How can the force of electromagnetism change the energy levels of two objects over a distance?

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How can two objects affect each other’s energy level without being in contact with one another simply by the virtue of their electric charge?

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If you’re talking about wireless charging, that’s because electric currents can change the local magnetic field. Additionally, and conversely, a changing magnetic field can induce a current in a circuit. So a wireless charger gets a current run through it from the power outlet. This changes the magnetic field around it in a certain way. Your phone or other mobile device has an electric circuit in it that gets a electric current induced in it by the changing magnetic field. The current is routed into the battery of the device, charging it.

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