Magnetic dipole–dipole interaction

Magnetic dipole–dipole interaction, also called dipolar coupling, refers to the direct interaction between two magnetic dipoles. Magnetic dipole–dipole interaction, also called dipolar coupling, refers to the direct interaction between two magnetic dipoles. Suppose m1 and m2 are two magnetic dipole moments that are far enough apart that they can be treated as point dipoles in calculating their interaction energy. The potential energy H of the interaction is then given by: where μ0 is the magnetic constant, r̂ is a unit vector parallel to the line joining the centers of the two dipoles, and |r| is the distance between the centers of m1 and m2. Last term with δ {displaystyle delta } -function vanishes everywhere but the origin, and is necessary to ensure that ∇ ⋅ B {displaystyle abla cdot mathbf {B} } vanishes everywhere. Alternatively, suppose γ1 and γ2 are gyromagnetic ratios of two particles with spin quanta S1 and S2. (Each such quantum is some integral multiple of 1/2.) Then: where r̂ is a unit vector in the direction of the line joining the two spins, and |r| is the distance between them.