Intuitive

• Flux is the amount of “something” (electric field, bananas, whatever you want) passing through a surface.
• The total flux depends on strength of the field, the size of the surface it passes through, and their orientation.

Vector Calculus: Understanding Flux by Kalid Azad

Concrete

• A perfect explanation of the flux in vector calculus can be found in Section 3 of Vol. 2 of Feynman's Lectures on Physics, which are available here
• See also Vector Calculus: Understanding Flux by Kalid Azad

Abstract

Why is it interesting?

Once you understand flux intuitively, you don’t need to memorize equations. The formulas become “obvious” dare I say. […] Your vector calculus math life will be so much better once you understand flux. And who doesn’t want that? Vector Calculus: Understanding Flux by Kalid Azad