Given an infinitely long wire, carrying a linearly increasing current, what is the shape and direction of the electric field induced by the magnetic field?
Given increasing magnetic flux in a cylindrically symmetric region, the shape of the induced electric field is circular. In this case, using the Faraday-Maxwell equation, and rectangular loops in 3 mutually perpendicular planes, we can prove that the resultant electric field is composed of straight lines, and is directed opposite the current.
However, induced electric field lines always form closed loops. I would greatly appreciate it if someone could diagrammatically show me the individual closed loops (with direction), and explain how they vectorially add to form the resultant field..