Energies carried by electric and magnetic fields in plane waves

Question

This is a newbie question. I'm trying to understand what I think must be a very basic concept with an obvious answer, but I want to be sure.

Do plane wave electric and magnetic fields of equal strength at the same frequency and same waveform carry equal amounts of energy?

In other words, if a dipole and a loop antenna of equal length encounter plane waves in free space at the same frequency and with the same waveform, and signal source power levels are adjusted so that the electric field to which the dipole is exposed is equal in strength to the magnetic field to which the loop is exposed, and all other variables are equal, is the current induced in each antenna equal? Please assume ideal antennas that convert all of the energy they receive into current and that have no other properties that affect the results.

Answer 1

Do plane wave electric and magnetic fields of equal strength at the same frequency and same waveform carry equal amounts of energy?

An analogy: -

If I put 377 V RMS across a 377 ohm resistor the power would be \$V^2/R\$ = 377 watts and the current would be 1 amp. If I calculated power using current it would be \$I^2R\$ = 377 watts.

signal source power levels are adjusted so that the electric field to which the dipole is exposed is equal in strength to the magnetic field to which the loop is exposed

If both antennas have equal sized apertures (aka capture area) and are designed to be resonant at the incoming frequency then no adjustment is necessary. One will convert volts/m (E field) and the other will convert amps/m (H field) and both will produce the same power/signal output.

Answer 2

An electromagnetic wave carries energy. That's the fundamental 'currency' of physics. This energy is carried in both electric and magnetic fields.

If we measure the amplitude of each field, and find their ratio is 377 ohms, this tells us as much about the specific units we have chosen to use to make the measurement as it does the fields themselves.

You can launch and intercept an EM wave with either an electric dipole, or a magnetic dipole. They both couple completely to the energy-carrying wave in the far field. They are different in the near field, where the non-travelling component of the fields is more nearly electric or magnetic respectively.

For any given antenna configuration, you can define an effective area (at a certain frequency, in a certain direction) that designates its coupling with the far field. In some types of antenna, for instance a parabolic reflector dish, what contributes to the 'area' is obvious. In other types, a Yagi array for instance, the 'area' increases as more elements are added in the direction of the wave. Different configurations will have different physical size to electrical area ratios, it's more the specific configuration than whether it's primarily electric or magnetic that controls this.

In the absence of losses, the power output from an antenna is equal to the energy it intercepts from the wave. For small antennae like a short electric dipole or small area magnetic loop, their terminal impedance will be high or low respectively, so if you restrict yourself to measuring their current output, the outputs will indeed be different. Instead, measure the power output into a matched impedance.