Hi. It's Mr. Andersen and this is AP Physics essentials video 22. It is on the vector field.
If I could hold the moon in place and just let it go, it would crash into the earth.
And the reason why is that there is a gravitational force that is pulling the moon towards the
earth. And we could represent that with a vector field. And that is a set of arrows
that show where this force is pointing. And in this one those smaller circles say that
the force is getting greater the closer that moon that gets to the earth. Now we know that
the moon does not just crash into the earth. We know that it orbits around the earth. And
the reason why is that it has a certain amount of velocity. And that velocity allows it to
just keep missing the earth. And so what is a vector field? Well it shows the position
in 2 or 3 dimensions of a vector quantity. Now vectors remember are different from scalars.
Vectors are going to have not only a magnitude of a force or a velocity for example, but
they are also going to show the direction in which that force is pointing. And so in
Physics 1 you should really understand how to do vector fields for objects related to
their gravitational attraction. And then in Physics 2 it is more with electromagnetism.
And so let's say we have two charges, a positive and a negative charge, you should be able
to sketch out the vector field, the force of attraction between those two. Now you also
should be able to look at a vector field like that and figure out where are those charges
and how big those charges are. To do that a lot of the time you have to add the vectors
or do vector addition. So we will go over that. And so what is a vector? Remember it
shows not only the magnitude but the direction. And if you have ever played Angry Birds, this
is an angry bird that I drew and so it is not very good, what you do is you pull back
on the sling shot and then you are going to apply a force to that angry bird. And so you
are not only showing how big that force is, but you can vary the direction in which it
is pointing. And so you could pull it back a different distance in a different direction
and we would give it a different vector. Now imagine you are playing multi-player angry
birds, which I do not think you could do, but let's say both players have to pull back
that angry bird and they both pull it back in different directions with a different force.
How would you ever figure out which way that bird is going to go? Well thankfully in physics
we can use vector addition. What you do is take those two arrows and you line them up,
tail to tip, tail to tip. And then we can go from the origin of that first one that
shows us the vector of those combined forces. And so mapping vector fields is kind of hard
to wrap your head around and so we are going to use angry birds again to do that. And so
in Physics 1 this would be dealing with gravity, so the attraction between two objects that
have mass. And in then in Physics 2 it would be attraction between opposite charges or
opposite poles if we are looking at magnetism. And so let's take one of these angry birds
are we are just going to pin it there. So that is going to be the source that we are
going to try to map. And the other one we will just use as a sensor. So if we take that
angry bird two it is going to be attracted to the first one and so we could represent
that attraction with an arrow. We can then just move its location and we would see that
there is also going to be attraction here but it is going to be at a different angle.
Same thing here. As we move it farther away that attraction is going to be less and so
we could map those out here as well. And now we have created a vector field. And so we
have the source here in the middle and then all of these arrows represent the vector field.
Not only the magnitude, but the direction in which that force is pointing. And you can
see that all of them are pointing to the source. But let's say that they are pushing away from
each other. And so now we have like charges or like poles. So let's set up our source
again. And then we are going to use our sensor. In this case it is pushing it away. And so
as we move it, same thing, we are starting to plot that vector field. The farther we
go away, the less push there is. And so now we have the source in the middle and then
we have this vector field that we mapped. Now you can see that all of the arrows are
pointing away from the source. And that will be important when we are trying to figure
out where that source is. Let's say we have two sources now. So we have a positive and
a negative charge for example. So how do we figure that out? Well we have to remember
that vector addition. And so we could look at the force between the two reds. And so
that would be a repelling force. And then we would have the attractive force between
the red and the green. And so what we can do is line those two vectors up and that would
be the vector sum. Let's say we go off angle. If it is up here then we have this repulsion
here and this attraction here. So we line them up. And so we get that vector sum right
there. And so we could map those vector fields. And you could do that using magnetism. So
we could use a compass for example. It is working as that second angry bird or you could
just put iron filing on that bar magnet. Put paper over it. And we could see that no matter
where we move that compass it is parallel to those fields. In this case those magnetic
fields. And so a really good game that you could play, it is a phet simulation, called
the electric field hockey, kind of plays around with this. And so we are going to use a puck
that has a positive charge. And then we will put a source somewhere else. And so you can
see when we start it there is repulsion. So we could put it on the other side of the puck
and we could start it. And then we could score a goal. So that is great. Now lets map the
field. So you can see that as I move this source we start to see the vector fields.
And so the brighter the arrows are in this case the bigger that force is. We could now
grab an opposite charge, and you can see now that the arrows are pointing towards it. So
I could position it behind the goal. And so it is slow now. But as the force gets greater
we get more acceleration. Now this game gets harder when you start to put objects in the
way. And so if we just start it now you can see that it is going to collide with that
wall. So that would be a fail. We could now move it up here. So maybe we set this negative
attraction up here. And now we start it. You can see that it is pulling it towards us.
But now we have lost that puck forever. So now we could use multiple charges. So we add
those multiple charges, you can see that we are building a field that is a curved field.
Again it is not quite great enough for us to score a goal, but this would be something
that is fun to play with. Another thing you should be able to do is given a vector field
figure out where the source is. Figure out how many there are, what is its location and
what is its relative size. And so looking at this vector field right here, you are looking
for an area where all the arrows point away from that location or towards it. And so I
would say that there is one source, it is located right here. And it is hard to compare
it to any other sources because there is only one. If we move to another vector field, you
could think about this for a second, how many sources do you see? Well I see one right here.
And then I see another one right over here. So again, looking for areas where all the
arrows move away or they move towards that one point. So those would be to the two locations.
What is their size? Well since all the arrows are of about the same density, I would say
that they both have equal charge. What about right here? How many different sources do
you see now? Well I see one source right here. And then I see another source right here.
You can see since the arrows on this side are more dense, we would say that this is
a greater charge than this charge is going to be over here. So what about this one? How
many do you see? Well I see three. So there is going to be 1, 2 and 3. And so I would
say they all have like charges.Or how many right here? So again, pause the video. Try
to figure out how many sources are there and then their relative size.And so did you learn
how gravitational and electromagnetic sources affect a vector field? I hope so. And I hope
that was helpful.