Hi. It's Mr. Andersen and this is AP Physics essential video 36. It is on equipotential
lines which are going to be lines of equal electric potential. So imagine we have a positive
charge right here. If you were to draw the electric field what would that look like?
Again by convention we are are going to move the arrows away like that. And so what is
an equipotential line? It is going to be connecting areas in that electric field that have similar
potential. And so if we look at these arrows you can see they are changing their gradient
according to the strength of the electric field. Well this arrow and that arrow and
that arrow all look about the same color. And so what we could do is we could connect
those with equipotential lines or isolines is what they are called. If we were to take
a negative charge like this. We are going to have all of those electric field lines
pointing in. And so our equipotential lines would look like that. What if we had a positive
and a negative charge? What would the electric field look like? Well we would have to combine
that, the negative and the positives. So you would have to do a little bit of vector addition.
But we would get electric field lines that would look like this. Where are those equipotential
lines going to be? Well they are going to be a little more difficult to draw and they
would look something like that. And so equipotential lines, in the last video we talked about contour
lines that show lines of equal elevation and therefore equal gravitational potential energy.
Well we are going to use that as an analogy to explain what is really going on if we are
looking at areas of equal electric potential. And so if you have an electric field, and
we have these electric field arrows representing the electric field, an isoline is going to
be lines of equal electric potential. And so equal potential, and that is why we call
them equipotential lines. And so one thing you should know is that they are always going
to be perpendicular to the electric field. And so if I look at, for example this electric
field right here, you can see it is pointed in the downward direction and we can see it
is totally perpendicular to that and to that and to that. It is always going to be perpendicular
to the lines of the electric field. And so if we take a test particle, if we take a positive
particle and we are moving it against the electric field, remember, we are going to
have to do a certain amount of work to move it in that direction. But a take home message
you should get is if we take a test particle like this and we move it along the isoline,
since the potential energy is never changing, it requires no work to do that. It is kind
of like walking along a mountain side but you are staying at the same elevation. Now
you might be spending energy to move in the horizontal, but you are not spending any energy
to move in the other direction. And so if we have two parallel plates like this, I have
drawn the electric fields, and we have talked about that. Do you remember how the potential
is going to differ as we move across that gradient? Well again, it is not. And so we
would draw those equipotential lines like this. In other words it is going to be the
same slope. It does not matter where we put it. It is going to be the same potential difference
between the two sides. As long as they are close enough together in relation to the length
of the overall parallel plates. And so you can think of this almost like a inclined plane.
And so since these lines are equally spaced, then the slope is going to be consistent from
the left side to the right side. We are going in the direction of the gradient. And so if
we were to take a ball and put it at the top, it is going to experience the same potential
as a ball that we put farther down. And likewise if we are going to move it up we are going
to have to do work in this direction to move it that direction. But it is going to be consistent
amount of work as we move up. And so this is a consistent electric field. And therefore
we have consistent equipotential lines. So now let's look at an electric field that is
not consistent throughout. So imagine we put a charge right here in the middle. So we are
going to put a positive charge here in the middle. If we were to draw equipotential lines
they are going to look like concentric circles. But again the closer we get to that test charge
we are going to see an increase as that inverse square of the radius, Coulomb's Law. And so
if I were to represent this three dimensionally, and this is my best try, I drew a bunch of
concentric circles like this. And now I am going to simply lift those concentric circles
to the potential that they are at. And I am going to project it like that. So what we
get is a three-dimensional progression. And really what we are showing is a topographic
profile. The closer we get to that charge, the higher the potential energy is going to
be. And so you can think of putting a test charge here on the side of it is like putting
a ball on the side of hill. It is going to move down. And so it is going to fall at faster
rate when it is close to that positive charge. Let's say we try a negative charge. We are
going to get a similar relationship like this. If we were to graph those concentric circles
again, in three dimensions, and we project them, it is going to be like a giant hole.
And so if you put a test charge on the side of that, where is it going to go? It is going
to spiral into the inside of that. What if we had something like this though, if you
were given a bunch of electric fields and you have to figure out where those equipotential
lines are. Well one thing that you should always remember is the equipotential lines
are going to act perpendicular to the electric field. And so what I have done is gone through
on each of these arrows and drawn a simple straight line that is perpendicular to that
arrow. And if we get rid of the arrows you can start to envision where these equipotential
lines are going to be. And so if I show you where they actually are they would look like
that. So we are really going to have, if you think about it, let me turn this sideways,
we are going to have a mountain on one side and a valley on the other side. And so what
would happen if we were going to put a positive charge right here? It is going to clearly
move in the negative direction. Or if we have a charge here we are going to have to do a
lot of work to move it in that direction like that. And so did you learn to determine the
structure of isolines? Again it is going to be lines of equal electric potential. Did
you learn to predict the structure of those equipotential lines if you are given the electric
field? Again always remember that we are drawing perpendicular lines. And then finally do you
know how that is going to affect a charge? So if we put a charge inside here, it is clearly
going to move in that direction. But if we move along that equipotential line, since
we are not changing the electric potential we are not doing any work. And I hope that
was helpful.