Comment: A really nice
water analogy for the field properties Divergence, Curl and Gradient from the Blog
Starts With a Bang ....it's pretty mathematically intensive, but what's missing from most textbooks and E&M courses are
physical explanations of what the
mathematics means. For instance, I've started teaching about fields, and pretty much every textbook out there goes on and on about the properties of fields. They say you can do three things to fields, take the
gradient,
divergence, or
curl of them. (Are you asleep yet? I'm sorry!) What do these things mean? An easy way to picture it is in terms of water. If you placed a
drop of water anywhere on, say,
Earth, the
magnitude and direction of how it rolls down is the
gradient of the Earth's elevation. If you let that drop of water flow, as it goes downhill, it can either spread out or converge to a narrower stream. When we quantify that, that's what the
divergence of the field is. And finally, when that water is …
Robert E Dickinson 
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