In this paper we derive four main results. Firstly, we find an exact and explicit non-cylindrically symmetric (but axially symmetric) solution for charged dust rotating with constant angular velocity in Newton-Maxwell theory for particles with equal mass and charge. Secondly, we find a general solution of the main equation describing differential rotation in Newton-Maxwell theory for particles of equal mass and charge. Thirdly, we derive a new exact and explicit solution of the cylindrically symmetric Einstein-Maxwell interior equations for charged dust rotating with constant angular velocity. An interesting property of the solution is that it is regular and well behaved for certain values of the parameters occurring in it. Fourthly, we show that for cylindrically symmetric, differentially rotating charged dust in general relativity there exists a solution in which the Lorentz force on a typical particle vanishes.