Answer:
[tex]E_{rms} = 2.27 V/m[/tex]
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
[tex]S = \dfrac{P}{A} = c\epsilon_0 E_{rms}^2[/tex]
Now,
[tex]E_{rms} =\sqrt{\dfrac{P}{Ac\epsilon_0}}[/tex]
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
[tex]E_{rms} =\sqrt{\dfrac{13\times 10^3}{7.853 \times 10^{11}\times 3 \times 10^8 \times 8.85\times 10^{-12}}}[/tex]
[tex]E_{rms} =\sqrt{\dfrac{13\times 10^3}{7.853 \times 10^{11}\times 3 \times 10^8 \times 8.85\times 10^{-12}}}[/tex]
[tex]E_{rms} = 2.27 V/m[/tex]
