00:03
So this question is asking about the electric field and electric potential as shown on a graph.
00:11
On the graph we're talking about looks something like this.
00:15
We have a horizontal axis where we're giving the position in a region that has some electric field and electric potential and we're told the potential of these positions.
00:33
So this is on the vertical axis is potential and on the change that would occur if we were to move in our potential from one position to another.
00:56
Let's say we go from this position here to this position here.
01:00
What are the changes that are going to occur? well the change in potential will be this much.
01:16
Now on a graph you sometimes call that the rise.
01:18
In this case since we're starting over here at position one and then we're calling this position two, the rise is negative.
01:28
It doesn't look like much of a rise, it looks like a fall, but it's the change in the vertical position.
01:33
And this over here, well that is just the distance between position one and position two.
01:40
You know so this is up here is is b1, down here is b2, and this is position one and this is position two.
02:02
Well then the slope of this line, i didn't draw the line, let me do that, we're talking about something that changes.
02:13
In our situation here the potential changes linearly.
02:19
That's what we're going to deal with.
02:21
So what we found is that the slope of this line is the change in potential divided by the change in position.
02:42
What's the change in position? it's just the distance between position one and position two on the x -axis.
02:47
So we could also say this is equal to the change in potential divided by the distance along the x -axis there.
02:59
So what is that quantity? well in this unit we learned that the electric field is equal to a negative of the change in potential per distance over which that change occurs.
03:20
So the electric field is just equal to a negative of the slope.
03:30
If you have a potential that is changing in a linear way, you can just say calculate the slope of that potential and take the negative of it, and that should give you the electric field.
03:43
And that gives you the direction too.
03:45
In the simplified way we're dealing with it, direction either plus or minus.
03:48
See the electric field is negative or electric field is positive.
03:52
In this particular case here, since the slope is negative, the electric field will be positive because the particle that goes from position one to position two is losing potential, which means it's going along with the electric field.
04:06
So let's use that information to see if we can answer the question here now...