Two point charges are at x=0 and x=L, respectively, and free to move. A third charge is placed so that the entire three-charge system is in static equilibrium. What are the magnitude, sign, and x-coordinate of the third charge.

Explanation:

The point will lay at x = L/2 ( in the middle)

Let the charge given be Q at x = 0 and L ,  and q is the charge required.

Force on charge put on x = 0 , due to charge in the middle

k Q q / .5 L

Force on charge put on x = 0 , due to charge at x = L

= k Q q /  L

Total force

= k Q q / .5 L  + k Q² /  L  = 0,  FOR BALANCE.

2q = - Q

q = - Q / 2

In the middle , half the charge of either of equal charge placed at x = 0 and L should be placed . Its nature negative .

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