What must be the charge and placement of the third charge

[shashaeee]

Two charges -Q_o and -3Q_o, are a distance l apart. These two charges are free to move but do not because there is a third charge nearby. What must be the charge and placement of the third charge for the first two to be in equilibrium.



This would be easier if I was given an l amount, but since all I know is l, I'm now stuck. I know that it has to be in the middle because putting it on either sides will give a net value.

Can someone just guide me on how to get started on this?

 

[TSny]

This would be easier if I was given an l amount, but since all I know is l, I'm now stuck.

Since the value of l is not given, you'll express the answer for the location of the third charge in terms of l. And the magnitude of the third charge will be expressed in terms of Q_o.

You already know that the third charge, Q₃, will be placed between the two given charges. So, let x be the distance from one of the charges. Express the distance to the other charge in terms of l and x. Try to set up two equations that contain the two unknowns, x and Q₃. It will help to write the third charge as Q₃ = aQ_o and take the two unknowns to be a and x.