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At the coffee shop I go to there is a wireless charging power mat made by Powermat. Is it harmful to my laptop to put it near or above the wireless phone charger?

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No. This should not damage your laptop or any other non-Wireless charging device you place on it.

Wireless charging uses a very low power detection mechanism and only switches to a higher power field for charging once a wireless charging device has been detected and has negotiated with the transmitter.

Your laptop, lacking the charging circuitry, will not negotiate with the charger and so will not trigger the higher power charging phase.

The page Wireless Electricity Transmission from the Wireless Power Consortium explains a lot, though this image in particular shows setup and power negotiation without which the field strength will be far below anything that could damage components.

transmitter receiver flow diagram

The penultimate image on that page shows that the transmitter could be working to actively detect a charging coil, but in the example the power is 3 orders of magnitude less (5mW vs 5W) to check for possible receiver coil presence than to actually provide full power. Your laptop, lacking an inductive coil, will almost certainly still not trigger the resonance (inductive coil) check phase, though it may briefly trigger the initial capacitance check phase. This will still not be enough power being radiated to do any damage whatsoever and the charger should quickly fall back to its standby and detect mode.

transmitter standby overview

Without these low power active-detection mechanisms we would be radiating away enormous amounts of power from wireless chargers, something that is unacceptable in this day where everything is being geared towards minimising energy footprints.

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No -- Powermats are inductive charging devices with very limited range (the device has to be right on the mat). That field strength should drop off with the square of distance as well.

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No, it's fine.

The susceptibility of hard drives, and of electronics in general, to external magnetic fields is grossly overestimated. See my answer here: Is CRT degaussing really dangerous for nearby laptops? for a description of a relevant experiment. If your laptop has an SSD instead of a hard drive it's even less susceptible, if that's possible.

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