New expression for calculating magnetic fields due to current-carrying solid conductors

A new closed-form expression based on double integral computation is introduced for 3D magnetostatic fields of current-carrying solid conductors whose vector density satisfies the condition that its curl is zero. Such a reduced expression is derived for a toroidal conductor with radial current flow, solved analytically, and used for 3D field computation. For illustration, by applying the same reduction principle, the 3D magnetic fields are computed for cylindrical and rectangular conductors with longitudinal flowing current.