distance. If the magnet is long (), a measurement of the magnetic flux density very close to the magnet is roughly related to by the formula The effective magnetic dipole moment can be written as where is the volume of the magnet. For a cylinder this is , and is the magnetisation field of the dipole. When the point dipole approximation is obtained, Which matches the expression of the force between two magnetic dipoles. Ampère model French scientist André Marie Ampère found that the magnetism produced by permanent magnets and the magnetism produced by electromagnets are the same kind of magnetism. Because of that, the strength of a permanent magnet can be expressed in the same terms as that of an electromagnet. The strength of magnetism of an electromagnet that is a flat loop of wire through which a current flows, measured at a distance that is great compared to the size of the loop, is proportional to that current and is proportional to the surface area of that loop. For purpose of expressing the strength of a permanent magnet in same terms as that of an electromagnet, a permanent magnet is thought of as if it contains small current-loops throughout its volume, and then the magnetic strength of that magnet is found to be proportional to the current of each loop (in amperes), and proportional to the surface of each loop (in square meters), and proportional to the density of current-loops in the material (in units per cubic meter), so the dimension of strength of magnetism of a permanent magnet is amperes times square meters per cubic meter, is amperes per meter. That is why ampere per meter is the correct unit of magnetism, even though these small current loops are not really present in a permanent magnet. The validity of Ampère's model means that it is allowable to think of the magnetic material as if it consists of current-loops, and the total effect is the sum of the effect of each current-loop, and so the magnetic effect of a real magnet can be computed as the sum of magnetic effects of tiny pieces of magnetic material that are at a distance that is great compared to the size of each piece. This is very useful for computing magnetic force-field of a real magnet; It involves summing a large amount of small forces and you should not do that