The electric field in terms of the electric scalar potential, and the magnetic vector potential is:
$E = -\nabla\phi - \frac{\partial A}{\partial t}$, where $A$ is such that $B = \nabla \times A$.
In this field configuration:
a change in the poloidal current sheet $J$ will cause a change to propagate through $A$ and a corresponding electric field pulse, coextensive with the changing $A$. Is this $E$ field accompanied by a non-0 $B$ field other than the one already inside of $J$? Does the change propagate at the speed of light?