Now that we've defined the electric field
which again tells us how much force a particular charge would experience
if we placed it in the presence of another charge,
we're ready to move on to our second definition
which is the definition of the electric potential and voltage.
The way we define the electric potential is very similar to the electric field
in that we take a given charge and start asking about different aspects of distances from that charge.
The difference between the electric potential field
and the electric field that we discussed is that the electric potential field
is defined as k times q simply divided by the distance that you are away from a charge
and secondly, this electric potential field is a scalar not a vector and this is very important.
Before I go into the scalar nature of the electric potential field,
note the symbol that we used to define the electric potential field is the Greek letter, phi.
This letter phi is often used sometimes in angles just like theta
but in this context we're going to be using it as an electric potential field.
The fact that this field is a scalar rather than a vector field
without having directions means that we would draw it a little bit differently.
There are few ways to try to represent a scalar field but one of them is shown here.
What I've done is simply represented the magnitude of the scalar field by the size of the dot.
So, for example, the magnitude of the scalar field close to the electric charge here
is much greater and as you move further and further away from the charge,
the scalar potential dies away and becomes smaller and smaller.
This scalar electric potential has units of joules per coulomb or volts.
This electric potential field as we're going to discuss is related more to the energy
that a charge would have if it were moved through this field.
Because what we care about is the energy that a charge would experience
or the energy we need to move a charge through the field,
what we usually care about in this context is something called the voltage
while even though we discussed volts as a unit,
it's also used to measure the difference in the scalar electric potential field
from one position to the other.
So, for example here on the right, what I could do is take the scalar potential value
at one point and at another point and take the difference between the electric potential fields
at each of these points. The difference in that value is called the voltage.
The voltage, this scalar potential field difference between the two points
is of course measure in volts and we give this voltage,
this difference in the electric potential field between two points, a variable letter V.
As I mentioned, the units of volts, one volt is one joule per coulomb.
So, what is this trying to tell us?
What this is saying is that to move one coulomb a certain distance across a particular voltage,
how many joules or how much energy do I need in order to take the charge
and move it through my electric potential field?
The electric potential field just like the vector fields also follows an idea of superposition.
Meaning that if I know what the electric potential field is from one charge and another charge independently,
I can simply add the electric potential at each point in space and find the total electric potential field.