00:01
Hello, in the question we have given four point charges are located at corners of rectangle as shown in figure.
00:08
So, we will take so they are saying that take this capital q as 9 nano coulomb.
00:14
So, we have to find out the resultant force on the following charges.
00:17
So, that is 2 minus 2q and minus 3q on this we have to find out the resultant force.
00:23
So, now, there will on this minus 2q charge there will be a force due to this plus 2q charge then this charge and minus 3q charge.
00:33
So, we will see one by one.
00:35
Now, due to this plus q charge the force will be attractive because this is plus this is minus.
00:40
So, it will be f1.
00:42
So, let us call it as f1.
00:43
Now, this is minus this is minus.
00:46
So, the force will be repulsive.
00:48
So, we so it will be in this direction.
00:50
So, let us call it as f2.
00:52
Now, this is minus this is plus.
00:54
So, this force will be attractive and it will be in this direction.
00:58
So, now, this this force is at some angle.
01:02
So, this is angle 37.
01:04
So, if this angle is 37 this then this angle will also be 37 by using the parallel lines and transversal concept.
01:11
So, i can resolve the this f3 we will do that.
01:15
So, now, f1 f1 will be so we know the coulomb's law.
01:20
So, force is equal to kq1q2 divided by r square.
01:24
So, same thing.
01:25
So, k into q times 2q divided by the distance between them is 4.
01:31
So, distance between them is 4 centimeters.
01:34
So, it will be 4 into 10 raised to minus 2 meters and square of this in the x direction.
01:39
So, we just plug the value of k that is 9 into 10 raised to 9 into 2 and q square it will be and q is given 9 into 10 raised to minus 9 square.
01:48
So, everywhere we are going to do the same thing.
01:50
So, and divided by the denominator as it is in the x cap.
01:54
So, if we calculate this we will get f1 as 9 .1125 into 10 raised to minus 4 newtons in the x cap direction.
02:01
So, similarly f2 f2 is what the force on 2q by 3q.
02:06
So, it is repulsive.
02:08
So, it is in the positive y direction.
02:10
So, we are taking this coordinate system like this x and y.
02:14
So, it will be f2.
02:16
So, it will be in positive y.
02:18
So, it is k 2q 3q divided by the distance between them is 3 centimeters.
02:24
So, it will be 3 into 10 raised to minus 2 meters and square of that.
02:28
So, if we just plug the value of k.
02:30
So, 2 3's are 6 which i have taken out and q square.
02:33
So, this is q and this is square.
02:35
So, if i calculate i will get f2 as equal to 48 .6 into 10 raised to minus 4 newtons in the y cap direction.
02:42
Now, this f3 we will find magnitude first.
02:46
So, we will first find the magnitude and we will resolve the component of this force.
02:51
So, this f3 is k 2q square divided by because it is 2q into 2q.
03:00
So, this will be 2q square.
03:03
So, this f3 will be k times 2q square divided by the distance between them is 5 into 10 raised to minus 2 square.
03:10
So, we have found out this distance by using the pythagoras theorem over here.
03:13
So, this is 3 4.
03:14
So, this is a pythagorean triplet.
03:16
So, that is why we have directly put here the value that is 3 4 and 5 centimeters.
03:21
So, and this angle 37.
03:23
So, we are considering this right angle triangle.
03:26
So, in this right angle triangle, we know that the angle...