00:01
Hi there, so for this problem, we have three point light charges that are placed at the corners of an equilateral triangle, as is shown here in this figure.
00:11
The value of the separation between the charges, a, equals to, this equals to 30 centimeters.
00:26
And we need to find the magnitude of the electric force exerted on the charge q3.
00:31
So let me just draw all these three charges.
00:35
One, two, and three.
00:41
They are separated by a distance a.
00:46
So then we label this as q1, q2, and q3.
00:55
A, a, and a.
01:00
Once we have this, we are going to draw the forces atene on q3.
01:06
So that will be, remember that when the charges are with the same sign, the force is repulsive, and when they are of different sign, the force is attractive.
01:21
So then in this case, the charge q3 is positive.
01:27
Okay, so this is positive.
01:31
Q2 is positive, well, and q1 is negative.
01:35
So what we are going to have in here is that q3 is going to feel attracted by q1, so let's level that as the force f1, but it's going to feel repulsive due to q2.
01:51
Let's label that as f2.
01:54
Now we know that this angle in here meets an angle of 60 degrees with the horizontal, the same with this angle.
02:02
So we complete the triangle in here.
02:10
Also, we know that this angle in here is 60.
02:17
Okay.
02:20
And if we know that this in here is 30 or half of 60, of course, this will be also be 60.
02:34
Okay, so we can complete 90 degrees in there.
02:39
So with that said, once we know this, we are going to write these forces.
02:45
So the force f1, for example, in magnitude, will be columns, comes on times the part between the charges.
02:52
In this case, is the charge q3 in magnitude times the charge q1, and this divided by the separation distance.
02:59
In this case, is the separation distance a to the square.
03:03
While for the force f2, that will be columns comes on the charge q3 times the charge q2, and this divided by the separation distance, which is a, s -square.
03:16
Once we have this, what we need to do is, well, first let's determine this magnitude.
03:21
So, for example, for f1, that will be columns, constant, that is the value of 8 .99 times 10 to the 9.
03:30
This times the charge q3, where the charge q3 in magnitude is 2 .30 micro, so that means 10 to the minus 6.
03:42
So then this times q1, where q1 is 3 .10 times 10 to the minus 6.
03:51
Then we divide this by the separation distance that we are given.
03:55
That is 30 centimeters, that meters will be 0 .3 and that to the square.
04:00
So this will give us a value of high there.
04:05
So i'm going to give you this with four decimal places.
04:09
That will be 0 .71, 22 in units of newtoms.
04:15
And the force f2 in magnitude will be 8 .99 times 10 to the 9, columns constant...