Question

Two free positive charges 4q and q are a distance L apart. What charge Q is needed to achieve equilibrium for entire system and where should be placed from charge q ?( also mention charge of Q)

Answer 1

Answer:

Let"r" be the distance from the charge q where Q is in equilibrium .

Total Force acting on Charge q and 4q:

F=kqQ/r² + k4qQ/(l-r)²

For Q to be in equilibrium , F should be equated to zero.

kqQ/r² + k4qQ/(l-r)²=0

(l-r)²=4r²

⇒l-r=2r

⇒l=3r

⇒r=l/3

Taking the third charge to be -Q (say) and then on applying the condition of equilibrium on + q charge

kQ/(L/3)² =k(4q)/L²

9kQ/L²=4kq/L²

9Q=4q

Q=4q/9

Therefore a point charge -4q/9 should be placed at a distance of L/3 rightwards from the point charge +q on the line joining the 2 charges

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