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Suppose we have two negative charges, one located at the origin and carrying charge −9e, and the other located on the positive x-axis at a distance d from the first one and carrying charge −36e. Determine the location, polarity and magnitude of a third charge whose placement would bring the entire system into equilibrium.

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braza909

Answer:

It would have to be in between the two charges and be positive for force on 9e to be zero

k 9e q/x^2= k 36e 9e /d^2

q/x^2 = 36e/d^2

q = 36e x^2/d^2

Now we need force on 36e to be zero

k 36e q/(d-x)^2 = k 36e 9e/d^2

q/(d-x)^2 = 9e/d^2

36 x^2/d^2 = 9/d^2 (d-x)^2

36 x^2 = 9 (d-x)^2

x=d/3

q = 36e (d/3)^2/d^2 = 36e/3^2 = 4 e

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