Question

Can electric fields be ever non conservative? . If so give an example.

Answer 1

Electrostatic fields, like gravitational fields are conservative because the work \[ \int\limits_{a}^{b}F* dl\] is path independent. To make it nonconservative, we have to disturb it by adding a magnetic field or moving an electric charge (they are basically the same thing).

Answer 2

Electric fields are non-conservative in the presence of a changing magnetic field. Mathematically, a field is non-conservative when its curl is nonzero, and Faraday's law says that

curl (E) = -dB/dt.