  A significant challenge for experiments requiring a highly uniform magnetic
field concerns the identification and design of a discretized and finite-sized
magnetic field coil of minimal size. In this work we compare calculations of
the magnetic field uniformities and field gradients for three different
standard (i.e., non-optimized) types of coils: $\cos\theta$, solenoidal, and
spherical coils. For an experiment with a particular requirement on either the
field uniformity or the field gradient, we show that the volume required by a
spherical coil form which satisfies these requirements can be significantly
less than the volumes required by $\cos\theta$ and solenoidal coil forms.
