Charge question

notmetalenough
I'm doing my first electromag homework so there will probably be a few more of these.

Two small beads having positive charges 19q and q are fixed at the opposite ends of a horizontal insulating rod extending from the origin (the location of the larger charge) to the point x = d. As in the figure below, a third small charged bead is free to slide on the rod.

So I figure that

F = ((k * 19q Q)/ x^2) - (k* q * Q)/(d-x)^2)

so 19/x^2 = 1/(d-x)^2

d-x = x / sqrt(19)

d = x + x/sqrt(19)

= x * (1+sqrt(19))/sqrt(19)

so x = d * (sqrt(19))/(1 + sqrt(19))

apparently it's the wrong answer. Can anyone tell me why, or where I went wrong?

whozum
Are you trying to find the point of equilibrium for the third charge? If so, it will find equilibrium at the point where the force from both charges cnacel each other out (equal each other) or when the electric field is zero. These occur at only one point and they are the same point.

notmetalenough
right, but i have to find it as a ratio of d.

i can't find anything wrong with how i set it up, I made the charges proportional, and equal to each other and then solved for x, my answer should be sound, but the program won't accept it.

notmetalenough
okay, false alarm. I did have the right answer, my program wouldn't accept it without the leading 0 and wouldn't tell me that that was the reason I was getting it wrong.

whozum
((k * 19q Q)/ x^2) = (k* q * Q)/(d-x)^2) is where you should start, solving for x.