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tokens: transformation back to the lab frame then gives an electric field and an associated electrostatic potential in the lab frame. We assume here that the jet velocity greatly exceeds the difference J / ne between electron and ion drift velocities, so the jet velocity is nearly the same as the Harris-frame velocity. This means that in the jet frame the electric field and associated electrostatic potential are zero. The nonrelativistic Lorentz transformation relates the jet-frame electric field E ′ to the lab-frame electric field E byBecause the Harris construction in the jet frame gives E ′ = 0, and assuming a jet velocity Equation ( 20 ) gives the lab-frame radial electric field asUsing Equation ( 14 ), the lab-frame radial electric field can then be expressed asSince a gauge with has been assumed, the radial electric field reduces toCombining Equations ( 22 ) and ( 23 ) and integrating gives the lab-frame electrostatic potential asso using Equation ( 16 ) we have 5. Construction of the Electric and Magnetic Field Vectors We now have sufficient information to construct the complete lab-frame electric field. Because of axisymmetry, the electrostatic potential V is independent of φ , so the toroidal electric field isthis electric field component is missing in the static models used by Mestel ( 1961 ), Blandford Payne ( 1982 ), Lynden-Bell ( 2003 ), and Pudritz et al. ( 2012 ); it also differs from the singular E φ proposed in Contopoulos ( 1994 ). The axial electric field in the jet region iswhere Equation ( 24 ) has been used and the last line comes from Equation ( 17 ). The radial electric field using A r = 0 is given by Equation ( 21 ) asThe lab-frame magnetic field is There is no lab-frame electric field parallel to the magnetic field sincewhere Equation ( 9 ) has been used. 6. Demonstration That the Time-dependent Induction Equation Is Satisfied Because ψ is time dependent, both the electric and magnetic lab-frame fields are time dependent. This contrasts with the previous analytic models (e.g., Mestel 1961 ; Sauty 1994 ; Beskin 2010 ; Contopoulos 1994 ) where the jet fields were assumed to be independent of time and the lengthening of the jet was not taken into account. These previous analytic models assumed that the magnetic field is independent of time, so the induction equationis reduced to , which forces U × B to be the gradient of a potential. In contrast, time dependence of the magnetic field is retained here, so U × B is not the gradient of a potential. Using , we see thatsoDirect calculation of the time derivative of Equation ( 29 ) giveswhich on invoking Equation ( 9 ) becomesComparison of Equations ( 33 ) and ( 35 ) shows that the time-dependent induction equation, Equation ( 31 ), is exactly satisfied. Various points of view have been expressed on how the detailed flow moves with respect to the magnetic field. According to one point of view (e.g., Blandford Payne 1982 ), the predominant flow is along magnetic field lines (beads on a