If I had an iron core solenoid, and was able to measure the force at different distances by say, using a piece of metal attached to a string on a scale, and knew current and other properties of the magnet, would I be able to determine the magnetic intensity, and if so what would the formula look like?
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2 Answers
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No. An $r^2$ falloff would be expected for a monopole field, but magnets and electromagnets have no monopole contribution.
If you model the magnet as an ideal dipole, it can be calculated. https://en.wikipedia.org/wiki/Dipole#Field_of_a_static_magnetic_dipole and https://en.wikipedia.org/wiki/Magnet#Fields_of_a_magnet.
The strength tends to fall off as $r^3$ once you are "far enough" away from the magnet.
answered Jul 30, 2020 at 23:11
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The force depends on how far you are from one end of the magnet. Close to one end, the magnetic field B looks like the field from a magnetic monopole, even though there is no monopole. This field would be $2\pi MA/r^2$, where M is the magnetization (in Gaussian units) of the magnet, A is the area of the end of the magnet, and r is the distance from the end of the magnet. This B provides the force you see when you use a bar magnet to attract an iron object. Further away, the magnet looks like a magnetic dipole, $\mu=MAL$, and then the Wikipedia article gives the magnetic field.
answered Jul 31, 2020 at 14:32