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
**E****⃗** 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.

A
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