Say I create a structure from copper that looks like the figure shown below. It's an open circle whose ends terminate in protruding wires of length x. If I excite this with an out-of plane time varying magnetic field B (say B0*cosft), will the protruding wires emit EM waves? If yes, will the emitted radiation have a frequency of f? And will x affect the power of the emitted radiation? Any brief explanation will be helpful..
will the protruding wires emit EM waves?
Yes. But then, there will be EM waves all over such a setup anyway.
If yes, will the emitted radiation have a frequency of f?
Yes, of course. This is a linear, time-invariant (LTI) system, so it couldn't have any other frequency.
And will x affect the power of the emitted radiation?
Yes. Look up dipole antenna. The radiation varies in a complex way, depending on how x relates to the frequency (wavelength) and how the inductance and capacitance of the coil resonate with the antenna.
Biot-Savart solved this a long time ago. In short the only the magnetic field inside the coil will drive a current. This is reversible, a current will also drive a magnetic field. This is due to the way the fields integrate around the coil. See this. The field already in place opposes changes to it slides