# Energy Density of a Magnetic Dipole

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A circular conductor with the current and the radius lies in the plane at . The vector potential in the direction as a function of and has the same symmetry as the current density in cylindrical coordinates , , . According to the cylindrical symmetry the observation points in the plane can be taken at . The source is described by the angle , running from to . The following computations are made: • the magnetic field in the direction • the magnetic field in the direction • the magnetic energy density • the integrated magnetic field in the direction • the integrated magnetic field in the direction • the integrated magnetic energy density • the integrated vector potential in the direction The fields at can be regarded as a good approximation of the integrated fields. The four field , , , are displayed for the four independent variables , , , . The observation points are described by , and the source by , .

Contributed by: Franz Krafft (March 2011)

Open content licensed under CC BY-NC-SA

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"Energy Density of a Magnetic Dipole"

http://demonstrations.wolfram.com/EnergyDensityOfAMagneticDipole/

Wolfram Demonstrations Project

Published: March 7 2011