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I was wondering if it would be possible to power a little 3.3V microcontroller, by harvesting an electromagnetic field around an in-wall insulated 240V 50Hz AC power cable.

Something like contactless inductive charging, like in an electric toothbrush.

Efficiency would be poor, but for a low power device may be an alternative to batteries.

Does the EM field only exist when there is a load on the wire or is it always there, regardless if there is any device connected?

A limitation would be the power harvesting device would need to attach to an existing straight AC wiring without cutting the insulation. No coil on the "transmitter" side.

Is 50Hz way too low to be useful?

I came up with the idea after using a stud finder which has a little red LED that illuminates in the presence of live wires with a few cm range.

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I came up with the idea after using a stud finder which has a little red LED that illuminates in the presence of live wires with a few cm range.

The electric field generated close to a pair of live-neutral wires is sufficient to be detected and amplified in order to light an LED. At anything more than a few inches distant, the e-field strength is quite low and, if trying to extract power, the localized e-field will collapse.

Regarding the magnetic field generated by load currents flowing in the wires it's a similar story - current travels down live wire in one direction and returns up the neutral wire in the opposite direction i.e. ampere-turn cancellation. At a few inches (and beyond) there is very little usable power.

Think about the power losses in metal conduits if this were not the case.

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No you can't, there's not enough energy you can harvest that way. Your stud finder is almost certainly a battery-powered non-contact AC voltage detector, which looks something like this from electrical standpoint:

enter image description here

Also check answers to this question which explain how much energy you can actually collect (spoiler: fetmowatts).

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