How Is Equilibrium Distance Calculated Between Charged Spheres?

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To calculate the equilibrium distance between two charged spheres, one with charge nq and the other with charge q, the position of a third sphere along the pole can be determined without knowing its charge. The equilibrium position, x, is found by analyzing the electric fields produced by the two end charges at that point. The distance from the third sphere to the right sphere can be expressed as y = d - x. By setting the net force on the third sphere to zero, the equilibrium condition can be established. Thus, the charge of the third sphere is not necessary for solving the problem.
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At the two ends of a pole there are two + charged spheres.One has a charge n times that of the other (nq and q). Along this pole, of length we will call d, there is another charged sphere which is located at an equilibrium position we will call x units away from the first sphere. My task is to find the distance x. I will call the distance of the middle sphere from the “right” sphere y = d – x
 
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Well, what have you done so far and where are you stuck?

Hint: Find the field from each of the end charges at the point x.
 
Thanks
 
how can u solve it wothout knowing d charge of d 3rd sphere??
 
TROGLIO said:
how can u solve it wothout knowing d charge of d 3rd sphere??
You don't need to know the charge on the third sphere to figure out the equilibrium point. (Just call it Q, if you like.)
 

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