Difficult Coulombs Law questions

[Basher]

Homework Statement

Q1.Two Charges, -Q and -3Q, are a distance l apart. The two charges are free to move but don't because there is a third charge nearby. What must the third charge be and where must it be placed for the first two to be in equilibrium?

Homework Equations

Coulombs Law: F = k.qQ/r^2

The Attempt at a Solution

 

[rock.freak667]

Well what do you think would be the first step to do? (if the two charges are -ve, would they repel or attract one another? Hence where should the third charge be placed such the charges do not move, between or outside the charges?)Draw the free-body diagram and put in the charges and distances.

 

[Basher]

Well what do you think would be the first step to do? (if the two charges are -ve, would they repel or attract one another? Hence where should the third charge be placed such the charges do not move?)

Yes I do know I must place a +ve charge between them, sorry I should have mentioned that however it's the magnitudes. It must be closer to the smaller charge.

 

[ideasrule]

Define a coordinate system and place the positive charge at an arbitrary distance from one of the negative charges. Call this distance x+. Can you write out the equilibrium condition for both negative charges in terms of x+?

 

[Basher]

Define a coordinate system and place the positive charge at an arbitrary distance from one of the negative charges. Call this distance x+. Can you write out the equilibrium condition for both negative charges in terms of x+?

So the distance between -Q and +Q is x - l? I'm lost with this one. you may have to elaborate.

 

[ideasrule]

It's l-x, because l is larger. I think you should draw out the configuration, placing all three charges along the x axis. For convenience, put one of the negative charges at x=0.

 

[Basher]

So the distance between -Q and +Q is x - l? I'm lost with this one. you may have to elaborate.

ah wait the distance between -Q and +Q is x. The distance between -Q and -3Q is L. And the distance between +Q and -3Q is L - x. Yes diagrams do help!