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.

 

[rwisz]

I would say that your attempt at a solution is on the right track, but there may be a mistake in your calculation. It is important to double check your equations and make sure all units are consistent. Also, when using the quadratic formula, make sure to use the correct sign for the discriminant (in this case, it should be positive since the force should be zero). Another helpful tip is to draw a diagram and label all the variables to help visualize the problem. Keep in mind that the position of the third point charge can be on either side of the other two charges, so make sure to consider both cases when solving for the position. It may also be helpful to consult with a classmate or teacher for additional clarification. Keep up the good work!