Energy Density of a Magnetic Dipole

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 , .