Two immobile point charges Q1 and Q2 of values +q and +3q respectively are some distance apart. Q3, with value +2q is placed between them and does not move. What is the ratio of the distance between Q3 and Q2 to the distance between Q1 and Q3?

As Q₃ remains stationary, it is clear that it is not accelerating. Thus we can deduce from Newton's second law that there is no resultant force acting upon the charge. However there are still electrostatic forces acting on the charge from Q₁ and Q₂. Thus as there is no resultant forces, we can deduce that the force between Q₁ and Q₃ is equal to the force between Q₂ and Q₃. Knowing this we can use coulomb's law to equate the two forces and rearrange for the desired ratio. F_(1,3) = F_(2,3). If we call the distance between Q₂ and Q₃ d, and the distance between Q₁ and Q₃ s, then: k*(4q²)/s² = k*(6q²)/d² where we are trying to solve for d/s. Rearranging gives d/s = (3)^1/2.