I am working through electrodynamics at the moment and I have a rather elementary question - which I apologize for. But after some research on google I am still not sure if I have understand "the point" of stokes' theorem correctly:
So let's say we have a given electric field and a given curve for which we should estimate the work done.
Stokes' theorem can only be used for closed curves
Stokes' theorem can not be used for open curves
Stokes's theorem can only be used in non-conservative fields (otherwise curl=0)
Since closed curves in conservative fields imply W=0 and got no curl, it only makes sense to have a method for closed curves embedded in non-conservative fields.
The given electric field must have been produced by a magnetic field, because electric fields created by charges do not have curl.
Have I understood that correctly ?
I know that this question is extremely elementary but I am trying to get the whole idea of this and trying to understand the "joke" about stokes' theorem.