Electric Force - Coulomb's Law

Alright. Let's talk about electric force quantitatively. And this is called Coulomb's law after a physicist who first developed it in 1783.

Alright. Now, we know that like charges repel and that opposite charges attract. It's almost like the universe is trying to hide the fact that there's charge. If there's ever a big charge anywhere like a big positive charge, it's going to attract all the negative charges to it and try to hide itself, shield itself away and at the same time, all the positive charges are going to be pushed away. Alright.

Well, we know that this, this positive charge and this negative charge are going to attract each other but how much? Well, Coulomb's law says that the force of attraction or repulsion is given by a constant called the Coulomb's law constant, times charge one times charge two divided by the distance between them squared. So it's the inverse square law case. Just like gravity. In fact it's exactly the same as gravity except that this constant, this Coulomb's law constant is huge in this case. 8.98 times 10 to the 9 Newton meters squared per Coulomb squared. The reason for that is that the coulomb is is an immensely large unit of charge. You'll never see an entire coulomb of charge anywhere because it will just strip the electrons and other charge off of neighboring atoms until it has shielded itself.

Now, one easy way to remember this number is to write as approximately 9 times 10 to the 9 and then I always tell my students to think of it as 9 e 9, 99. Easy enough. Alright. Let's do couple of problems.

We'll start off with some ones where, we already know the force. So two charges feel an attractive force of 36 newtons. So now, I want to know what the force will change to if I make the following modifications. First, I'm going to triple the distance between them. Alright. So I'm not changing the charges but I'm tripling the distance. Now Coulomb's law says that the distance appears squared and downstairs. So that means I got one over tripling squared. 36 divided by 9 is 4. And therefore, the force becomes 4 newtons. Alright.

What if I double the distance and I triple one of the charges? Well, the charges appear upstairs. So the tripling is upstairs. The distance appears downstairs but it's squared. So we'll have two squared and then we'll have 36. 36 divided by 4 is 9 and 3 times 9 is 27. So there we go. See, it's real simple. We don't even need a calculator to do most of these problems. Alright. What about if the distance and both of the charges are tripled? Well, in this case each of the charges is upstairs. So I got triple triple. Downstairs I'm tripling the distance, so that's 3 squared and then i got my 36. But here, all that business cancels. So that means if I do the same thing to both of the charges and to the distance, force is totally unchanged. So this is just 36 newtons.

Alright. Second problem. Now in this one we got to determine the force from Coulomb's law. What is the magnitude of the force between a two nanocoulomb charge and a -3 nanocoulomb charge that are separated by 3 milimeters? Alright. One of the big things about electric charge is that the coulomb is such a big unit. So you almost never see coulomb by itself. It almost always comes with prefixes like micro and nano. Remember that micro is 10 to the -6 and nano is 10 to the -9. So let's go ahead and calculate this force. Force k q1, q2, r squared. Alright and plug in. 9 times 10 to the 9. Now I got to use SI units. So our first charge is 2 nanocoulombs, so we got 2 times 10 to the minus 9. Second charge is -3 nanocoulombs. And the distance is 3 milimeters. Again, I got to make that in SI. Now, this always happens or almost always happens when we're doing electri- electrostatic problems and also in gravity problems. We've got bunches of numbers and bunches of tens all multiplied and divided. The easiest way to do this is to do all the numbers first and then do all the tens. So I'll write this as 9, 2, -3, 3 squared. So I just did the numbers and now I'll do the tens 9, -9, oh, this should be -9. Look at that. -9, right, and then it's -3 squared. So these two because this is in the exponent, I'm going to multiply. So it will be -6, but it's downstairs. So really it's +6. And then we'll have 9 cancels. 2 times -3 is -6. 9-9 is 0. -9+6 that's -3. What's my unit? Well, it's SI and it's a force, so it's got to be newtons.

So I'll write the magnitude as 6 milinewtons. Notice I dropped the minus sign because all the minus sign is telling me, is that it's attractive. Alright? That's Coulomb's law.