Question

A 130-kW radio station broadcasts its signal uniformly in all directions. Part A) What is the average intensity of its signal at a distance of 7.60 km from the station?

Part B) What is the rms value of the electric field in this radio wave? Express your answer to three significant figures and include appropriate units. Part C) If a 1.22-m receiving antenna is oriented parallel to the electric field of the radio wave, what rms voltage appears between its ends?

Answer 1

a) 1.8 x 10⁻⁴ Wm⁻²

b) 0.26 N/C

c) 0.32 Volts

Step-by-step explanation:

a)

P = Power of the signal emitted by radio station = 130 kW = 130000 W

r = distance of the location = 7.60 km = 7600 m

I = average intensity of its signal

Using the equation

P = I (4πr²)

130000 = I (4(3.14) (7600)²)

I = 1.8 x 10⁻⁴ Wm⁻²

B)

E = rms value of electric field

Intensity of electromagnetic wave is given as

I = ε₀ E² c

1.8 x 10⁻⁴ = (8.85 x 10⁻¹²) (3 x 10⁸) E²

E = 0.26 N/C

C)

V = rms voltage between the ends

d = distance between the ends = 1.22 m

rms voltage between the ends is given as

V = E d

V = (0.26) (1.22)

V = 0.32 Volts