Question

A satellite beams microwave radiation with a power of 13 toward the Earth's surface, 550 away. When thebeam strikes Earth, its circular diameter is about 1000. Find the rms electric field strength of the beam at the surface of the Earth.

Answer 1

`E_(rms) = 2.27 V/m`

Step-by-step explanation:

Power of microwave radiation = 13 kW = 13 x 10³ W

Diameter = 1000 m

Radius = R = 1000/2 = 500 m

distance, r = 500 Km

r = 500 x 10³ m

Electric strength of beam of light is given as

`S = (P)/(A) = c\epsilon_0 E_(rms)^2`

Now,

`E_(rms) =\sqrt{(P)/(Ac\epsilon_0)}`

c is speed of light

ε₀ is permittivity of free space

A is the area of circle = π r² = π x (500 x 10³)² = 7.853 x 10¹¹ m²

`E_(rms) =\sqrt{(13* 10^3)/(7.853 * 10^(11)* 3 * 10^8 * 8.85* 10^(-12))}`

`E_(rms) =\sqrt{(13* 10^3)/(7.853 * 10^(11)* 3 * 10^8 * 8.85* 10^(-12))}`

`E_(rms) = 2.27 V/m`