Abstract: A first set of three spherically or elliptically shaped coils is provided which generates a homogeneous linear gradient magnetic field in its interior. A second set of three spherically or elliptically shaped coils is located concentric to and in close proximity with the first coil set such that the fringing fields outside the second coil set are substantially zero. The coil sets can be separated at their equator and preferably are spherical in shape. The current distribution for each coil is described as well as the winding pattern on the surface of the first sphere which generates the perfectly homogeneous linear gradients inside the sphere. The second concentric sphere having a second coil set thereon which has a similar current distribution and winding pattern to the first coil set such that it will perfectly shield the inner sphere while reducing the linear gradient inside the first sphere by only a factor of 1-(R.sub.1 /R.sub.2).sup.5, where R.sub.1 and R.sub.