We show that if µ is a probability measure with infinite support on the unit circle having no singular component and a differentiable weight, then the corresponding paraorthogonal polynomial Φ n (z; β) solves an explicit second order linear differential equation. We also show that if τ = β, then the pair (Φ n (z; β), Φ n (z; τ )) solves an explicit first order linear system of differential equations. One can use these differential equations to deduce that the zeros of every paraorthogonal polynomial mark the locations of a set of particles that are in electrostatic equilibrium with respect to a particular external field.