I have posted this question earlier also. But i am changing my sentences a bit. This is regarding conservative and non-conservative nature of magnetic field. I have two points to make here: (1) Since the work done by magnetic field is zero in any closed path, thus the magnetic force is conservative in nature. (2) Since amperes law is saying that the integral of magnetic field in closed loop is not zero. Thus the magnetic field as such is not conservative. Please comment!! So, if my understanding is correct, then i would conclude that the fact that the field is conservative doesn't mean that the force due to the field will also be conservative and vice-versa.