Answer to Question #143304 in Electricity and Magnetism for Elias

Question #143304
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?
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Expert's answer
2020-11-10T06:57:14-0500

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

F1=14πe0q1q3L132F_1 = \frac{1}{4πe_0} \frac{q_1q_3}{L_{13}^2}

Force on particle 3 from particle 2 is

F2=14πe0q2q3L232F_2 = \frac{1}{4πe_0} \frac{q_2q_3}{L_{23}^2}

Total force

FT=F1+F2=0F_T = F_1 + F_2 = 0

L13=L12+L23=2L23  as  L23=L12L_{13} = L_{12} + L_{23} = 2L_{23} \;as \;L_{23} = L_{12}

q14+q2=0\frac{q_1}{4} + q_2 = 0

q1q2=4\frac{q_1}{q_2} = -4


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