We consider the trajectory of a charged particle in an arbitrary external magnetic field. A local orthogonal coordinate system is given by the tangential, curvature, and torsion vectors. We write down Maxwell's equations in this coordinate system. The resulting partial differential equations for the magnetic fields fix conditions among its local multipole components, which can be viewed as ageneralization of the usual multipol expansion of the fields of magnetic elements. 0-7803-7739-9