I was trying to think of more impossible electric fields than my book has. I understand it is anything that breaks the rule that the path integral is zero. One example is a circular field. I was trying to picture some more complicated 3d examples. Are all magnetic fields an impossible electric field? I just mean visually, in appearance.
You can have any kind of electric field so long as they obey the boundary relations. "Path integral" (The correct term is line integral, a path integral is something we use in quantum mechanics) being zero around a loop is only true for an electric field generated by stationary charges, in general accelerating charges will generate non conservative electric fields.
Thanks, and yes I was trying to say something like "closed path line integral" I think. So, I could use a computer simulation that generates magnetic fields and moving charges to "see" some impossible electric fields? Such as the 3d magnetostatics one here: http://www.falstad.com/mathphysics.html ?