Definition of flux in two dimensions

In two dimensions, the flux of a vector field across a plane curve is defined to be the "flow rate" of the vector field. In many cases vector fields involve no motion (e.g. electric fields, magnetic fields), this definition can be very difficult to comprehend at first. A nice context for working with flux in order to understand its definition is by considering the velocity vector of a fluid (so now we do have motion). In two dimensions, the flux of a fluid across a plane curve is given in units of area per unit time. In other words, the flux tells us how much the fluid (volume) passes through a given surface in one second.