Why are induced field lines circular?

Whenever we have a changing magnetic flux through a conductor an induced electric field is generated. It is often said that these induced electric field lines are circular in shape.But why is this so?Why are these field lines not elliptical for example? How can this shape be mathematically derived?

Also does this have anything to do with equipotential surfaces?Do such non-conservative electric fields even produce a potential field?If not why?

• They can be elliptical. The shape of the induced electric field depends on the shape of the changing magnetic field. – S. McGrew Oct 19 at 14:33
• How can this shape be mathematically derived? – Schwarz Kugelblitz Oct 19 at 14:44
• What can be done to attract answers – Schwarz Kugelblitz Oct 20 at 18:34
• "How can this shape be mathematically derived?" It is pretty straightforward if you know vector calculus. Just use Maxwell's equations to describe a changing current density, and solve for the induced electric field. – S. McGrew Oct 26 at 20:38
• I don't know vector calculus – Schwarz Kugelblitz Oct 26 at 20:56