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I know a temporary magnet is one that loses its magnetic field when it is not inside another magnetic field, and that a permanent magnet is one that keeps its magnetic field (and one that always has its poles in the same place; a temporary magnet can switch its poles round depending on how you orientate it in the second magnetic field). However, it occurred to me that actually, all magnets are sitting inside the magnetic field of the earth, so I am wondering if permanent magnets are like temporary magnets in that they are only exerting a magnetic field because they themselves are in one already, or not? In other words, would a permanent magnet keep its magnetic field even if you took it into space way away from the magnetic field of the earth, or would the so called permanent magnet actually lose its field as soon as it was outside the earth's magnetic field, just as a temporary magnet would lose its field as soon as it was outside of the permanent magnet's field?

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No, the magnetic field in a natural or artificial permanent magnet is "cooked into" the magnet material and will remain even if the earth's magnetic field were to disappear.

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A good example of a big "magnets" retaining their field even when the Earth magnetic field changes

In short, the magnetic field of the Earth switches direction once in a while. And some permanent magnets retain the field from the times when they became permanent (because of cooling below their Curie point).

On the other hand, quite a few of ordinary permanent magnets (e.g. like the ones in your fridge door) have field orders of magnitude stronger than the Earth's magnetic field. These fields are oriented in whatever direction we want that is generally different from the North-South. One cannot assume they are somewhat created from the Earth magnetism.

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In a ferromagnetic material, there are inter-atomic forces which allow the atomic magnetic dipole moments to maintain alignment in spite of thermal agitation. These forces are strongest when the dipoles are in line with a crystal axis. Generally, the crystals are randomly oriented. If a strong external magnetic field is applied, the dipoles align themselves with it. If the external field is then removed, the dipoles may drop back into alignment with the handiest crystal axis. Depending on the alloy, this can leave a significant “remnant” magnetization. This now “permanent” magnet generates its own field, and does not require an external field. Due to thermal agitation or exposure to other magnets over time this magnetization can be lost. (As a college lab supervisor, I had to periodically re-magnetize the magnets used in the lab, and the compass needles would occasionally get reversed.)

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