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}F1=4πe01L132q1q3
Force on particle 3 from particle 2 is
F2=14πe0q2q3L232F_2 = \frac{1}{4πe_0} \frac{q_2q_3}{L_{23}^2}F2=4πe01L232q2q3
Total force
FT=F1+F2=0F_T = F_1 + F_2 = 0FT=F1+F2=0
L13=L12+L23=2L23 as L23=L12L_{13} = L_{12} + L_{23} = 2L_{23} \;as \;L_{23} = L_{12}L13=L12+L23=2L23asL23=L12
q14+q2=0\frac{q_1}{4} + q_2 = 04q1+q2=0
q1q2=−4\frac{q_1}{q_2} = -4q2q1=−4
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