00:02
In this prong, we have a graph of potential versus the position x, x in centimeters, even though really we're not calculating numbers, which is going to be looking at relative of magnitudes of the electric fields.
00:19
The scale here, again, not of great importance.
00:23
The graph shows vs up here after 10 marks, so that would indicate each division is one -tenth of that, so this would be the half point.
00:34
Like i said, again, without not trying to get specific after field values, we're just trying to rank between these five regions, which has the greatest magnitude, what the order of magnitude is in terms of one region to the next.
00:54
Okay.
00:55
Now, how do we read a graph for this? first off, at the most fundamental level, x, we're just talking about one dimension.
01:05
Now is actually the minus derivative of v respect to x.
01:11
That's for any curve.
01:13
It doesn't have to be, this graph here is nice.
01:16
It's made up of linear segments.
01:18
It's going to make life easier.
01:20
Graphically, this is the minus at a point, minus of tangent line at a point.
01:33
So if i wanted to know the electric field here, i draw a tangent line and calculate it slope.
01:39
I draw one here.
01:40
I get the electric field there, that 1 .5.
01:43
Wherever i want the electric field, the actual value, i draw a tangent line at that point and take the minus, get that slope and then multiply by minus 1 and i have the electric field.
01:55
That's what i do in general.
01:56
If i have a curve, a real curve, there's something that's not linear segments.
02:01
But, now if you have a linear segment, though, what's nice about it is the following.
02:07
If you got linear, minus the slope, of line or the linear portion, i should say, really, it's not the whole thing.
02:21
Line if graph is linear.
02:25
What does that mean? so if i were to draw a tangent line at that point, and then draw another one here, aren't they the same as the slope of the whole line? so that's what i mean when the slope of tangent lines along any linear portion, it's going to be the same as the line itself.
02:47
So you could just calculate it and you got it at all of those points because it's all the same.
02:52
So one calculation will give me electric field in between one centimeter and three centimeters.
02:58
I'll know it at any value between there.
03:01
It's constant.
03:03
It's the same in magnitude and direction.
03:07
So that's what's nice.
03:09
When you've got linear segments, just minus the slope and you have it at all the points in that linear region.
03:17
And now i've just go to another region.
03:18
You got to get the slope of one of those points and that line, and you got it at all points in that region.
03:26
It's by region, by linear region, by linear region.
03:31
So, let's start.
03:33
Ex for region a minus, and then the slope.
03:37
Well, we got, we have 0 .9 vs and 0 .9vs.
03:45
So the slope would be this point minus this point divided by 1 minus 0 .0.
03:51
So 0 .9 v .s, minus 0 .9 v .s.
03:57
1 centimeter minus 0 centimeter.
04:00
That's the slope of that linear segment.
04:02
And that will be electric field, and that obviously is zero.
04:05
That means the electric field at any point between 0 and 1 is 0.
04:13
It's the equal potential.
04:14
There's no, that whole idea of having to do work as you move against the electric field.
04:23
There's no work being done, so there's no electric field.
04:29
It shows you there's no electric field, i should say, because you're on the same potential.
04:32
This is a constant potential going along that from zero to one.
04:39
So there's no work needing to be done to go from those points.
04:44
That means by definition the electric field cannot be along that direction.
04:49
It's zero.
04:53
Okay, so we have that value.
04:57
Ex for b minus.
04:59
Now this one, this one is this point and this point.
05:05
So 0 .3 minus 0 .9.
05:11
So it's minus 0 .3 v .s minus 0 .9 vs.
05:23
And it's 3 centimeters minus 1 centimeter.
05:28
And this works out to be 0 .3 v .s.
05:33
You know, obviously units are funny because vs carries the unit.
05:36
If vs is 5 volts, the volts come from that.
05:42
But i'll write it as best i can there.
05:44
So this gives me that the magnitude, because they want it in terms of magnitudes, the answer.
05:51
So it's 0 .3v .s.
05:53
For centimeter.
05:55
Now, let's talk about something.
05:58
This, remember, the electric field points in the direction where the, gives you the direction, the temperature field gives you the direction of the force on a positive charge.
06:11
So this would indicate that the force, if you were to place a charge here, the force it would experience would be in the positive x direction.
06:21
That's fine.
06:23
So that seems to be saying it's pointing the direction of negative decreasing potential.
06:32
So delta v is negative.
06:35
Is this consistent with what we know? obviously gravitationally your objects falls from rest in the direction of lower potential energy that's what happens and the force is in that direction lower potential energy is the direction of the force do we so that does that seem to be true yes for positive charges but let me let me give you a little note give you some heads up on this from rest the change of potential energy not potential with potential energy is less than zero from rest.
07:18
Implies that q delta v, remember, that's how you get the, this is the potential now.
07:24
That's how you get the potential energy for a charge q in the field of some other charges.
07:28
Q delta v, then is less than zero from rest, implies.
07:36
Now, this is where we differ from gravitation.
07:40
Delta v is a v.
07:43
Delta v is less than zero for a plus charge...