It’s fun to think about the fundamental physical constants. These are special values used in our models of the physical universe. They include things like the speed of light, the gravitational constant, and Planck’s constant, and they’re “fundamental” in the sense that we can’t derive them theoretically, we can only measure them.
We use these in solving physics problems all the time, so it’s easy to take them for granted. But why are there such numbers in nature, and why do they just happen to have those specific values? Because, listen, if they were only slightly different, the universe might be incapable of supporting life. Did some cosmic clockmaker set these parameters? Isaac Newton thought so.
One of the most basic of these numbers is the electric constant, k. It’s a value that lets us calculate the forces between electric charges. That’s a big deal when you consider that all matter is made of just three things—electrons, neutrons, and protons, two of which have an electric charge. The interaction between electrons is what forms molecules to create you and everything around you. Otherwise it would all be just some undifferentiated soup.
But how do we know the value of the electric constant? Also, what does it have to do with other fundamental constants? And for that matter, is it really fundamental? Let’s investigate.
Coulomb’s Law and Constant
When we say something has an electric charge, we mean it has a different number of protons and electrons. If your clothes dryer removes some electrons from your socks, they become positively charged. If they gain electrons, they’ll be negatively charged. (Note: You can’t take away protons, since they’re in the nucleus of the atom. It would involve a nuclear reaction, which nobody wants.)
If you have two objects with opposite charges, they attract. If they have the same charge, they repel. Here’s a demo you can do yourself: Take a piece of clear tape and place it on a smooth table. Then put a second piece on top of that one, and pull them off together. Now, if you separate them, one will be positive and one will be negative; hold them in proximity and they will bend toward each other.
If you repeat the process, you’ll have two positive and two negative tapes. Hold two with similar charges near each other, and you’ll see that they repel, like in the picture below:
