Estimate the amplitude of the electric field at this distance.?
FM radio station KRTH in Los Angeles broadcasts on an assigned frequency of 101 MHz with a power of 50,000 W.
(a) What is the wavelength of the radio waves produced by this station?=2.97 m
(b) Estimate the average intensity of the wave at a distance of 40.9 km from the radio transmitting antenna. Assume for the purpose of this estimate that the antenna radiates equally in all directions, so that the intensity is constant over a hemisphere centered on the antenna.=4.757e-06 W/m^2
(c) Estimate the amplitude of the electric field at this distance.=?
FM radio station KRTH in Los Angeles broadcasts on an assigned frequency of 101 MHz with a power of 50,000 W.
(a) What is the wavelength of the radio waves produced by this station?=2.97 m
(b) Estimate the average intensity of the wave at a distance of 40.9 km from the radio transmitting antenna. Assume for the purpose of this estimate that the antenna radiates equally in all directions, so that the intensity is constant over a hemisphere centered on the antenna.=4.757e-06 W/m^2
(c) Estimate the amplitude of the electric field at this distance.=?
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a) speed of wave = frequency x wavelength
frequency = 1.01x10^8 Hz
speed = 3x10^8 m/s
wavelength = 3x10^8m/s / 1.01x10^8 Hz = 2.97m
b) average intensity a distance r from a point source is
Power/4 pi r^2 = 50,000W/(4 x 3.14 x 40,900m^2) = 4.76x10^-6 W/m^2
c) the intensity of an electromagnetic wave is given by
= average intensity = (epsilon0 c/2)E^2
where epsilon0=the permittivity of free space = 8.85x10^-12 in MKS units
c=speed of light, and E is the electric field strength (what we are looking for), so we have that
4.76x10^-6W/m^2 = (8.85x10^-12 x 3x10^8)E^2 / 2
E = 0.06Volts/m
the answer to this last question involves knowledge of the Poynting vector, a vector which describes the magnitude and direction of energy flux
frequency = 1.01x10^8 Hz
speed = 3x10^8 m/s
wavelength = 3x10^8m/s / 1.01x10^8 Hz = 2.97m
b) average intensity a distance r from a point source is
Power/4 pi r^2 = 50,000W/(4 x 3.14 x 40,900m^2) = 4.76x10^-6 W/m^2
c) the intensity of an electromagnetic wave is given by
= average intensity = (epsilon0 c/2)E^2
where epsilon0=the permittivity of free space = 8.85x10^-12 in MKS units
c=speed of light, and E is the electric field strength (what we are looking for), so we have that
4.76x10^-6W/m^2 = (8.85x10^-12 x 3x10^8)E^2 / 2
E = 0.06Volts/m
the answer to this last question involves knowledge of the Poynting vector, a vector which describes the magnitude and direction of energy flux