"So today no new concepts, no new ideas, you can release a little bit and I want to discuss with you the connection between electric potential and electric fields.

Imagine you have an electric field here in space and that I take a charge Q in my pocket, I start at position A and I walk around and I return at that point A.

Since these forces are conservative forces, if the electric field is a static electric field, there are no moving charges, but that becomes more difficult, then the forces are conservative forces and so the work that I do when I march around and coming back at point A must be zero. It's clear when you uh look at the equation number three that the potential difference between point A and point A is obviously zero. I g- start at point A and I end at point A and that is the integral in going from A back to point A of E dot DL and that then has to be zero.

And we normally indicate such an integral with a circle which means you end up where you started. This is a line now this is not a closed surface as we had in equation one..."