In order to obtain an improved estimate of Neptune's magnetic field and hence the size and structure of the magnetosphere, a new scaling law for planetary magnetic fields has been developed. Starting from magnetostrophic balance between the coriolis force and the j¿B ponderomotive force, we have derived a scaling relation which can be used to calculate magnetic field strengths using only the observable properties of a planet. Specifically, using the planet's mean density, radius, mass, rotation rate and internal heat source luminosity, we can obtain an estimate of the magnitude of the planet's magnetic field from the same parameters for the earth and earth's magnetic field. The estimated magnetic field is, however, an upper bound and good agreement with observations is expected only if the planet' dynamo is fully developed.

This is apparently true for earth, Jupiter, Saturn, and Mercury for which good agreement is obtained between predicted and observed magnetic fields. In contrast, the moon, Venus, and Mars appparently lack currently active internal dynamos and force balance may not hold. From a comparison of theory and observations, we conclude that planetary dynamos are two state systems with either zero intrinsic magnetic field or a field near the upperbound determined from magnetostrophic balance. The calculated upper limit for the Uranus magnetic field is 0.3 at the equator 1 bar level.

The value for Uranus' magnetic field reported by Ness et al. based on Voyager observations is 0.23 G. Given this excellent agreement between calculation and observation and also noting that Neptune possesses a large internal heat source, we expect Neptune's magnetic field at the 1 bar level to be between 0.5--0.4 G. The expected bow shock stand-off distances range from 20--40 RN (Neptune radii). Hence, Neptune's satellite Triton at 14.6 RN lies within the magnetosphere. Nonthermal radio emission generation may be possible in regions of sufficiently low polar ionospheric plasma densities. Finally, we show that agreement between observed and predicted magnetic fields derived from Blackett's ''Bode's law'' scaling relation are fortuitous and are owing to a weak sensitivity of predictions to some combinations of parameters appearing in our scaling law.