00:01
In this problem, we have the following configuration.
00:04
We have this, let's say, the x -axis here.
00:09
And we have two point charges, let's say, q1 and q2.
00:14
And they are separated by a distance of a.
00:17
So q1 is equal to minus 10 nanocoulombs, so minus 10 times 10 to the power of minus 9 coulombs.
00:26
And the other charge is equal to 15 nanocoulombs.
00:30
15 times 10 to the power minus 9 coulombs.
00:33
And its distance is 0 .5 meters.
00:37
And we also remember the coulomb constant.
00:40
9 times 10 to the power 9 newton meters squared per coulomb squared.
00:46
Okay, we have two questions.
00:49
In the first part, we want to put a third charge of 20 nano coulombs so that the net force on it will be zero.
01:01
So where do we put this? in the second question, we are going to take this third charge as negative 20 nc and assume the same as the rest of the problem.
01:13
Okay, as we will see, the sign of the third charge or in fact the entire magnitude of the third charge will not matter.
01:22
So once we solve this question for a certain configuration for any third charge so it will be true for all possible third charges okay now let us proceed as follows now we want to introduce q3 equal to 20 nanocoulombs so 20 times 10 to the power minus 9 coulombs and we want okay let's say we put it it's at a point x on this real line and we want the total electric field to be equal to zero so k q 1 q 3 x minus 0 okay now we need to assume that we put the first charge at the origin and the second one at x equal to plus a okay we have x minus 0 over x minus 0 absolute cube so this is a target minus the source okay plus k q2 q3 times again target minus this time the source is at a so we have x minus a absolute cube and we want this guy to be equal note that we can cancel out k and q3 because right hand side is equal to 0.
02:50
So we have q1 x over epsilon x cube plus q2 x minus a over x minus a epsilon cube equal to 0...