We've now introduced how to talk about electricity
as well as electric charges and the forces between electric charges.
We're now ready to go into some fields, ideas of electric fields,
as well as the energy stored in electric fields.
As a summary, remember that what we're going to be doing next
is circuits and magnetism but as we wrap up this part on electricity
and talk about fields and energy, we're going to be introducing three new quantities
aside from the electric force and they have similar names sometimes
and they also can appear similar and so it's very important
as we go through this that you are able to keep them distinct in your mind.
So, as we go through the next few definitions,
really be thinking about what the differences between them are,
what the peculiarities between them are,
and I'm going to try to point them out and emphasize them as well.
The first of these quantities, these three that we'll introduce, is the idea of an electric field.
We'll then talk about electric potential and how that's related to voltage,
and then finally, get in to talking about energy, electric potential energy.
We'll start with electric fields though.
As we've seen, what if I had a negative charge near a positive charge
we know that there's going to be a force trying to pull them together.
What we could do is maybe put this electric charge,
the positive one, at different places around the negative charge
and ask ourselves a simple question, what would happen to it?
In which direction would it want to move?
We could plot that which I've done in the green arrows here.
If I put this positive charge at any place around this negative charge,
it's going to be attracted to the negative charge with the force given by Coulomb's law.
We could then ask ourselves a new question
which is instead of what is the force and what is the direction of the force?
What if I only care about this sort of green arrowed field that I've drawn
and I don't particularly care right now about which charge I put in that field
because I'm only interested in the central charge which is causing the field in the first place?
In order to do this, we might do what you could expect which is for the force equation,
the force given by Coulomb's law, we could simply divide the force equation
by the second charge and come up with a new quantity
which has nothing to do with that second charge
that we put around the first charge and only has to do with the first charge itself.
This is called the electric field.
We represent the electric field by the letter E and the magnitude of the electric field
as we said is equal to the Coulomb force divided by one of the charges.
So, the electric field is simply something derived from a single charge and asking,
what force would a charge feel if I put it in the presence of my central charge?
For given charge q in this electric field, we could then reacquire our equation for the force,
our Coulomb's equation, simply by multiplying that new charge.
So, if I introduce a charge back into this field
and I want to find out what is the force on my charge, I simply multiply by that charge.
I multiply the electric field by whatever that charge is no matter how many charges I put into the field.
The units of the electric field are as you would expect from how we derived the electric field.
It would be Newtons from the force equation from Coulomb's law
divided by Coloumbs since we divided the force equation by the second charge.
So, we have Newtons per Coloumb.
In other words, how many Newtons of force do I experience per Coloumb introduced into the field?
Finally, it is also important to notice that just like the force field,
the electric field is a vector field which is different from some of the fields
we're going to introduce shortly.
What I could do is point out some properties now about the electric field lines.
First of all, the electric field lines as we discussed when we were deriving this
are always pointing in a direction that a positive charge would move
and so if you're ever trying to plot the electric field lines or interpret electric field lines,
always remember this definition that they are pointing the direction
that a positive charge would move if I placed the charge at that location.
Also, for this exact reason, it is not possible for field lines to cross
because if they did, I could ask myself, what happens at the crossing point of those field lines?
And if I put an electric charge there, I suddenly have an ambiguity,
which direction is it going to move since I have two different lines it could follow?
And so electric field lines could never ever cross.
Also, the way we draw electric field lines is to make them more dense.
We draw more field lines as I've done here in the case that we have more electric charge
or a stronger electric field.
We've talked already about the idea of superposition
which just means that we can add vector fields on top of each other
so that at any point in a field like the force field,
we could find the total force at that point
by simply adding up the force from all the different contributors.
The electric field follows the same principle.
So, for example if I had two charges like we have here one next to the other,
I could draw the electric field lines from each
and then simply by adding the value of the electric fields at each point,
I could come up with the shape of the electric field for the two charges together
as we see below here as well.
The direction of the electric field lines are going to depend on the charge that is producing them
and this just comes directly from the fact that we said the electric field lines always follow
whatever direction a small positive charge would move if I placed it in the electric field.
So for example,
in this top picture what we have is a negative charge and a positive charge.
Since we know a small positive charge would move away from the positive charge
that we have on the right here.
We know that the field lines should go away from our diverge,
away from the positive charge while going in towards a negative charge
and again, you can think of this as this picture introducing a small positive charge
and then following where it would need to go
by being repelled by one charge and attracted to the other charge.