Question

Suppose a 20-kW radio station emits EM waves uniformly in all directions.

Part A

How much energy per second crosses a 1.4 m2 area 1 km from the transmitting antenna?

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

Part B

What is the rms magnitude of the E⃗ field at this point, assuming the station is operating at full power?

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

Part C

What is the voltage induced in a 1.4-m-long vertical car antenna 1.0 km away?

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

Part D

What is the voltage induced in a 1.4-m-long vertical car antenna 75 km away?

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

Answer 1

A.) Energy(P) = I/A = (Po/Atotal)*A

P = [(20,000)/(4*pi*(1*10^3)^2)]*(1.4)

P = 2.23 mW

B.) Since, S= c*epsilon*Erms^2 = P/(4*pi*r^2)

Erms = sqrt[P/(4*pi*r^2*c*epsilon)]

Erms = sqrt[2.23*10^-3/(4*pi*(10^3)^2*(3*10^8)*(8.85*10^-12)]

Erms = 0.26 mV/m

C.)

Vrms = Erms*d

Vrms = 0.26*10^-3*1.4

Vrms = 0.36 mV

D.)

Erms = sqrt[2.23*10^-3/(4*pi*(75*10^3)^2*(3*10^8)*(8.85*10^-12)]

Erms = 3.45*10^-6 V/m

So, Vrms = Erms*d

Vrms = (3.45*10^-6)*1.4

(3.45*10^-6)*1.4

(3.45*10^-6)*1.4

(3.45*10^-6)*1.4

Vrms = 4.83*10^-6 V

please upvote.