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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.structure.

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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.

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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

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