Now that we have an idea of what charge is
and how to describe charge in terms of both its units and some particular magnitudes,
let's talk about Coulomb's law which is how these charges react
when they're in the presence of each other.
Coulomb's law is a law that describes the force that two particles will experience
if they're both charged and they're in each other's presence.
The magnitude of this force and it's important to emphasize it's the magnitude
because this will also have a direction which we'll talk about.
The magnitude of the force between these two charges, q1 and q2 for the two charges,
separated by some distance, r is given by the force equaling,
k times the product of these two charges divided by the distance between the two charges squared.
The direction of the force will be together for opposite charges.
So for example, this positive and negative charges would be
attracting each other whereas for the same charge it would be apart.
So, opposite charges attract and like charges repel.
This k value that we've introduced in the equation for force is a constant number k
which is 9 times 10 and it's a very big number
so you see that this number, unlike gravity, is a very, very big number.
So, it's worth emphasizing that this force equation is simply a force equation
like any for equation we've introduced.
It's a particular kind of force and so it will still follow Newton's second law
meaning that if I know the force between these two charges
and I also know their masses, then I can find out how they will accelerate
under each other's influence of the electric force.
So we're going to do this sometimes if we know the mass of an electron
and the mass of a proton, remembering that the mass of the proton is much, much greater,
we can find the accelerations of either object by knowing their masses
and by knowing Coulomb's law for the force that they experience from each other.
This force will be equal and opposite.
Equal in magnitude and opposite in direction for each charge.
In other words, this still follows Newton's third law.
So these forces that each object will experience are still on opposite directions of each other.
Finally, it's worth pointing out the similarity that this equation that we have,
Coulomb's law for the electrical charges has with the gravitational force
that we've already talked about.
Comparing these two equations you see that you're still taking the product of two numbers.
In one case you care about the mass, in the other case,
in this case, you care about the electric charge.
It still depends on the distance between the two squared
but for each of these forces we have a different number pulled out on front.
In the gravitational case we have G which we saw was a very, very tiny number
whereas in the electrical case we have k which we saw was a very, very great number.
So, it's a great thing to know, a good thing, an important thing that is to know
that the electrical force is far, far, far stronger than the gravitational force.
The gravitational force being one of the weakest forces that we are aware of in physics.
One last thing that's really important to understand
about the nature of these electrical forces is that they follow a law of Superposition.
All that means is that suppose we have a charge that's experiencing a force
from multiple different directions and we want to find the total force
that this object is experiencing all we have to do is add up
the two forces that it's experiencing from the two different places.
We have to be very careful about the direction here though
because one force might be pointing in one direction
while one force might be pointing in another direction.
In other words, these are vectors and so we have to be careful with the magnitude
as well as the direction of these vectors,
what components these vectors have while we're adding the forces together.