Question

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 RRR which focuses the electromagnetic energy incident from the satellite onto a receiver which has a surface area of 5 cm2cm2. How large does the radius RRR of the dish have to be to achieve an electric field vector amplitude of 0.1 mV/mmV/m at the receiver

Answer 1

R₁ = 0.126 m

Step-by-step explanation:

Let's use the definition of intensity which is the power per unit area

I = P / A

the generated power is constant

P = I A

power is

P = E / t

if we perform the calculations for a given time, the wave energy is

E = q V

we substitute

P =
`(q V\ A)/(t)`

we can write this equation for two points, point 1 the antenna and point 2 the receiver

V₁A₁ = V₂A₂

A₁ =
`(V_2)/(V_1) \ A_2`

A₁ = 0.1 10⁻³ 5 10⁻⁴ /V₁

A₁ = 5 10⁻⁸ /V₁

In general, the electric field on the antenna is very small on the order of micro volts, suppose V₁ = 1 10⁻⁶ V

let's calculate

A₁ = 5 10⁻⁸ / 1 10⁻⁶

A₁ = 5 10⁻² m²

the area of ​​a circle is

A = π r²

we substitute

π R1₁²= 5 10⁻²

R₁ =
`\sqrt{ (5 \ 10^(-2) )/(\pi ) }}`

R₁ = 0.126 m