Question

The emitting antenna of a 100-kW radio station radiates equally in all directions.

Part A

What is the magnitude Emax 600 m from the antenna?

Express your answer to two significant digits and include the appropriate units.

Emax =

Part B

What is the magnitude Bmax 600 m from the antenna?

Express your answer to two significant digits and include the appropriate units.

Bmax =

Part C

For the distance of 600 m from the antenna, calculate the maximum potential difference caused between the ends of a receiving antenna that is 1.0 m long, assuming the antenna is aligned perfectly with the electric field of the radio wave.

Express your answer to two significant digits and include the appropriate units

V =

Part D

What is the magnitude Emax 50 km from the antenna?

Express your answer with the appropriate units.

Emax =

Part E

What is the magnitude Bmax 50 km from the antenna?

Express your answer with the appropriate units.

Bmax =

Part F

For the distance of 50 km from the antenna, calculate the maximum potential difference caused between the ends of a receiving antenna that is 1.0 m long, assuming the antenna is aligned perfectly with the electric field of the radio wave.

Express your answer with the appropriate units.

V =

Answer 1

a)

P = power = 100 kW = 10⁵ Watt

r = distance = 600 m

I = intensity

Intensity is given as

I = P/(4r²)

I =  10⁵/(4 (3.14) (600)²)

I = 0.022 W/m²

amplitude of electric field is given as

E_max = sqrt(2I/(c))

E_max = sqrt(2(0.022)/((8.85 x 10^-12) (3 x 10⁸)))

E_max = 4.1 N/C

b)

amplitude of magnetic field is given as

B_max = E_max /c

B_max = 4.1/(3 x 10⁸) = 1.4 x 10^-8 T

c)

L = length of recieving antenna = 1 m

maximum potential difference is given as

V_max = E_max L = 4.1 x 1 = 4.1 volts

d)

P = power = 100 kW = 10⁵ Watt

r = distance = 50 km = 50,000 m

I = intensity

Intensity is given as

I = P/(4r²)

I =  10⁵/(4 (3.14) (50000)²)

I = 3.2 x 10^-6 W/m²

amplitude of electric field is given as

E_max = sqrt(2I/(c))

E_max = sqrt(2(3.2 x 10^-6)/((8.85 x 10^-12) (3 x 10⁸)))

E_max = 0.049 N/C

e)

amplitude of magnetic field is given as

B_max = E_max /c

B_max = 0.049/(3 x 10⁸) = 1.63 x 10^-10 T

f)

maximum potential difference is given as

V_max = E_max L = 0.049 x 1 = 0.049 volts