Magnetic Moments and Dipoles
What is a magnetic dipole moment?
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Magnetic field due to a hypothetical dipole
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The magnetic moment (µ) is a vector quantity used to measure the tendency of an object to interact with an external magnetic field. In NMR, the object of interest is typically a molecule, atom, nucleus, or subatomic particle. The object's intrinsic magnetic properties are often visualized as emanating from a tiny bar magnet with north and south poles (the "dipoles"), and is therefore also called the magnetic dipole moment.
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Magnetic dipole modelled as a current loop
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The concept of the magnetic dipole is not restricted to the modeling of atomic-sized particles and can be applied to much larger objects and collections of objects. A compass needle, MR scanner, and even the earth itself might be considered giant dipoles. When the field lines of two magnetic moments cross, a dipole-dipole interaction occurs. This is an important mechanism for magnetic relaxation between two protons or between a proton and an electron in NMR about which much more will be addressed in later Q&A's.
An alternative and more quantitatively useful definition of the magnetic moment is to model it as arising from a tiny current (i) traveling around the edge of a loop of cross sectional area (A). The magnetic dipole moment (µ) is a vector defined as µ = i A whose direction is perpendicular to A and determined by the right-hand rule.
Like a compass needle, the magnetic moment (µ) will seek to align with an externally applied magnetic field (Bo). It will experience a torque (τ) or twisting force given by the vector cross product τ = µ x Bo. When perfectly aligned parallel to Bo, µ will be in its lowest energy state and experience no torque. When pointing opposite to Bo, µ will be in its highest energy state because extra energy would be required to move and maintain it in this position. For any other direction the energy (E) of the magnetic moment (µ) would be given by the vector dot product: E = − µ • Bo. The negative sign is required to account for the energy being lower when µ is aligned with Bo.
References
"Magnetic Moment." Wikipedia, The Free Encyclopedia.
"Magnetic Dipole." Wikipedia, The Free Encyclopedia.
Acosta D. Magnetic dipoles. PHY2061 Enriched Physics Notes, University of Florida, 2006. An excellent college-level physics set of diagrams explaining the dipole and related concepts. Even has an understandable explanation of why magnets stick together on pp 4-5 (in case you wondered).
"Magnetic Moment." Wikipedia, The Free Encyclopedia.
"Magnetic Dipole." Wikipedia, The Free Encyclopedia.
Acosta D. Magnetic dipoles. PHY2061 Enriched Physics Notes, University of Florida, 2006. An excellent college-level physics set of diagrams explaining the dipole and related concepts. Even has an understandable explanation of why magnets stick together on pp 4-5 (in case you wondered).
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