the whole problem looks like this.
A Positive charge q is between 2 other postive charges Q and 2Q. the distance between Q and 2Q is 1 meter. There is a point on the line between Q and 2Q where the power in the charge q is zero. Where is that point?
If so then the net force on charge q at a position d (measuring a positive direction to the right) is:
So if the net force is 0:
<-- Multiply both sides by
<-- Use the quadratic formula:
Now, since we must take the "+" solution (since the "-" solution gives a negative d.) Thus
(Note also that d is less than 1, which makes sense as that puts it between the charges.)
For the record, the negative value of d also makes sense: There is a point on the far side of Q where the repulsion of q from Q is equal to the attraction of q to the 2Q charge. But, of course, that isn't what we are specifically looking for.