Question

Particle 0 experiences a repulsion from particle 1 and an attraction toward particle 2. For certain values of d1 and d2, the repulsion and attraction should balance each other, resulting in no net force. For what ratio d1/d2 is there no net force on particle 0?

Answer 1

To solve the problem one assumption has to be made: Particle 0 is not between particles 1 and 2, otherwise, the net force will be always greater than 0. That is because the force than particles 1 and 2 make to particle 0, have the same direction.

Answer:

$\frac{d1}{d2} = \sqrt{\frac{q1}{q2} }$

Explanation:

Coulomb's law states that Fe = (K*q1*q2)/d^2

We want the force  that particle 1  makes over 0  to be equal and opposite to the force that particle 2 makes over 0, that is:

F10 = F20

(K*q1*q0)/d1^2 = (K*q2*q0)/d2^2 (d1 is the distance between particle 1 and 0 and d2 is the distance between particle 2 and 0)

Solving the equation:

q1/d1^2 = q2/d2^2

d1/d2 = √(q1/q2)