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By simple, I mean classroom here. Everybody knows the use of metal filings dispersed on a sheet of paper to visualise the magnetic lines of field but I would like to find a way to measure the amplitude of the field as well. A manner which would not require expensive or hard to provide equipments, ideally as basic as the metal filings trick. I have an idea already: a thin conductive elastic thread under tension. When an electrical current goes through, it should curve and the curvature should be related to the magnetic field. I could not find anything about that subject. Is the idea stupid? Or is it a technique so old that it is not discussed anymore? More to the point, could that be made to work?

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I think calculating the magnetic field from such a magneto-torsion measurement might be difficult. Still, that sort of thing was investigated in the mid- to late-1800's by Wiedemann, and then Gore, and maybe many others. In any case, I would recommend using an early form of magnetometer, such as that of Gauss. Conversely, a Hall effect sensor can be used, but this would appear to be more of a black-box sensor to students.

For Gauss' magnetometer, according to his 1832 paper The Intensity of the Earth's Magnetic Forced Reduced to Absolute Measurement, all one needs is a gold wire and a magnetized needle or bar of iron. It's not particulary simple in its interpretation and analysis, but it provides a very good, macroscale detection of magnetic field strength. He mentions that the oscillations of a magnetized needle are commonly used for magnetic field measurements, and improves upon the idea by removing some assumptions with further measurement. Further research would be needed to implement such a device, but it would provide good measurement of the magnetic force at the given point.

There is also the idea of using electromagnetic induction to perform the measurement. With a sufficiently small loop of e.g. copper, moved at a constant rate of speed for a sufficiently small distance, one would be able to approximate the field strength in that region with a multimeter. For a closed loop, measure current, and for an open loop, measure voltage. One may be better suited than the other, depending on expected magnitudes and available instrumentation. I think this would be too difficult, though, without plenty of controlled experiments to verify results. As a general recommendation, look into magnetometers.

Edit: See also this paper if you haven't already.

Second Edit: I think magnetic torsion experiments are more prevalent than I originally thought! Magnetic Torsion by Moreau appears as an abstract in a few periodicals around 1898. Can't find anything more, however.

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