Abstract: Gradient coil assemblies and shim coil assemblies are disclosed for magnetic resonance imaging ("MRI") devices, wherein the coil assemblies comprise a coil support and a conductive wire having a locus described by a solution of a current continuity equation over a finite interval for which certain terms of the magnetic field expansion are equal to zero, for generating non-uniform magnetic fields. The gradient coil produces gradient fields and magnetic fields which cancel non-uniformities in the magnetic field of the magnet of the MRI device. Shim coils cancel such non-uniformities, as well. A method of manufacturing such coils is also disclosed.