Voltage Across the Terminals of a Receiving Antenna

Deduce the no-load (open-circuit) voltage Voc across the terminals of a short, center-fed linear dipole antenna of half height h when excited by a plane wave of wavelength λ h whose electric field vector Ein is parallel to the dipole antenna. The ratio Heff = |Voc/Ein| is called the effective height of the antenna. Also deduce the current Isc that would flow between the terminals if they were short circuited. Then, according to Thévenin’s theorem the receiving antenna acts on any load connected to it like a voltage source Voc with internal impedance ZA = Voc/Isc. You may assume that the antenna conductors have a diameter small compared to the height h, and that they are perfect conductors. The gap between the terminals is also small compared to h. By dimensional analysis, the no-load voltage has amplitude of order E0h, where E0 is the amplitude of the incident wave. The problem is to show that to a good approximation the voltage is actually E0h. This problem can be addressed using techniques that are simplifications of those appropriate for antennas comprised of thick wires with complex geometries.