Apparatus for imposing a gradient magnetic field intensity on a static magnetic field intensity in a nuclear- magnetic-resonance (NMR) system. The gradient field has a predetermined error relationship with respect to a desired characteristic of the gradient field within a selected region. The selected region is substantially smaller in volume than the volume «enclosed» by a surface or surfaces on which electrical conductors are distributed to generate the gradient field. The surface current densities in a grid-like pattern of differential areas on the surfaces are chosen such that, within the selected region, the predetermined error relationship results. The gradient field intensity outside of the selected region generally does not have the characteristic desired within the region. The predetermined error relationship can be established in a linearly-varying field intensity in a spherical volume enclosed by a cylindrical surface. Generally hyperbolically-shaped electrical coils on the cylindrical surface can provide surface current densities required for a constant transverse-gradient (a linearly varying magnetic field intensity in a direction transverse to the axis of the cylinder).