Abstract
The problem of a cylindrically symmetric configuration of charged rotating dust is studied under the additional assumption that the Lorentz force on a typical particle of the fluid vanishes. Exact solutions with differential rotation are presented both in Newtonian physics and in general relativity. In the Newtonian case one particular solution exists which is regular, but which has a vanishing matter density on the axis. For the relativistic case the general solutions of the problem can be given in terms of hypergeometric functions; particular families of solutions are discussed for which the relevant physical quantities are regular on the axis.
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