How Does Charge Polarity Affect Electrostatic Equilibrium Position?

[badd99]

Homework Statement

An electric point charge of Q1 = 5.23 nC is placed at the origin of the real axis. Another point charge of Q2 = 1.89 nC is placed at a position of p = 2.63 m on the real axis. At which position can a third point charge of q = -2.62 nC be placed so that the net electrostatic force on it is zero?

1.643 m (SOLVED)


Let the sign of Q2 be changed from positive to negative. At which position can the point charge q be placed now so that the net electrostatic force on it is zero?

The Attempt at a Solution

Okay so I set up k(q1)(q2)/d^2=k(q2)(q3)/(D-d)^2 where D = 2.63m

I then used the quadratic and since there is no b, I used 0.

I got:
7.12E-6d^2+0d-3.62E-5 and did the quadratic to get 2.25m but this is not right?

Help? Thanks!

 

[Doc Al]

The first thing to figure out is which region the charge must be placed: to the left of Q1, between Q1 and Q2, or to the right of Q2. Only one region will give you a sensible answer.

 

[badd99]

so the answer should be negative then? I am still having trouble ugh.

 

[Doc Al]

The Attempt at a Solution

Okay so I set up k(q1)(q2)/d^2=k(q2)(q3)/(D-d)^2 where D = 2.63m

Define d and D more clearly.

Better still, pick a region and define your distances so they are all positive.