I guess my question can really be boiled down to two questions:
1. Can an electric field function be mathematically possible while its curl is non-zero?
and
2. Can an electric field function be mathematically IMpossible while its curl is zero.
I have a question pertaining to mathematically possible E fields.
I've always known the curl of the field has to be zero for the field to be a possible electric field, but is this the sole determining factor? What about if the potential is some wonky function that doesn't seem plausible, and...