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).Imagine that the satellite described in the problem introduction is used to transmit television signals. You have a satellite TV reciever consisting of a circular dish of radius R which focuses the electromagnetic energy incident from the satellite onto a receiver which has a surface area of 5 cm^2.How large does the radius R of the dish have to be to achieve an electric field vector amplitude of 0.1 mV/m at the receiver?

Answer 1

Step-by-step explanation:

We have the following relation between power, P and intensity, I

`I = P/(4*pi*r^2)`

=
`10^3/(4*pi*(35000*10^3))`

=
`6.5*10^-14 W/M^2`

We also have the following relationship between electric field and electromagnetic radiation thus

`I = (ceE^2)/2`

Hence
`E = √(2I/ce)`

substituting the values of I, c and e, we have

`7*10^-6 V/m`