# Three charges located on a straight line

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1. Jan 21, 2015

### yzphysics

1. The problem statement, all variables and given/known data
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.

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

3. 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?

2. Jan 21, 2015

### Staff: 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.

3. Jan 21, 2015

### yzphysics

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?

4. Jan 21, 2015

### Staff: Mentor

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.)

5. Jan 21, 2015

### yzphysics

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

6. Jan 21, 2015

### Staff: Mentor

Consider the directions of the forces on Q3. Could they cancel in that region?

7. Jan 21, 2015

### yzphysics

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.

8. Jan 21, 2015

### Staff: Mentor

Rethink this. What is the direction of the force exerted by Q1 on Q3? The force exerted by Q2 on Q3?