# Three charges located on a straight line

## Homework Statement

Three charges, Q1, Q2 and Q3 are located on a straight line. The charge Q3 is located 0.169 m to the right of Q2. The charges Q1 = 1.56 μC and Q2 = -3.03 μC are fixed at their positions, distance 0.268 m apart, and the charge Q3 = 3.18 μC could be moved along the line. For what position of Q3 relative to Q1 is the net force on Q3 due to Q1 and Q2 zero? Give your answer in meters, and use the plus sign for Q3 to the right of Q1.

## Homework Equations

Coulomb's Law: F=(k(q^2))/r^2

## The Attempt at a Solution

(k*Q3*Q2)/r^2 = (k*Q3*Q1)/ (r+0.268)^2

After setting it up, I noticed that k and Q3 on both sides cancel out which leaves me with:
(Q2)/r^2 = (Q1)/ (r+0.268)^2

(3.02*10^-6)/r^2 = (1.56*10^-6)/(r+0.268)^2

Then, I got a quadratic formula: 1.47*r^2 + 1.62*r +.2176

so r is equal to -0.157m and -0.945m

but none of the two is right. What am I doing wrong?

Doc Al
Mentor
Your equation assumes that Q3 is to the right of Q2. That's why your solutions do not make sense. What other region can you try?

Generally, it's a good idea to figure out which region makes sense before you try to solve for the exact location.

I thought that "charge Q3 is located 0.169 m to the right of Q2" means that the point charges are at this order Q1---------Q2----.169-------Q3

Are the point charges supposed to be at this order: Q1------Q3-----Q2?

Doc Al
Mentor
I thought that "charge Q3 is located 0.169 m to the right of Q2" means that the point charges are at this order Q1---------Q2----.169-------Q3
Sure, that's what that means, of course. But then they said you can slide Q3 around. (So I have no idea why they gave you an initial position for Q3, unless there are multiple parts to this problem.)

Would you set up Q3 to be between Q1 and Q2?

Doc Al
Mentor
Would you set up Q3 to be between Q1 and Q2?
Consider the directions of the forces on Q3. Could they cancel in that region?

When Q3 is placed between Q1 and Q2, it will cause the charge to move like this: <--Q1 (+), Q3 (+)-->, Q2 (-)
So overall, the charge does cancels out.

Doc Al
Mentor
When Q3 is placed between Q1 and Q2, it will cause the charge to move like this: <--Q1 (+), Q3 (+)-->, Q2 (-)
So overall, the charge does cancels out.
Rethink this. What is the direction of the force exerted by Q1 on Q3? The force exerted by Q2 on Q3?