Question

An electric dipole of length 1 m is operated in air, then the time average power radiated by the antenna assuming that it is excited at its centre by a sinusoidal current of amplitude 200mA at a frequency 1.5MHz is

• A. $192mW$
• B. $192\mu W$
• C. $394\mu W$
• D. $394mW$

Answer 1

The correct option is C $394\mu W$

$\begin{array}{cc}{P}_{rad}& =\frac{1}{2}{I}^2{R}_{rad}\\ R_{rad}& =80{\pi }^2{\left(\frac{\ell }{\lambda }\right)}^2\\ \lambda & =\frac{c}{f}=\frac{3\times {10}^8}{1.5\times {10}^6}=200m\\ R_{rad}& =80{\pi }^2{\left(\frac{1}{200}\right)}^2\\ P_{rad}& =\frac{1}{2}{(200\times {10}^{-3})}^2\frac{80{\pi }^2}{(200{)}^2}=3.94\times {10}^{-4}W=394\mu W\end{array}$