A Novel Method of Accurate Calculation of the Magnetic Dipole Field in Both the Near and Far Fields

The magnetic dipole serves as a fundamental concept in understanding electromagnetic phenomena. It has extensive applications across various fields such as geophysics and indoor navigation, which require accurate determination of its magnetic field. Although the magnetic dipole approximation yields satisfactory results in the far field, its computational accuracy is poor in the near-field region. Here, we propose a method of accurately calculating the magnetic dipole field in both the near and far fields. This method encompasses three steps: first, calculating the magnetic field strength B_T at the position r; second, determining the direction of the magnetic field at r; and third, calculating three components of the magnetic field. Numerical tests show that the calculation error of B_T is < 1% at r > 1.2 R, and is < 0.1% at r > 10 R, where R is the radius of the magnetic dipole. Additionally, the magnetic field direction can be precisely modeled via multi-parameter fitting, yielding angular errors < 0.1° in most regions at r > 1.2 R. Integration of the direction and B_T enables us to accurately calculate three components of the magnetic field with an error of < 1% at r > 1.8 R. These results indicate that our method is able to achieve high accurate calculation of the magnetic dipole field in both the near and far fields. This method can provide an effective computational algorithm for the applications relying on magnetic dipoles.