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| '''Magnetic dipole–dipole interaction''', also called '''dipolar coupling''', refers to the direct interaction between two [[magnetic dipole]]s. The [[potential energy]] of the interaction is as follows:
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| ::<math> H = - \frac{ \mu_0 } {4 \pi r_{jk}^3 } \left( 3 (\bold{m}_j \cdot \bold{e}_{jk}) (\bold{m}_k \cdot \bold{e}_{jk}) - \bold{m}_j \cdot \bold{m}_k \right) </math>
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| where '''e'''<sub>jk</sub> is a unit vector parallel to the line joining the centers of the two dipoles. r<sub>jk</sub> is the distance between two dipoles, '''m'''<sub>k</sub> and '''m'''<sub>j</sub>.
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| For two interacting nuclear [[Spin (physics)|spin]]s
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| ::<math> H = - \frac{ \mu_0 }{ 4 \pi } \frac{ \gamma_j \gamma_k \hbar^2}{ r_{jk}^3 } \left( 3 (\bold{I}_j \cdot \bold{e}_{jk}) (\bold{I}_k \cdot \bold{e}_{jk}) - \bold{I}_j \cdot \bold{I}_k \right) </math>
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| where <math>\mu_0</math> is the [[magnetic constant]], <math>\gamma_j</math>, <math>\gamma_k</math> are [[gyromagnetic ratio]]s of two spins, and r<sub>jk</sub> is the distance between the two spins.
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| Force between two magnetic dipoles:
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| : <math>
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| \vec{F}_{ab}= \frac {3 \mu_0} {4 \pi |r|^4} [ (\hat r \times \vec{m}_a) \times \vec{m}_b + (\hat r \times \vec{m}_b) \times \vec{m}_a - 2 \hat r(\vec{m}_a \cdot \vec{m}_b) + 5 \hat r ((\hat r \times \vec{m}_a) \cdot (\hat r \times \vec{m}_b)) ]
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| </math>
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| where <math>\hat{r}</math> is [[unit vector]] pointing from magnetic moment <math>m_a</math> to <math>m_b</math>, and <math>|r|</math> is the distance between those two magnetic dipole moments.
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| == Dipolar coupling and NMR spectroscopy ==
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| The direct dipole-dipole coupling is very useful for molecular structural studies, since it depends only on known physical constants and the inverse cube of internuclear distance. Estimation of this coupling provides a direct spectroscopic route to the distance between nuclei and hence the geometrical form of the molecule, or additionally also on intermolecular distances in the solid state leading to [[NMR crystallography]] notably in amorphous materials. Although internuclear magnetic dipole couplings contain a great deal of structural information, in isotropic solution, they average to zero as a result of rotational diffusion. However, their effect on nuclear spin relaxation results in measurable [[nuclear Overhauser effect]]s (NOEs).
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| The [[residual dipolar coupling]] (RDC) occur if the molecules in solution exhibit a partial alignment leading to an incomplete averaging of spatially anisotropic magnetic interactions i.e. dipolar couplings. RDC measurement provides information on the global [[Protein folding|folding]] of the protein-long distance structural information. It also provides information about "slow" dynamics in molecules
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| ==References==
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| *Malcolm H. Levitt, ''Spin Dynamics: Basics of Nuclear Magnetic Resonance''. ISBN 0-471-48922-0.
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| == See also ==
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| *[[J-coupling]]
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| *[[Magic angle]]
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| *[[Residual dipolar coupling]]
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| *[[Nuclear Overhauser effect]]
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| *[[Magnetic moment]]
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| {{DEFAULTSORT:Magnetic dipole-dipole interaction}}
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| [[Category:Electromagnetism]]
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| [[Category:Nuclear magnetic resonance]]
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