Analytic Model for the Time-dependent Electromagnetic Field of an Astrophysical Jet

An analytic model of the time-dependent electric and magnetic fields of an astrophysical jet is presented. These fields satisfy the time-dependent Faraday's law and describe a jet with increasing length. The electric field contains both electrostatic and inductive parts. The electrostatic part corresponds to the rate of injection of toroidal magnetic flux, while the sum of the electrostatic and inductive parts results in the electric field parallel to the magnetic field being zero everywhere. The pinch force associated with the electric current provides a peaked pressure on the jet axis and a pressure minimum at the radius where the poloidal magnetic field reverses direction.