Well, what I do is to bring a simple and cheap "throttle" or inductance coil - one I have frequently employed to demagnetize the heads of tape and cassette reorders - by first plugging this longish oval device, with no moving parts, and which fits easily into the palm of my hand, into the power line - say, the wall socket.
Then I move the tip - slowly, slowly downwards - to touch the back of the watch, just over the pulsating hair-spring of the escapement - a bit of tape on it will prevent scratching - and leave it there for several seconds; you can swirl or rotate it, again - slowly, slowly.
Then I withdraw the tip - slowly, always! slowly, upwards - to prevent remagnetization, which can occur with an abrupt withdrawal.
This, albeit primitive, method will surely show an effect if your watch has become magnetized. Whether it is as effective as a more professional device, I really can`t say.
Could it hurt the watch in any way? I doubt that very much! But please don't make me responsible - or liable - for any of the things that we all know can happen!
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One way to *magnetize* a steel screwdriver is to point it towards North and bang it a few times with a hammer on the grip, or handle. That may be sufficient for it to pick up a loose screw that has fallen into the inner chassis of, say, a hifi amplifier. The earth's magnetic field takes care of that, weak as it is. A soft-iron bar will be more effective to demonstrate that it actually works.
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Watch-making tools, especially those made by hand, can become magnetized, and therefore become themselves magnets and thus magnetize parts of the watch that they are expected to adjust and repair.
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Before we all go mad, one way NOT to demagnitize a watch is to "to point it towards North and bang it a few times with a hammer", etc. But a great test for shocks!
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My doctor has detected too much iron in my blood. Should I be banged on the head to be magnetized - or remagnetized?
Hope that this has been some interest or service to you,
while returning your Kindest Regards,
Amery