Thursday, April 07, 2016

Coulomb's worth of sand?

I teach Coulomb's Law to my regular Physics (mostly juniors and seniors) as well as my freshmen Conceptual Physics students during our Electrostatics unit.  The younger students struggle every year and because of their math level I agonize over including it in Conceptual Physics at all. The sheer size of the numbers involved confuse them and then the use of this "strange unit" called a Coulomb doesn't help. Every year I try to equate the use of the Coulomb as the unit of charge to a dozen eggs which helps some but not all.

A few years ago I decided that I wanted to make them a visual, something they could see that would help them understand the size of the Coulomb. I thought of the Mole cubes I had seen in Chemistry, they are about a cubic foot and proudly proclaim "1 Mole of" and list the masses of different gases. I could do the same thing and say I had a box with a Coulomb's worth of air in it but since they couldn't see the air this probably wouldn't help with their understanding. I wanted a Coulomb Cube, I just had to figure out how big to make it and what to put in it.

I tell my students this story as a way of introducing a Coulomb and they follow the same thought process I had when asked: "What is something fairly uniform and small that we could gather a Coulomb worth of?" Students usually volunteer answers: "Marbles! Rice! Sugar! Salt!" and then usually arrive just as I did at grains of sand.

When I first looked into this problem I found quite a few resources on the different sizes of grains of sand on math websites. Apparently it is a common estimation problem to figure out how many grains of sand there are on a beach, in a dessert or on the whole planet. Using the smallest average grain of sand CosmologyScience.com determined a cubic foot of sand would hold one billion grains of sand.

The Math Dude estimates "8,000,000,000 grains of sand per cubic meter." Since his are in metric, I'm going to discuss the calculation with his values. If we take a Coulomb to be 6.25x1018 charges ("grains of sand"), if we divide a Coulomb by the estimated number of grains of sand in a cubic meter we get:
Since I wanted to build a cube, (although at this point I already realized I was in trouble) I found the cube root of this amount of cubic meters to see how large my cube was going to be on a side.
So, I didn't build a Coulomb Cube, and realized that I had trouble grappling with such a large number as well. When I tell my students this story and tell them I would need a cube that was almost a cubic kilometer their jaws drop. While I don't have a physical manipulative to show them, discussing the thought problem at least illustrates the sheer volume of a Coulomb. Get it? *ba-dum-bum-CHING*