Can anyone tell me the physical interpretation of the flux of an electric field through a closed surface. I think I do understand what flux is: Like in a water pipe a flux integral over the surface of the pipe would be the volume of water passing through the surface per second. What is the electric field dotted with the area? I've seen things like: It's the number of field lines passing through etc. but I don't like that picture, since field lines are not really a physical thing to me.