Two point charges +9e and +e are kept at a distance

Question

Two point charges +9e and +1e are kept at a distance of 16 cm from each other. At what point between these charges should a third charge q be placed so that it remains in equilibrium.

Answer 1

Given charges: +e and +9e

Let the third chare q be placed at a distance x from e and hence its distance from 9e is 16-x cm

For the system to remain in equilibrium,

F₁ = F₂

Therefore,

F₁ = K(e q)/x²

F₂ = K(9e)/(16-x)²

Equating F₁ and F₂ , we get,

9/x² = 1/(16-x)²

Taking square root on both sides:

3/x = 1/(16-x)

Solving for x, we get,

x = 12cm

Hence, the charge q should be placed at 12 cm from +9e.