Complete Question
A satellite in geostationary orbit transmits data using electromagnetic radiation, positioned 35,000 km above the Earth's surface, with an isotropic power output of 1 kW (although actual satellite antennas transmit with less power but more directionally).
Now, imagine this satellite relays television signals and you have a satellite TV receiver with a circular dish of radius R that focuses the electromagnetic energy from the satellite onto a receiver with a surface area of 5 cm2.
What radius R must this dish have to achieve an electric field vector amplitude of 0.1 mV/m at the receiver?
Assuming your house is situated directly beneath the satellite (as calculated previously), that the dish reflects all incoming signals to the receiver without any losses in the reception process, and that the dish has a curvature where R refers to its projection perpendicular to the direction of the incoming signal.
Present your answer in centimeters, rounded to two significant figures.
Answer:
The radius of the dish is 
Explanation:
The question indicates that
The orbital radius is = 
The power output is 
The electric vector amplitude is noted as 
The receiver's area is
Overall, the intensity of the dish can be mathematically expressed as

Here, A represents the area of the orbit, described as the surface area of a sphere, thus calculated as



Ultimately, substituting the values into the intensity equation


Therefore, the intensity received by the dish can be mathematically evaluated as

With c symbolizing the speed of light which has a constant value of
is the permittivity of free space, valued at 
indicates the electric field present on the dish
Assuming no loss, the intensity from the satellite equals the intensity hitting the receiver dish
Setting the electric field intensity as the subject of the formula

Inputting values


The power incident on the dish reflects what is delivered to the receiver

Where
symbolizes the power incident on the dish expressed mathematically as


And
is the incident power on the dish represented as


Equating the two gives

Solving for R yields

Substituting values gives

