Electricity and Magnetism Electric Field Problem

[astrolady022]

1. Problem Statement:
Find positions on the x-axis for the charges Q1 = -1 C and Q2 = +3 C so that the electric field is zero at x = 0.

Homework Equations

:[/B]
I'm thinking I need to use Coulomb's law for this one. I'm just having trouble figuring out where to start. Coulomb's states E=kQ/r^2.

3. My Attempt:
So far I have set up a drawing. I am not sure if I need to be considering the electric field lines for this and if they have a role in the problem. I have considered using the forces to try to relate the distances between the three points but I have had no luck.

 

[berkeman]

Welcome to the PF.

I'm thinking I need to use Coulomb's law for this one. I'm just having trouble figuring out where to start. Coulomb's states E=kQ/r^2.

Yes, do use that equation, and remember that the electric field points from + to -. There are actually many solutions to this problem, unless the position of one of the charges is fixed. Was that the whole problem statement? Is there a diagram (use the Upload button to add a PDF or JPEG image to a post).

 

[astrolady022]

Welcome to the PF.

Yes, do use that equation, and remember that the electric field points from + to -. There are actually many solutions to this problem, unless the position of one of the charges is fixed. Was that the whole problem statement? Is there a diagram (use the Upload button to add a PDF or JPEG image to a post).

The above is the entire problem. There was no image. Using the electric field equation, I get (using r1 and r2 as the two distances from the zero point) the equation -r2^2=3r1^2. From here should I just plug in arbitrary values to get a distance?

 

[berkeman]

remember that the electric field points from + to -.

Or said better, the electric field points away from a + charge, and in toward a - charge.

 

[astrolady022]

Or said better, the electric field points away from a + charge, and in toward a - charge.

That makes sense.

 

[berkeman]

From here should I just plug in arbitrary values to get a distance?

The issue is that you can see how once you pick one distance for either charge, that determines the position of the other charge. But if the first charge's position is arbitrary, then there are infinitely many solutions. Usually in this type of problem, one of the charges is fixed somewhere on the axis, and you are asked to find the position of the other charge to make the E-field zero somewhere...

 

[astrolady022]

The issue is that you can see how once you pick one distance for either charge, that determines the position of the other charge. But if the first charge's position is arbitrary, then there are infinitely many solutions. Usually in this type of problem, one of the charges is fixed somewhere on the axis, and you are asked to find the position of the other charge to make the E-field zero somewhere...

Those are the problems I have previously seen. I think that's why this one got me a little confused.

 

[berkeman]

Well, I think all you can do is express the position of one charge in terms of the other with an equation. You can show some example solutions given some position of the + charge as examples, I suppose.