Find power of antenna from emf on coil

[MrElectrical]

I want to find power of the electromagnetic waves generated from a welding cable. I built my own coil antenna that is 6.5 inches in diameter (circular) with 50 turns and hooked up the ends to a digital oscilloscope to measure the voltage (the internal resistance is 1MΩ if it matters). I measured 11Vpp with T=2.75μS on the coil when it was placed directly on top of the welding cable. The coil is placed directly on top of the cable, so it receives approximately 180 degrees of the signal.

I know that Emf = N*dPhi/dt (where N=# of turns) and that Phi = Area*B*cos(θ).

I've found what I thought was the right math to find the Poynting vector, but I am getting vastly insane numbers such as 139W/m^2 which cannot be right.

How do I calculate 1) The power of the welding cable as an antenna, and 2) The intensity of the wave?

 

[marcusl]

Welcome to PF!

It's not easy to measure EM waves at low frequencies (I assume your welder is AC, right?). For one thing, you need to be in the far field to properly measure a propagating wave. No antenna that is shorter than one-half wavelength radiates well, however, and in your case the antenna (welding cable) is negligibly long compared to one-half wavelength, which is 2500 km at 60 Hz. All electrically small antennas are poor radiators, but yours is really not an EM antenna at all.

Your coil could couple inductively (that is, magnetically) to the current in the wire, but by placing the coil directly and symmetrically on top of the wire, you ensure that inductive coupling is zero. Reposition it so that it lies in the same plane as the wire, and you'll measure an induced electromotive force, that is, you'll have a transformer. At present, you are probably getting capacitive coupling from the wire voltage to the high impedance scope input.

You might want to try an experiment at high frequency with a proper antenna. Members of your local ham radio club could help you set up an experiment to, e.g., verify that the Poynting power flux density falls off as 1/R^2 in the far field of a UHF antenna.