  We deduce that charged liquid droplets minimizing Debye-H\"uckel-type free
energy are spherical in the small charge regime. The variational model was
proposed by Muratov and Novaga in 2016 to avoid the ill-posedness of the
classical one. By combining a recent (partial) regularity result with Selection
Principle of Cicalese and Leonardi, we prove that the ball is the unique
minimizer in the small charge regime.
