Answer to Question #143304 in Electricity and Magnetism for Elias

Question

3. In the figure three charged particles lie on an x axis. Particles 1 and 2 are fixed in place. Particle 3 is free to move, but the net electrostatic force on it from particles 1 and 2 happens to be zero. If L23 = L12, what is the ratio q1/q2?

Answer 1

According to Coulomb's Law, force on particle 3 from particle 1 is

$F_1 = \frac{1}{4πe_0} \frac{q_1q_3}{L_{13}^2}$

Force on particle 3 from particle 2 is

$F_2 = \frac{1}{4πe_0} \frac{q_2q_3}{L_{23}^2}$

Total force

$F_T = F_1 + F_2 = 0$

$L_{13} = L_{12} + L_{23} = 2L_{23} \;as \;L_{23} = L_{12}$

$\frac{q_1}{4} + q_2 = 0$

$\frac{q_1}{q_2} = -4$