A) Mean poynting vector is S =( 1/ 0 ) (Em*Bm )                                       S = 1/ 4*10^-7 * 278.6*10^-5 V /m * 92.86*10^-13 T                                           = 2059.92*10^11 W / m^2 Mean poynting vector is S =( 1/ 0 ) (Em*Bm )                                       S = 1/ 4*10^-7 * 278.6*10^-5 V /m * 92.86*10^-13 T                                           = 2059.92*10^11 W / m^2   B ) S mean energy is Smean = Bm * Em / 2                                           = 92.86*10^-13 T *(278.6*10^-5 V/m) / 2                                           = 0.12935*10^-13 W / m^2 C ) Amplitude of oscillation of magnetic field is         magnetic field is Bm = Em / c                                        = 278.6*10^-5V /m / 3.0*10^8 m/s                                       =92.86*10^-13 T D) Amplitude of oscillation of electric field is                                        = 278.6*10^-5V /m / 3.0*10^8 m/s                                       =92.86*10^-13 T D) Amplitude of oscillation of electric field is                           Em = Erms * 2                                  = (197*10^-5V /m)* 2                                   = 278.6*10^-5 V/m                                  = (197*10^-5V /m)* 2                                   = 278.6*10^-5 V/m E ) wavelength   is = c / f                                      = 3.00*10^8 m/s / 90.5 *10^6 Hz                                      = 3.31m

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