0:00
All right, hello, hello.
00:01
In this question, we're given this charge setup.
00:03
We have four charges on the corners of a square.
00:05
And then in the center, we have a positive charge of 0 .75 microcoulombs.
00:09
And we want to figure out what the net electrostatic or coulomb force is on this charge.
00:15
So in order to do this, i'm going to go ahead and draw arrows, draw vectors for each force.
00:20
So looking up here at qa, i have a positive charge.
00:23
And that is acting on a positive charge q.
00:26
So those are going to repel.
00:27
So qa is going to be pointed in that direction.
00:30
That's going to be the force from a.
00:32
And that is going to be oriented like all of these.
00:35
This is going to be a 45 -degree angle.
00:37
And that's because of symmetry.
00:39
It's inside a perfect square.
00:41
And so it's going to be acted at a 45 -degree angle.
00:43
Let's look at b.
00:44
Well, i have a negative charge.
00:45
So it's going to attract that positive charge.
00:49
And so that's going to be the force from b.
00:51
For c, i have a negative charge.
00:53
So that is also going to attract it.
00:55
So the force from c there.
00:56
And then for d, i have a repulsive charge because it's positive.
01:00
So i'm going to have some force d there.
01:03
Now, if i want to find the net force on this, it's going to just be the sum of all of my forces from, i suppose, a to d of my individual forces here.
01:16
I'm going to opt to do this to find the components in the x direction and then the components in the y direction and then add those together via vectors.
01:24
So in the x direction, if i define my axes conventionally here, i have the force from a acting in the positive x and the force from b acting in the positive x.
01:35
And then i have the force from c and the force from d acting in the opposite directions.
01:39
So i have negative signs here.
01:41
Well, what are these forces going to be? they're going to be a coolant force.
01:46
So i have k times q1, which is just going to be q, times qa over the distance squared.
01:53
Well, what is the distance? it's going to be the same for all of these.
01:56
And it's going to be the square root of 2 times a over 2, because i have here, i have a over 2 here, a over 2 here.
02:09
And so that hypotenuse distance there is going to be root 2 of that, which is going to be root 2 a over 2.
02:15
I could also write that as a over root 2, which is how i'm going to do it here.
02:19
So kqq over r, and that is r squared...