  We present a no-go theorem for spherically symmetric configurations of two
charged fluid species in equilibrium. The fluid species are assumed to be
dusts, that is, perfect fluids without pressure, and the equilibrium can be
attained for a single dust from the balance of electrostatic repulsion and
gravitational attraction. We show that this is impossible for two dust species
unless both of them are indistinguishable in terms of their electric charge
density to matter density ratio. The result is obtained in the main three
theories of mechanics, that is, in Newtonian Mechanics, in Special Relativity
and in General Relativity. In particular, as charged dust solutions have been
used to study the possibility of black hole mimickers, this result shows that
such mimickers can not be constructed unless the underlying charged particle
has the correct charge to mass ratio.
