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Given a standard reference system with axes x y z representing a 3 dimensional space and given a magnet whose north and south pole are at points $P_N=(x_N,y_N,z_N)$ and $P_S=(x_S,y_S,z_S)$ what is the law that describes the vector field of the magnet at any other point of the space? I'm interested in the law that associates to each point $P=(x,y,z) $ the direction and modulus of the vector of the magnetic field.

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The ideal dipole magnet has a $1/R^2$ field directed toward the S pole, plus a $1/R^2$ field away from the N pole. The vector sum of those two field elements is the field of the dipole. The Earth's North pole is attractive to the N pole of a magnet, and (confusingly) is thus a S pole.

$${\mathrm { \vec {B} = {(\vec P_S - \vec P) \over {|(\vec P_S -\vec P)| ^3} } - {(\vec P_N -\vec P) \over {|\vec P_N - \vec P|}^3} } }$$

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  • $\begingroup$ What is $R $ ? Could you give some reference please? $\endgroup$ – Alberto Apr 25 '17 at 6:47
  • $\begingroup$ R is displacement from the point (the pole) to the measurement location. I'm using R as the general indicator of distance, as though it were a spherical radial-distance coordinate. $\endgroup$ – Whit3rd Apr 25 '17 at 7:02
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Biot Savart, or if idealize the situation, Ampere's law Imagine a magnet as a current loop rotating around the north direction (right hand's rule)

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  • $\begingroup$ Sampling the values of $\vec{B}$ for a set of points along a path how would you guess the positions of the poles? $\endgroup$ – Alberto Apr 28 '17 at 21:28

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