Why doesn't wireless charging work with DC current?

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pcvrx560
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As far as I know, they use two coils and rely on a changing electromagnetic field to transfer electric current. So would wireless charging not work for DC current since a constant voltage would create an unchanging electromagnetic field and therefore unable to induce a current in the other coil?
 
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It's like a transformer, in principle. A changing current is required.
 
But it's perfectly simple to convert DC to AC, transfer wirelessly, then convert it back.

In fact it's often done by converting to DC, then to AC again at a more convenient frequency than mains cycles - do the wireless transfer, then rectify back to dc to charge a battery.