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Magnetic dipole moment

Magnetic dipole moment. There exist no magnetic “charges” or ”monopoles” …but for static fields, they can be constructed mathematically The elementary magnetic source is the dipole formed by a loop of current:. Magnetic Potential.

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Magnetic dipole moment

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  1. Magnetic dipole moment • There exist no magnetic “charges” or ”monopoles” • …but for static fields, they can be constructed mathematically • The elementary magnetic source is the dipole formed by a loop of current:

  2. Magnetic Potential • If curl (B) = 0 (no current), field B can be presented as a gradient of a potential V: or: • Biot-Savart law: Cm depends on units

  3. Magnetic Potential • Therefore, the change in potential: The first equation here uses: The second equation assumes an infinitesimal loop • The contour integral gives the area of the loop: • Hence the change in potential:

  4. Magnetic Potential • Therefore, the magnetic potential equals: The const is usually taken zero, so that • Note two properties different from the monopole potential for gravity: • The potential decays with distance as 1/r2 • It also depends on the direction (zero within the plane orthogonal to m and opposite signs in the directions parallel and opposite to m)

  5. Poisson’s relation • The dipole field (~1/r2) equals a derivative of the monopole field (~1/r) with respect to the position of the source: This is simply the spatial derivative in the direction of the magnetic moment, m • Thus the magnetic field of a structure is related to its gravity field (Poisson’s relation):

  6. Monopole Magnetic Potential • The dipole field can be presented as produced by two monopolesseparated by an arbitrary (small) distance a: where and is the pole strength

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