00:01
So in this problem, we have a charges set up in a square in this configuration, and we want to find what is the force on the lower left -hand charge, so this q -1 charge.
00:11
So what we can first do is write out our equation for electric charge.
00:18
So the force due to an electric charge is equal to k times q1 times q2.
00:25
So those are the two different charges we're talking about over their distance squared.
00:32
And so, and this is going to be in the, obviously, r -hat direction.
00:41
And k is going to equal 8 .99 times 10 to the 9th.
00:52
And so what we can do is our strategy for each charge we want to calculate fe, right? and this should be a vector.
01:12
And then two, using superposition, add these together.
01:30
So our force is going to have a direction, and it's also going to have a magnitude.
01:35
So we first need to define a coordinate system.
01:40
So i'll just make the standard x, y coordinate system.
01:47
And we can also give these charges a name.
01:50
So i'll call this charge q2, this one q3, and this one, q3, and this one, q4.
02:03
So the force on q1 from q2 is going to be, right, if we look at the same charge.
02:15
And so like charges repel, meaning that the force from q1 to q2 is going to be in this direction.
02:27
And while we're here, we can also write out that the force on q1 from q4 is going to be in this direction.
02:37
And the force from q1 on q3 is going to be facing outward here.
02:46
The force on q1 from q2 is going to be 8 .99 % of the 9th, multiply by 1 times 10 to the negative 4th, multiply by 1 times 10 of the negative 4th, and that's because both of these charges have a charge of 1 times 10 to the negative 4th cullums.
03:10
And the distance between these two is two meters, so over two square, and this is going to be in the negative, if we look at the negative y -out direction.
03:32
And so plug in all this into our calculator, we're going to get 8 .99 times 10 to the 9th, times 1 is 10 to the negative 4th, times 1 times and negative 4 divided by 4.
03:48
Right, this 2 squared is 4.
03:51
So our f of q1, q2, is going to equal negative, and that negative comes right here, pointing in the downward direction.
04:05
22 .475, and that's in the y hat direction.
04:13
So let's remember this, because remember our strategy is going to be to find each of these forces, individually and then use superposition to add them together.
04:25
So now i'm going to skip to charge four because if we look quickly at our diagram, oops, if we look quickly at our diagram, we can see that the force from q4, right, we're the same distance away and they're the same charges.
04:49
So fq1, q4 is going to equal again, 8 .99 times 10 to the ninth.
05:01
1 times 10 to the minus 4.
05:04
1 times 10 to the minus 4...