What must be the charge and placement of the third charge

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To achieve equilibrium between the two charges, -Qo and -3Qo, a third charge, Q3, must be placed between them. The distance of Q3 from one charge can be expressed as x, while the distance to the other charge will be l - x. The magnitude of Q3 should be expressed as a multiple of Qo, specifically Q3 = aQo. Setting up equations based on the forces acting on the charges will help determine the values of a and x. This approach allows for a solution in terms of the variable l, facilitating the analysis of the system.
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Two charges -Qo and -3Qo, 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?
 
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shashaeee said:
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 Qo.

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 = aQo and take the two unknowns to be a and x.
 
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