Question

The amplitude of an electric field is 0.4 v/m 23 km from a radio transmitter. What is the total power emitted by the transmitter, if one assumes the radiation is emitted isotropically. The impedence of free space is 377 ohms. Answer in units of W.

Answer 1

To solve this problem we will apply the concepts related to the relationship between the voltage, the electric field and the distance, once the voltage is found we will use the definition of power, which is defined as the square of the voltage over the resistance. This is,

$V=Ed$

E = Electric field

d= Distance between the points

Replacing,

$V=0.4*23000$

$V=9200 V$

Now applying the relation for power we have,

$P=\frac{V^2}{R}$

Here

V = Voltage

R = Resistance

Replacing,

$P= \frac{9200^2}{377}$

$P=224509.3 W$

Therefore the total power emmited by the transmitter is 224509.3 W