Equilibrium of Three Positively Charged Beads

[define_normal]

Homework Statement

Two small beads having positive charges 3q and q are fixed at the opposite ends of a horizontal, insulating rod, extending from the origin to the point x = d. A third small bead (in the middle) is free to slide on the rod. At what position is the third bead in equilibrium? Can it be stable in equilibrium?

Homework Equations

Coulomb's Law
F = ke (q1q2)/r^2

The Attempt at a Solution

I'm not sure how to go about this problem because I don't know the charge of the third bead.

 

[turin]

... I don't know the charge of the third bead.

You don't know any of the values, do you? Work symbollically. That is, just use q's and r's and such, instead of "actual numbers".

 

[define_normal]

You don't know any of the values, do you? Work symbollically. That is, just use q's and r's and such, instead of "actual numbers".

Hmm. So in order for me to do that, I don't need to know the charge of the third particle?

 

[turin]

Hmm. So in order for me to do that, I don't need to know the charge of the third particle?

That's right. You would need to know the charge if you wanted to calculate a non-vanishing force. But, the problem stipulates equilibrium, so it doesn't matter. You are looking for the location where - something, regardless of the amount of charge that is placed there - will calculate to be zero. Even then, you have to calculate this location symbolically (i.e. in terms of d).