A satellite in geostationary orbit is used to transmit data via electromagnetic

Question

A satellite in geostationary orbit is used to transmit data via electromagnetic radiation. The satellite is at a height of 3.3×10^4 km, above the surface of the earth, and we assume it has an isotropic power output of 33.5 kW , (although, in practice, satellite antennas transmit signals that are less powerful but more directional).

Reception devices pick up the variation in the electric field vector of the electromagnetic wave sent out by the satellite. Given the satellite specifications listed in the problem introduction, what is the amplitude Eo of the electric field vector of the satellite broadcast as measured at the surface of the earth? Use e0, for the permittivity of space and 3x10^8 m/s for the speed of light.

Eo = ? V/m

Explanation / Answer

HELLOO! Intensity I = power/area = 1000/(4pr^2) w/m^2, where r = 3.5E7 m. I = 6.49612E-14 w/m^2 I = EH = E^2/376.73 (see ref. 1). ? E = sqrt(376.73*I) = 4.947 µv/m. Note: 376.73 is the value of free-space impedance Z0 in ohms. This number is derived from the electric constant e0 = 8.854187E-12 and magnetic constant µ0 = 1E-7*4p, as Z0 = sqrt(µ0/e0) = 376.73 ohms. Hope it helps! Have a nice day :)

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