Two charges q and -4q are intially held in place a distance L=0.25m apart along

Question

Two charges q and -4q are intially held in place a distance L=0.25m apart along the x-axis . Your goal is to add one additional charge Q to this system so all three charges will thn remain in place when released.

Note the q in the image given is to the left of -4q.

Will all charges remain in place when released if the additional charge Q (positive or negative as needed) is placed at the correct position on the x-axis to the right of charge -4q?

I am aware the answer it is impossible to do so but I dont understand how. Could you please show the work that supports that it is impossible?

Explanation / Answer

let Q be introduced in betweem q and -4q

let Q be at x units from q or (L-x) from -4q
so

for equillibrium at this Poition Enet = 0

Enet atQ = Eq = E due to 4 q

so

Kq/x^2 = K4q/(L-x)^2

(L-x)/x = sqrt4 = 2

L-x = 2 x

3x = L

x = L/3 = .25/3 = 8.33 cm = 0.0833 m

-------------------------------

yes all remain in equillibirum

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