Is the magnetic field of a bar magnet influenced by the magnetic field of the earth. If so, will the magnetic field of bar magnet be different in a region where there’s no other magnetic field.
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$\begingroup$ @john I read that the magnet’s North Pole aligns towards the geographic north pole of the earth which is the magnetic South Pole of earth… Is this incorrect? $\endgroup$– JasonCommented Nov 1, 2022 at 14:08
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2 Answers
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I actually disagree with @John's answer. Electromagnetism is linear. I.e. electromagnetic fields simply add to each other; the fields do not influence each other. See Why is classical electromagnetism linear?, Why is the Principle of Superposition true in EM? Does it hold more generally?, In classical physics (classical electrodynamics), why linearity of Maxwell's equations prevent interaction of electromagnetic waves?
The above said, I do agree with @John that Earth's magnetic field will yield a force on the bar magnet itself.
answered Oct 31, 2022 at 14:01
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$\begingroup$ Thank you for the follow-up. Please see an edit to my answer addressing your point. $\endgroup$– JohnCommented Oct 31, 2022 at 21:25
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Yes it does. The magnetic field of the Earth applies a torque on the bar magnet so the magnetic field of a bar magnet in a region with the magnetic field of the Earth is present will be such that the north pole of the bar magnet is pointing towards the North (magnetic) Pole of the Earth. The device making use of this is called compass.
EDIT: To dispell possible confusion in response to the answer by @WAH, the magnetic fields do interact. The thing is that Maxwell's equations are only linear in the absence of charged matter. Once there are movable/polarizable/etc entities around, fields start talking to each other via those entities (charges, dipoles, quadrupoles, etc). This is most prominent in nonlinear optics, but the alignement of a dipole by an external field and subsequent modification of a total field is also strictly speaking a nonlinear electromagnetic effect.
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$\begingroup$ I agree with you that the magnetic field does influence the magnetic field of a bar magnet and will apply a torque to the bar magnet. I think that this influence will also change the magnetic field of the bar magnet. The change might be very slight but it would change the field and the way that it would be measured. Even if the bar magnet is aligned with the magnetic field of the earth and there isn't any torque applied to the bar magnet the earth's magnetic field will still have an impact. $\endgroup$– AnyoneCommented Oct 31, 2022 at 17:06
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$\begingroup$ Responding to @John's edit. Classical electromagnetism is perfectly linear. Non-linearities appear only when one considers loop corrections in quantum electrodynamics, arxiv.org/abs/hep-th/0406216, or extensions of electromagnetism, arxiv.org/abs/hep-th/0309108. The quantum corrections are tiny, ~1% or less, and, for all practical intents and purposes, unseen. Certainly these non-linear effects are unmeasurable with a standard bar magnet interacting with Earth's magnetic field. $\endgroup$ Commented Nov 2, 2022 at 5:33