Hi. It is Mr. Andersen and this AP Physics essentials video 29. It is on the
electric field of a dipole. And when I say dipole the one thing that jumps to mind is
a magnetic dipole. A magnet has a permanent north pole and a south pole. But is there
an analog in electrostatics? Do we have a permanent electrostatic magnet? We do. It
is called an electret. And it was developed in the1960s. And what scientists do is they
take something that is an insulator, generally like wax. They melt it so that it is a liquid.
And then they apply high voltage to it. And what it will do is it will polarize those
atoms. And then as it becomes a solid, you have solid permanent electret. So it is going
to have a permanent charge. And these actually are really important in electronics. If you
have a smart phone then the microphone inside it is probably an electret. Because it does
not require any energy. It is permanently charged. And so far we have talked about monopoles.
Where we have a point charge or a sphere and we can see those those electric field lines
are going to go out from that since it is positive. Or if it is negative they are going
to come in. But we have only dealt with them separately. What happens if we bring those
two charges right next to each other? We now have created a dipole. And to understand what
is going on, for example right here, when we have the addition of those two electric
field vectors, we have to use vector addition. And that will allow us to figure out at any
point around this dipole what is the net electric field. And what you get is a map that looks
somewhat like this. It is crazy. And by the end of this if you really understand vector
addition, you should be able to take a point, within up to four different charges and feel
where that electric field is pointing. And to understand that you really have to understand
vector addition. So remember a vector not only has magnitudes, so magnitude of the electric
field, but it also has the direction. And the magnitude is the length. And then the
direction is going to be in which way that arrow points. And so imagine if we have one
point being acted by two electric fields. And one of them we will say is pointed in
that direction. And the other one on this point is pointed in that direction. So what
is the sum? It is the green arrow. So how does that work? Well if you line the vectors
up, tail to head and tail to head, what you will find is they are going to add up to that
green. Let's say we have a point being acted on by these two electric fields. That would
be the sum. Again if we go tail to tip, tail to tip you can see our sum. And we could get
really complex with this. We could have up to 6 different fields. I mean an infinite
number of fields acting on one point. And so if we want to figure out the sum all we
do is start putting them together. Tail to tip. Tail to tip. And by combining all those
vectors we can figure out what is the sum and we get right to the tip of that green
point. And so to show you this we are going to use a phet simulation. What I have here
is a monopole. So we put a positive charge right here. And then we have these e-sensors
around the outside. What they are measuring is the strength of the electric field. And
so you can see as we move farther and farther away, the strength of the electric field is
going to drop off. Now if we take a negative charge, if we put a negative charge right
here you can see the field lines are pointed towards the charge. But it is the same kind
of a relationship. And this is going to be that inverse square of the radius. But since
we are dealing with dipoles what I have down is, let's change the opacity of this one,
now let's just kind of overlap those two fields. And so what we could say is let's do a vector
addition right here. And so this positive is pushing on this in that direction. The
negative is pulling on it in that direction. So if we add those two arrows, I am adding
this one to that one, I should get a net electric field that is pointed in that direction. Or
if we go over here, this one is pulling in that direction. This one is pushing in the
other direction. Our net force should be right here, or net electric field. If we were to
go down here for example, in that direction, in that direction and so our sum should be
somewhere like right here. And so now I have overlapped all of the sum of these two point
charges. Now we are looking at the vector of a dipole itself. And if we were to do that
for every point around these charges, we start to get an electric field. And so if we clean
that up a little bit you can see that this is the electric field of a dipole. And the
only way we could have figured out what is going on at any of these points is by summing
up those vectors of the individual point charges by themselves. And so let's do a little bit
of application of this. What we have here is a negative charge here and then we have
three positive charges. And they are acting on this one point here. So could you just
figure out in your head which way is the net electric field going to be forcing? Well if
you think about it, this positive and this positive are both pushing against that point
and so we could say that they cancel each other out. This positive would be pushing
in that direction and the negative would actually be pulling in that direction. And so we would
see a sum that is going to look something like that. What if we were to put a point
down here? Could you figure out which way it is going to point here? I mean you could
pause the video before I show you the answer. Okay, but if we look right here, so these
two are kind of canceling each other out. This positive is pushing away in this direction.
This is negative is pulling in that direction. But since it is farther away here than it
was here, we would have smaller arrow that is going to be pointed in that direction.
We can actually make this quantitative as well. And so let's say we have a point right
here. So this is a negative charge and then we are measuring it at this one point. And
then again let's put this in two images so it is the same point, but now we have a negative
charge over here. This one is around 9 volts per meter. And this is 9 volts per meter down.
If I want to add those up I could overlap them. Or I could do vector addition. And so
if I create a triangle we have a 9 on this side, a 9 on that side. So to figure that
out, A squared plus B squared equals C squared. So 9 squared, which is 81 plus 81, so to figure
out what that hypotenuse is, it is the square root of 162 or it is around 12.7. And so did
you learn to distinguish between a monopole, that is when we just have one point or one
sphere and a dipole? And then finally did you learn how to use vector addition to figure
out the magnitude of the net electric field on up to 4 points? I hope so. And I hope that was helpful.