Hi. It's Mr. Andersen and this is AP Physics essentials video 23. It is on the scalar field.
In the last video we talked about a vector field which shows the position of vector quantities.
And a scalar field is essentially the same thing but instead of showing the direction
of all of those quantities, it just gives the magnitude of the quantity itself. And
so we will see these in pressure scalar fields. We will see them in temperature scalar fields.
And then we will also deal with some in electric potential. And so can you figure out what
this is a picture of? Well this is a thermal image. And so it is a scalar field. We could
look right here and we would see the temperature at that one point or that one position. I
would say it is around maybe 32.5 degrees celsius. We could also look right here and
find what is the temperature at that point? So we match up the color and I would say maybe
it is around 24 degrees celsius. But have you figured out what it is? Have you figured
out the source of this scalar field? Well this is a human who is warm-blooded with a
snake wrapped around its hand. And so what is a scalar field? It shows us the position
of scalar quantities. Now scalar quantities are just a magnitude. And so in Physics 2
these are going to be, the most important one would be dealing with a scalar field of
electric potential. In other words, if you are given charges you should be able to figure
out the scalar fields of that area. And to do that lots of times you will have to add
different scalar quantities. And so we have to understand how scalar addition works. And
so let's say I give you a bunch of random numbers like this. Can you see any patterns
in these random numbers? Certain areas they are higher. Certain areas they are lower.
But if I were to connect a lot of these with what are called isolines, where we are seeing
they are the same value then you start to see an image here. And so this would be a
topographic map essentially. It is showing us where the elevation is the same. Where
are all of the scalar quantities equal. And if you know anything about this you would
be able to figure out what this object looks like in three dimensions. We would have areas
where it is higher. Areas where it is lower. One thing that you will notice is that none
of these isolines ever cross. They are never going to have the same elevation for example
at one point. And we will find the same thing in physics. And so now let me study electric
potential. This is phet simulation. You could go there and play around with this on your
own. And so what I am going to give you is a bunch of voltages in different areas in
two dimensions. And so we have high voltages you can see centered right around here. And
so you might guess that there is going to be a positive charge right there. And the
farther we move away, we are going to have a lower positive charge. And so we could draw
in isolines. 18 volt. 9 volt. 6 volt. And so we can start to see why this one right
here has a scalar quantity of 6.3 because it is somewhere between 6 and 9. Let's say
we were to look at a negative charge. And we were to plot all of the scalar quantities.
We would get a scalar field. You can see here that they are all negative values. Negative
18 here. Negative 9 around that. Negative 6 around that. And so that makes sense. The
farther we move away from the charge, the less voltage we have or the less potential
we have. How would you do it if we took those two charges however? How would you take those
two scalar fields and then bring them together? Well let's choose one point. So this one point
between remember the positive gave it positive 18 volts. The negative gave it negative 18
volts. And so all you have to do is simply add those two numbers together. And so what
would we get? 0 voltage is what we should find when we have those 2 quantities together.
What about up here? It is 9 volts. It is negative 6.3 volts from the negative charge. And so
we simply add those up and I get 2.7 volts at that one quantity. So scalar addition just
says take the two quantities and them together. And so when I use the phet simulation I found
out that one point is 2.7 volts. And so you can move it around and check your scalar addition.
You can also add color. And that color, just like that thermal image color shows us where
we are going to have positive values and where we are going to have negative values. You
can then add different charges and we can start to see how those scalar fields are affecting
each other. If I pause this for a second we would see right here in the middle, since
it is white in color there is going to be no charge. 0 volts. But you can see right
here in the middle there is going to be a certain amount of a negative charge right
there. And so did you learn how electric potential affects scalar fields which again just show
us the position of scalar quantities? I hope so and I hope that was helpful.