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Magnetic dipole–dipole interaction, also called dipolar coupling, refers to the direct interaction between two magnetic dipoles. Roughly speaking, the magnetic field of a dipole goes as the inverse cube of the distance, and the force of its magnetic field on another dipole goes as the first derivative of the magnetic field. It follows that ...
In the magnetic pole model, the magnetic dipole moment is due to two equal and opposite magnetic charges that are separated by a distance, d. In this model, m is similar to the electric dipole moment p due to electrical charges: m = q m d , {\displaystyle m=q_{\mathrm {m} }d,} where q m is the ‘magnetic charge’.
Unlike the expressions in the previous section, this limit is correct for the internal field of the dipole. If a magnetic dipole is formed by taking a "north pole" and a "south pole", bringing them closer and closer together but keeping the product of magnetic pole-charge and distance constant, the limiting field is
In particular, it would hold in the limit where the distance between the charges is decreased to zero while maintaining the dipole moment – that is, it would hold for an electric dipole. But if the theorem holds for an electric dipole, then it will also hold for a magnetic dipole, since the (static) force/energy equations take the same form ...
Instantaneous dipoles These occur due to chance when electrons happen to be more concentrated in one place than another in a molecule, creating a temporary dipole. These dipoles are smaller in magnitude than permanent dipoles, but still play a large role in chemistry and biochemistry due to their prevalence. See instantaneous dipole. Induced ...
where A is the Hamaker coefficient, which is a constant (~10 −19 − 10 −20 J) that depends on the material properties (it can be positive or negative in sign depending on the intervening medium), and z is the center-to-center distance; i.e., the sum of R 1, R 2, and r (the distance between the surfaces): = + +.
The interaction was first derived by Enrico Fermi in 1930. [7] A classical derivation of this term is contained in "Classical Electrodynamics" by J. D. Jackson. [8] In short, the classical energy may be written in terms of the energy of one magnetic dipole moment in the magnetic field B(r) of another dipole.
The most common mechanism is the magnetic dipole-dipole interaction between the magnetic moment of a nucleus and the magnetic moment of another nucleus or other entity (electron, atom, ion, molecule). This interaction depends on the distance between the pair of dipoles (spins) but also on their orientation relative to the external magnetic field.