- #1

jcap

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Transmitter antenna length ##L=1## m

Transmitter antenna area ##A=1\hbox{ cm}^2##

Number of electrons per unit volume in antenna ##n_e=10^{28}##

Radiation resistance of antenna ##R_R=10\ \Omega##

Power radiated by transmitter ##P_R=1## kW

Frequency ##f=100## MHz

Joules law for the antenna: ##P_R=I^2 R_R##

Current into transmitter antenna ##I=\sqrt{\frac{P_R}{R_R}}=\sqrt{\frac{10^3}{10}}=10## A

Current ##I## in transmitter antenna is related to the electron drift velocity ##v_e## by the relationship ##I=v_e\ A\ n_e\ e##

$$v_e=\frac{I}{A\ n_e\ e}=\frac{10^1}{10^{-4}\ 10^{28}\ 10^{-19}}=10^{-4}\ \hbox{m/s}$$

Electron acceleration ##a_e=v_e f=10^{-4}\ 10^8=10^4\ \hbox{m/s}^2##

Total charge in transmitter antenna ##Q=L\ A\ n_e\ e = 10^0\ 10^{-4}\ 10^{28}\ 10^{-19}=10^5\ ##C

Assume receiver antenna is at a distance ##D=1## km

The strength of the vertical electric field at the receiver, ##E_{rec}##, is given by the far-field radiation formula

$$E_{rec}=\frac{Q\ a_e}{4\pi\epsilon_0\ c^2\ D}=\frac{10^5\ 10^4}{10^{-10}\ 10^{16}\ 10^3}=1\ \hbox{V/m}$$

If the receiver antenna also has length ##L=1## m and radiation resistance ##R_R=10\ \Omega## then the power it receives ##P_{rec}## is given by

$$P_{rec}=\frac{V_{rec}^2}{R_R}=\frac{(E_{rec}\ L)^2}{R_R}=\frac{1}{10}\hbox{W}$$

Have I got this approximately right?