Yes, but it is harder than you might think. In the 60's several people (military contractors) experimented with powering things with a directed microwave beam. Expensive, inefficient, and dangerous. To deliver any useable amount of power, the beam field strength is so high it is physically dangerous to block.
Wireless charging for phones uses an air-core transformer, with the primary driven by the charger electronics and the secondary connected to the phone's internal battery charge manager. The coils are tuned to resonate at the same freq so efficiency doesn't totally suck. Still, small changes in the gap between the two coils has a large impact on recharge time.
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