00:01
So this question deals with some issues of electrostatics.
00:08
The first one wants to know what is the direction of the net electric force on a positive test charge placed at three different locations and they label them a, b, and c.
00:21
Well, let's take a look here.
00:22
What i've done, my version of the diagram, is i've drawn two little points over here.
00:28
And let's not consider the force from the entire semicircle here or a quarter circle.
00:37
Let's just consider the force from the charge at this location right here and the charge at this location right here.
00:46
And what we'll do is we'll draw a straight line because according to kulam's law, that force is going to go in a straight line.
00:55
And the force on a test charge put right over here at position a caused by just a little bit of the charge, whatever charge happens to be at that location i put on a dot at, the direction of that force is going to be along this line, and because it's a positive test charge and positive charge up there, the force is going to go this way.
01:21
Now similarly, down here we have a exactly symmetric situation, but we've located this point down here is exactly at the same relative position on its arc as the positive one was on its art.
01:38
But this charge is negative.
01:40
And so the force caused by the little bit of charge down here on the test charge is going to be going off this way.
01:55
Now, if it is correctly, i should have drawn the magnitude of the two charges forces should be easy.
02:01
Because they're both the same distance away from the test charge.
02:05
Each of these two charges should have equal magnitudes of forces, but they're going these different directions.
02:12
Because they're equal in magnitude, the horizontal component of these two forces is the same.
02:21
And so they end up canceling each other out, if you will.
02:24
The perpendicular component, the vertical component of these forces, though, they're going in the same direction.
02:32
So they kind of add up.
02:35
And so the net force at point a is straight down.
02:41
But you can do the same thing at the other two points as well.
02:44
Let's just erase some of these forces here.
02:51
Let's go over here and let's say what is the net force at point b here? well, again, if you just consider the net force caused by this charge right here and the corresponding charge on the bottom quarter circle.
03:24
The top one is going to produce a force going this way, and like that.
03:32
And then the bottom one is going to have a force going this way.
03:40
So it goes like that.
03:42
And again, because those two forces are equal in magnitude, perhaps didn't draw that very well, but this should be equal in magnitude.
03:48
Again, the net force in those two charges is going to be.
03:51
Going to be down like this in that direction.
03:55
But that could be said for any pair of charges like that.
04:00
You could take this little bit of charge up here and figure out its net force compared to this little charge down here.
04:09
So every charge in the positive quarter circle is going to have a corresponding charge in the negative quarter circle that ends up giving you a net force in the perpendicular direction, sorry, in the vertical direction...