Hi. It's Mr. Andersen and this AP Physics essentials video 46. It is on calculating
the electric force. In physics we will deal with problems like this where we have a normal
force, tension and friction. But what you have to understand is that if we zoom in we
will see that these are all atoms. And there are interatomic forces and then forces between
these objects. And they are almost hovering on top of each other. So to understand what
is really going on at this level you have to understand how these charges are interacting,
or these electric forces are interacting. And so if you ever have two charges that are
close to one another we are going to have an electric force between the two. Now those
electric forces can be attractive if the charges are opposite in charge. Or they could be repulsive
if they both have the same charge. But the formula is just Coulomb's law, to calculate
how big that electric force is going to be. Now if you look at that equation it is going
to look very similar to Newton's law of universal gravitation. They both have a constant, K
is Coulomb's constant where we had gravitation constant. Instead of multiplying the masses
times each other we are multiplying the charges. But it is also an inverse squared law where
we are taking the distance between the two and then we are squaring that value. And so
to calculate the electric force, all you need to know are the constant, which you should
memorize as quickly as you can, the two charges, we are going to multiply those times each
other. And then we are going to divide that by the square of the distance between the
two. And so in physics I you should be able to calculate the electric force between just
two charges. And then as you move on to physics II you should be able to calculate more charges
kind of piled on top of each other. And so here is Coulomb's law again. If we have two
charges that are equal in nature there is going to be a repulsive force, but the force
is going to be the same on both of those. And then if they are opposite then it is going
to be an attractive force. And here is our equation. It is going to be the same on both
charges. And so it is Coulomb's constant, which is 9.0 times 10 to the 9. And so that
is easy to remember as 9 E 9 newtons times meters squared divide by Coulomb's squared.
So that is a constant you should simply memorize. Then we are going to multiply our two charges.
In this case it would be q times q. And then we are going to divide that by the square
of the distances between the 2. How far the charges are separated. And so let me give
you an example of a problem. Let's say we want to calculate the electric force between
two charges that each have a 2.0 micro Coulomb charge. What is a micro? That is 1.0 times
10 to the negative 6. You also might see nano Coulombs. That is 1.0 times 10 to the negative
9. Coulombs are a really large charge. And let's say they are separated by 4.0 centimeters.
Now you are going to have to calculate to meters. And so let me show you how I would
solve this problem. I know Coulomb's constant. That is 9 times 10 to the 9. Now I know my
two charges which are going to be 2.0 times ten to the negative 6 Coulombs. And then I
am going to get my distance which is going to be 4.0 times 10 to the negative 2 meters.
Again I have to convert that to meters. So I am going to solve it like this. I have Coulomb's
constant here. Here are my two charges on the top. Since they are both positive I do
not have to do anything with it. But again it is going to be the absolute value of those
two charges. And then I am going to take the distance between the two and I am going to
square that value. That is a common mistake, that you will not square that value and it
is going to screw-up your answer. So let me kind of simplify a little bit. So I have multiplied
everything across the top. And I get 3.6 times 10 to the negative 2 newtons. Now what happened
to all of my other units? We had meters squared on the top and meters squared on the bottom.
So those cancel. And the we had Coulombs squared on the top, or rather on the bottom and Coulombs
squared on the top. So those are going to cancel. So I have a force now. I have a newton
force. And then if I solve that I get 22.5 newtons. Or using significant digits 23 newtons.
And since these both have the same positive charge, that is going to be a repulsive force.
It is a vector between the two. Let's solve another one. Calculate the electric force
between the proton and electron in hydrogen, which again has 1 proton and 1 electron. Let's
say the average distance between the proton and the electron is going to be 5.3 times
10 to the negative 11 meters. So what you should do is pause the video right now and
try to solve this one on your own. And then come back. But if you do not want to do that
let me show you how to set it up. So what I have is the Coulomb constant again. That
is going to remain constant. I am going to calculate my charges, now since I have a proton
and electron, what is their charge? It is not really given in the problem. Remember
that is going to be the elementary charge. And so we are going to have the elementary
charge of the proton and the electron, which is going to be a negative value. And then
the distance is given in the problem like that. So I am going to set it up like this.
I have my two charges at the top. Again it is going to be the absolute value. So the
negative has gone away. And then I have my distance, I am going to square that on the
bottom. The same way as I did it before. The units are going to be cancelled and now I
have the newton on the top. And then I simplify it and I get 8.2 times 10 to the negative
8 newtons. Since these both have opposite charges then it is going to be an attractive
force between the two. That is what is actually holding the electron in place. Let's say we
move into extra charges. Let's say I have a problem like this. So we have three charges.
They each have, we will say, a charge of q. And I want to figure out what is the charge
on C from both B and A. So how would you solve a problem like that? It is pretty simple.
If I know that there are 2 centimeters between each of these charges I could just do two
separate problems. I could calculate the force of A on C. And then I simply add that to the
force of B on C. Or you could even solve these things, instead of just getting a number you
could solve it qualitatively. And so in other words this is an actual AP Physics problem.
If I had another charge down here, what is going to be the force on B, of all other charges?
Well you could see that A and C are going to cancel because they are going to be equal
in size but opposite in direction. So I could just calculate it. It is going to be whatever
the force from D is. And so since this looks like a square I could figure out what the
distance is going to be here. So that is going to be my r squared value. And so that is how
you figure out electric charge. It is simply Coulomb's law. So did you learn to use Coulomb's
law to make predictions about the interactions between objects or charges? Can you connect
the concepts of electric force and gravitational force? And then finally can you use mathematics
to come up with a result? In other words what is the electric force between two charges,
three charges, four charges or evenly distributed charges? Well I hope that all makes sense
and I hope that was helpful.