Question

Three particles are fixed on an x axis. Particle 1 of charge q₁ is at x = - a, and particle 2 of charge q₂ is at x = + a. If their net electrostatic force on particle 3 of charge + Q is to be zero, what must be the ratio q₁/q₂ when particle 3 is at x = 1.50a? Important: Assume that the charge of particle 1 is positive.

Answer 1

r₁ = distance of q₁ from q₃ = 2.5 a

Magnitude of electric force on q₃ by q₁ is given as

F₁ = k q₁ q₃/r₁²

r₂ = distance of q₂ from q₃ = (0.5) a

Magnitude of electric force on q₃ by q₂ is given as

F₂ = k q₂ q₃/r₂²

net force on q₃ is zero , hence

F₁ = F₂

k q₁ q₃/r₁² = k q₂ q₃/r₂²

q₁ /r₁² = q₂ /r₂²

q₁/q₂ = r₁²/r₂²

q₁/q₂ = (2.5 a)²/((0.5) a)²

q₁/q₂ = 25

Since q₁ is positive and q₂ is negative, hence the ratio should be negative\

q₁/q₂ = - 25