Water Analogies for Divergence, Curl and Gradient
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, w...