MadSci Network: Physics Query:

### Re: Easy formula to calculate attraction of 2 magnets

Date: Thu Feb 17 08:56:31 2000
Posted By: Shella Keilholz-George, Grad student, Engineering Physics, University of Virginia
Area of science: Physics
ID: 949079164.Ph
Message:
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First, I apologize for the delay in posting this answer.  I was out of town
and forgot to notify the network.
Second, to obtain a simple formula, it is necessary to make some
assumptions.  I will assume that the magnets are perfect dipoles, which
means that the distance between the north and south pole of each magnet is
much smaller than the distance between the magnets.  If this is not true,
the equation gets quite complicated.
From "Introduction to Electrodynamics" by David J. Griffiths, Section 5.4,
the magnetic field of a dipole at the origin pointing in the +z direction
is
B=-mu/4pi *m/r^3 in the z direction at a point on the x axis
where m is the magnetic dipole moment and r is the distance from the
dipole.
Then the force of this dipole on another dipole situated on the x axis
pointing in the +x direction is
3 mu m1 * m2/(4pi * x^4)in the z direction
where m1 and m2 are the magnetic dipole moments of the first and second
dipoles respectively.
To model a theoretical force for equal magnetic dipoles, you can just let
m1 = m2 =an arbitrary constant.  You can work this out for different
orientations of the dipoles.  Griffiths is a good reference to use.

```

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