= Hertzian dipole fixed-current power scaling
{c}
{title2=$\overline P\propto I_0^2\ell^2/\lambda^2$}
A uniform electrically short <current element> of <length> $\ell$ with sinusoidal peak current $I_0$ has <electric dipole moment> <amplitude> $p_0=I_0\ell/\omega$. The mean <electric dipole radiation> <power> is $\omega^4p_0^2/(12\pi\epsilon_0c^3)$, so fixing current makes it proportional to $\ell^2\omega^2$, rather than $\ell^2\omega^4$. Current, charge excursion and dipole moment are different quantities to hold fixed when comparing antennas. The approximation requires $\ell\ll\lambda$ and does not impose the nonuniform standing-current profile of a long antenna.
Back to article page
