  Here we present a systematic study of force-free field equation for simple
axisymmetric configurations in spherical geometry. The condition of
separability of solutions in radial and angular variables leads to two classes
of solutions: linear and non-linear force-free fields. We have studied these
linear solutions Chandrasekhar (1956) and extended the non-linear solutions
given in Low \& Lou (1990) to the irreducible rational form $n= p/q$, which is
allowed for all cases of odd $p$ and to cases of $q>p$ for even $p$. We have
further calculated their energies and relative helicities for magnetic field
configurations in finite and infinite shell geometries. We demonstrate here a
method here to be used to fit observed magnetograms as well as to provide good
exact input fields for testing other numerical codes used in reconstruction on
the non-linear force-free fields.
