00:01
So let's first draw a dry gram showing all the charges that we have.
00:07
So let's say this is our x -axis and this is our y -axis.
00:16
And we have a charge here that has a magnitude q and another charge over here which has a magnitude 4 times this charge.
00:28
And the distance between these two charges is d and everything is in terms of variables.
00:45
So we don't have any numeric values.
00:49
And we need to find the position of another charge, small cube, and the position is x, such that the three charges, capital, q, small q and 4 times capital q.
01:09
So these three charges will be at equilibrium.
01:14
So let's say the third charge is at a distance x from capital q.
01:24
And we want to calculate this x first to determine the place of the charge q where the two electric fields have the same magnitude.
01:32
The electric fields due to capital q and 4 times capital q.
01:37
So this is x.
01:45
Now another thing, since all these three will be in equilibrium, therefore we can say that the electric field at this point where this charge small q is placed, the net electric field at that point will be equal to 0.
02:03
Now, this means that eq on q, that is electric field by, capital q on small q plus electric field by the charge capital 4 q on small q will be equal to 0.
02:23
Basically net electric field at this point x due to these two charges will be equal to 0.
02:29
Hence by superposition, this will be the net electric field will be vector sum of those two electric fields.
02:37
Now let's write down these two electric fields along with all the signs.
02:42
So this is k times capital q over x square and make sure you include the direction.
02:53
So over here since capital q is positive, the electric field will be away from capital q hence towards the positive x -axis.
03:01
So there should be a positive sign which there is already.
03:07
Now over here this will be k times 4xxx.
03:12
Q over d minus x whole square and this charge again since 4 q is positive therefore the charge over here will be sorry the electric field due to this charge will be away from that charge hence that will point towards the negative x axis hence there should be a negative sign before that and that is equal to zero because the net electric field at that point will be zero because we want all three charges to be in equilibrium.
03:49
Now solving this equation we'll find x to be equal to d over three.
03:55
This is really easy calculations.
03:57
So i'm not doing all the small calculations over here to save some time.
04:05
So now we know the position of where the charge q should be placed.
04:11
Now we want to determine the magnitude and the sign of this charge small q.
04:19
Now charges 4 times capital q and this small q exert a force on the charge capital q...