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Questions About Highly Coupled Magnetic Resonance

Physics Asked by JuniorG7 on December 3, 2020

This is one of very few in-depth sources of information I can find online about Highly Coupled Magnetic Resonance:

The last sentence of the third-to-last paragraph says that research is underway that may someday lead to vehicle charging on the move. I’m guessing that the reason that this requires extra research is that relative motion between the source and device resonators affects power transfer. So I’m curious, how would you begin to conceptualize the effect of motion (both linear and rotational) on Highly Coupled Magnetic Resonance?

On a related note, I’m curious what the equation for the magnetic coupling coefficient $k$ mentioned in equation 9 would be? The second paragraph after equation 9 defines $k$ as "a dimensionless parameter representing the fraction of magnetic flux that is coupled between the source and device resonators" and describes it as "a function of the relative sizes of the resonators, the distance between them and their relative orientation". Based on the description, I imagine it contains a $cos(theta)/r^3$, where $theta$ is the relative angle of the resonators and $r$ is the distance between them, but I’m not sure where the relative sizes of the resonators fit in.

I know that I could replace $theta$ with $2pi t/T + phi$, where $T$ is the period of rotation, $phi$ is the initial relative angle, and $t$ is time, to see the effect of rotation on power transfer over time; likewise, I could replace $r$ with $|vt + x|$, where $v$ is relative velocity and $x$ is the initial distance, to see the effect of linear motion on power transfer over time; however, I don’t think WiTricity would need to do extra research into charging on the move if those were the only effects. I think there must be a specific effect on the magnetic coupling itself as a result of relative motion.

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