00:01
In this problem, we have a square.
00:07
We have charges plus q, minus 3q, 5q, and plus 2q, as shown in the diagram here in the figure.
00:17
And the first thing we're going to look at is what is the kinetic energy.
00:21
It's actually at infinity for the 2q charge if everybody else stays fixed, but it gets, it's free to move.
00:31
Now one last thing we're going to need in this, before we get into the physics, it needs this diagonal distance, which is diagonal of the right triangle with d and d as its sides.
00:47
So this is d squared, plus d squared, which is d times square of two.
00:57
So we have that.
00:59
Now, how do we do a problem like this, where we release the two q? could we look at it from forces? yes.
01:11
That force, though, is not constant.
01:14
So we'd have to use a little more elaborate techniques.
01:16
But could it be done, certainly? what's the simplest way, though, of doing this? energy.
01:23
Energy conservation.
01:25
No, electrostatic force is a conservative force.
01:28
No, problems.
01:30
So let's write our energy conservation.
01:34
Point a and point b are our two points.
01:38
This is for the two q charge.
01:41
We're dealing with.
01:42
Well, technically, you know, it's 2q, and obviously potential energy is for 2q and the collection of the other three, just like for a mass and the earth.
01:57
Earth is made up of a large collection of masses, and that other one is separated out in a way.
02:04
So kinetic energy at a plus potential energy of 2q and the other charges.
02:13
Remember, potential energy is not really a property of one thing.
02:16
It's a property of the charge and the rest of the charges, just like i said, just like with the mass and the earth.
02:25
So it's a property of both.
02:30
Kinetic energy at b plus the potential energy at b.
02:36
Now, this starts from rest.
02:38
If we just kind of held in place, then we release it.
02:41
So this is zero immediately.
02:44
Now, potential energy at a is 2q.
02:49
Times the potential generated by the other three at a.
02:53
So this is 2q.
03:02
V at a, let me make sure that looks like a v.
03:09
V at a is equal to k .e at b at b plus 2q.
03:16
And the same would be true.
03:17
What's the potential from the other three at infinity? 2q, bb.
03:25
Well, each one at infinity, zero.
03:31
We're going to use the formula where the zero for the potential is at infinity.
03:38
Dealing with point charges here.
03:42
So this is zero.
03:44
So this just gives me the connect energy we're looking for, k -e -v, is equal to q2qv.
03:53
So we had our goal, really, the whole crux of the problems, to get the potential at a due to the other three charges.
04:01
Potential at a.
04:03
Remember, for a point charge with the zero and infinity, k times the charge over the distance to the point you care about.
04:12
That's what we're talking about.
04:15
So going from 1, 2, and 3, kq over d.
04:25
K, no absolute value is here.
04:26
This is the actual charge with its sign.
04:29
K minus 3q.
04:33
Now this, remember, this is charged 2 now.
04:36
So we got the diagonal distance to include.
04:39
D times the square root of 2.
04:43
And then we have k -5 -q over d.
04:50
Just the distance from the charge to the point we care about, which is point a.
04:55
And we can clean this up a little bit.
04:59
K -q over d, 1 minus 3 or square root or 2 plus 5.
05:09
So that's what we have.
05:10
I can calculate that out now, but when you're going to have another calculation in there, just do it at one time.
05:15
So k -e -b, we're going to get 2q, k -q over d, 1 minus 3, square root 2 plus 5, and this works out to be 7 .76 k, and we have q squared, q squared over d.
05:45
So that's the kinetic energy and infinity effectively for the charge 2q.
05:51
If you knew q and you're given d, you can get a number out of that.
05:56
They don't give either one.
05:58
So there's nothing, nothing, it wants it in terms of k, your q and d and any other constants.
06:07
Well, k is the other constant.
06:09
They tell you to use that, so that it went over four pipes on zero.
06:12
Okay.
06:13
So that is part a.
06:15
That's the, that's connect energy of the two q charge when it's free to move off to effect of the infinite.
06:21
A distance away from the other three.
06:25
Now, the part b wants to total the system potential energy.
06:35
You total? now, what is potential energy? potential energy, when we write a u term, that's the work you must do to bring the charge, say charge two, into the field of charge one.
06:53
Without changes, connect energy.
06:58
And we got to do that for all bringing charge two and bringing charge one.
07:02
From infinity to its location, two to its location, three to its location, four to its location.
07:10
Now remember, this is when charged 2q is at far distance away, it affects the infinity.
07:17
Don't forget that.
07:17
We're looking for this total system potential energy when effectively the 2q is at infinity.
07:25
But let me write it out in general, as if 2q was anywhere.
07:32
You one two you one three plus you one four plus you two three plus you two three plus you two four plus you three four so like i said this is bringing two into the field there is no term for one what work do you have to do what field are you fighting bringing one from infinity nothing just place it there's no nothing to fight you don't do any work you know if you think about it well you don't i have to, if it's at rest in infinity, don't have to give it some work to get it to move it? yes, but didn't you have to do at the end to take away that kinetic energy to get it at rest at its location? so your total work is zero...