We consider Benham’s model for strand separation in supercoiled circular DNA. This is a mean field model in external inhomogeneous field, conditioned to small values of the perimeter. Under some conditions on the external field, we prove a large deviations principle for the distribution of the magnetization under the Gibbs measure. The rate function strongly depends on the structure of the external field. It allows us to prove a law of large numbers and to study denaturation as a function of the temperature and the superhelical density.