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 35,000 km above the surface of the earth, and we assume it has an isotropic power output of 1 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 E0 of the electric field vector of the satellite broadcast as measured at the surface of the earth? Use = 8.85 Times 10-12 C/(V . m) for the permittivity of space and c = 3.00 Times 108 m/s for the speed of light. Express the amplitude of the electric field vector in microvolts per meter to three significant figures.

Explanation / Answer

Intensity I = power/area = 1000/(4?r^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 ?v/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 ?0 = 1E-7*4?, as Z0 = sqrt(?0/e0) = 376.73 ohms

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