Visualising Div and Curl

Some people are happy with just the maths equations. For myself, I want a geometric picture to really understand and use a concept. Thanks to Daniel Fleisch for the best description of how to visualise Div and Curl from this book. Click on the images to make them larger and readable.

A good introduction to Maxwell's Equations

Visualising the Div operator

Visualising the Curl operator

The Grad operator (on a scalar field), applied at a point on the surface, delivers the tangent vector pointing up the steepest slope, with its length measuring the steepness. That's pretty easy to visualise.

Richard Feynman commented somewhere that in the distant centuries yet-to-be, when people look back to the nineteenth century, they will remember it for just one thing: it was the century when Maxwell's equations were formulated.