# Point of Equilibrium between two charges

## Homework Statement

See figure attached for problem statement.

## The Attempt at a Solution

I'm a little confused on how to start on this one.

Okay so I know that the two particles with oppsite charge attract one another, and a 3q force of attraction is going to be larger than a -q force of attraction.(and vice versa)

So is it in cases (c) and (d) that an electron will find its point of equilibrium to the left of the particles?

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Doc Al
Mentor
and a 3q force of attraction is going to be larger than a -q force of attraction.(and vice versa)
Not always. What else does the force of attraction depend on?

Not always. What else does the force of attraction depend on?

The distance between the two charges?

Doc Al
Mentor
The distance between the two charges?
Yes. Now combine those two factors to see which arrangements can meet the criteria.

Yes. Now combine those two factors to see which arrangements can meet the criteria.

I'm still not seeing how to do that. Can you give me another nudge?

EDIT: The forces on eachother should be 0 in equilibrium so we're looking at the following,

$$F = k \frac{1*3}{r^{2}}$$

Now in some scenarios,

$$\vec{F_{ab}} = k \frac{1*3}{r^{2}} \hat{i}$$

and in others

$$\vec{F_{ab}} = - k \frac{1*3}{r^{2}} \hat{i}$$

Doc Al
Mentor
I'm still not seeing how to do that. Can you give me another nudge?
Sure. In order for the net force on the electron to be zero, what must be the relative size of F_1 and F_2? In which configurations is that not possible?

Sure. In order for the net force on the electron to be zero, what must be the relative size of F_1 and F_2? In which configurations is that not possible?

Are we to assume that the electron has a charge of -1q?

How do we know what force and electron will have on the given particles?

Doc Al
Mentor
Are we to assume that the electron has a charge of -1q?
That doesn't matter. (But you can assume that if you like.)

How do we know what force and electron will have on the given particles?
All we care about is the net force on the electron. Compare the force on the electron from each of the two charges. Hint: In some cases the force from one charge will always be greater than the force from the other, for an electron placed to the left.

That doesn't matter. (But you can assume that if you like.)

All we care about is the net force on the electron. Compare the force on the electron from each of the two charges. Hint: In some cases the force from one charge will always be greater than the force from the other, for an electron placed to the left.

Ah I see it now, it can only be done in cases a and b!

Doc Al
Mentor
Ah I see it now, it can only be done in cases a and b!
Right!