In volume two of the Feynman Lectures on Physics, Chapter 18, here: http://www.feynmanlectures.caltech.edu/II_18.html
There is a scenario in which an infinitely extending charged sheet is suddenly kicked into motion, parallel to its orientation. Electrostatic effects are being ignored here. Once this happens, a current is set up, and a 'wave' of magnetic field is propagated away from the sheet at a velocity $v$ in both directions, as shown in the following diagrams (taken from the Feynman Lectures website):
I understand the indicated directions of the magnetic field lines, this is a standard sheet current setup. Why are the induced electric field lines pointing in the indicated direction? Is this obvious from Faraday's Law, $\nabla{\times}{\textbf{E}} = -\frac{\partial{\textbf{B}}}{\partial{t}}$? Should the direction of the electric field lines not change on either side of the sheet?