At what point is the system in equilibrium?

[catch22]

Homework Statement

This is more of a math question but:

There are two particles fixed in place: a particle of charge +8q at the origin and a particle of charge -2q
at x=L. At what point (other than infinitely far away) can a proton be placed so that it is in equilibrium

Homework Equations

The Attempt at a Solution

The point should be at the right of the -2q charge, so it is farther away from the charge +8q.

diagram:

that was the answer, but would it be possible to use

8q / (L+x)² = 2q / (x)²

where L is the distance between the charges 8q and -2q.

I get x = L using this set up instead.

what went wrong? Shouldn't I get the same answer?

 

[Doc Al]

that was the answer, but would it be possible to use

8q / (L+x)2 = 2q / (x)2

where L is the distance between the charges 8q and -2q.

I get x = L using this set up instead.

what went wrong? Shouldn't I get the same answer?

The answers are the same! Realize that in the second approach you are measuring x from the second charge, not the origin.

 

[catch22]

The answers are the same! Realize that in the second approach you are measuring x from the second charge, not the origin.

Ah, so the point is L away from the -2q and 2L away from the origin.

 

[Doc Al]

Ah, so the point is L away from the -2q and 2L away from the origin.

Exactly. What's confusing you is that in the second method, "x" stands for "unknown", not the x-coordinate of the final location. You'll have to translate to that to report your answer, if you want them to match.