# Position of third charged particle

1. Oct 29, 2015

### Voidy

1. The problem statement, all variables and given/known data
Two particles are separated by a distance d, Particle A has charge +Q and Particle B has charge +3Q. At what distance from particle A along the line connecting particles A and B would you place a third charged particle such that no net electrostatic force acts on it ?

2. Relevant equations
F = kq1q2 / r^2

3. The attempt at a solution
Since there is no net electrostatic force on the third particle, the force from Particle A to C, and force from Particle B to C must be equal.

So I set up the equation
k(Q) / x^2 = k(3Q) / (d-x)^2

and solved for x using the quadratic formula.

I got

x = .366d

However, the answer is d/9, which is x = .111d

Can anyone help me ? Thank you

2. Oct 29, 2015

### Mister T

I get the same answer as you. The value can't be a rational fraction of the separation distance.

Note that they don't define d in the statement of the problem, yet they state their answer in terms of d. That's a clue right there that there's something amiss. Perhaps a typo!

3. Oct 29, 2015

### haruspex

I also agree with .366, but d is given.

The author seems to have made two errors:
Taken distance as inversely proportional to square of force, instead of the other way around;
Taken the ratio of the two distances instead of the ratio of the shorter distance to the total distance.
Very sloppy.

4. Oct 29, 2015

### Mister T

Oh, yeah, so it is. How'd I miss that?