There are a magnetometer and a magnet placed at some distance D from it. We can assume that the magnet is a generic bar magnet. We can also assume that the Earth magnetic field is zero since the magnetic field of the magnet is stronger than the Earth magnetic field.

What is the equation that describes the magnetic field B? What is the equation if I assume a generic magnet? How the equation changes if I consider the Earth magnetic field?

  • $\begingroup$ You can only consider the Earth's magnetic field to be negligible with respect to the magnet, NOT ZERO! So you have to consider the Earth's magnetic field under all circumstances. $\endgroup$ Sep 28, 2015 at 13:46
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    $\begingroup$ Let's say that I save the readings when the magnet is not close to the magnetometer (i.e. the readings are not affected by it) and then subtract this value from the readings, then when the magnet is far from the magnetometer the readings will be zero. Under this hypotheses can I assume the Earth magnetic field is zero? If I do then is it possible to have an equation to model the current situation? $\endgroup$
    – Alexander
    Sep 28, 2015 at 15:17
  • $\begingroup$ So I presume you intend to leave the Earth and go to outer space to carry out the experiment! For the Earth itself is a magnet. See this link ...kjmagnetics.com/blog.asp?p=earth-science $\endgroup$ Sep 28, 2015 at 15:21

1 Answer 1


Question 1
In the limit as Earth's field goes to zero, you could make an approximation that the bar magnet is just a simple dipole. You can find an equation if you look at this dipole moment link.

Question 2
For a generic current source, the general equation one would use is the Biot-Savart law. For a generic magnetic moment, consult Jackson's E&M book on multipole moments and the Biot-Savart law (i.e., Chapters 4 and 5, 3rd Edition). If there is geometric symmetry, one can often simplify this (greatly) by using Stokes' theorem to simplify Ampère's law.

Question 3
Inclusion of the Earth's field, ignoring any time or spatial variations, would just be a superposition of magnetic fields. First measure the background magnetic field (i.e., Earth's field), then measure the field of the general magnet. In equation form, I think you could just treat Earth's field as an external applied magnetic field (e.g., Chapter 5, Section 11 in Jackson's E&M book, 3rd Edition).


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