Question

Three charges lie along the x - axis as in figure. The positive charge q₁ = 9 μC is at x = 3 m, and the positive charge q₂ = 25 μC is at the origin.

Where must a charge q₃ be placed on the x - axis so that the resultant electric force on it is zero?

Answer 1

Gives

$q_1=9\mu c\\q_2=25\mu c\\x=3m\\third charge=q_3$

Equilibrium condition

$F_{13}=F_{23}$

$\frac{k\times9\times10^{-6}\times q_3}{(3-x)^2}=\frac{k\times 25\times10^{-6}\times q_3}{x^2}$

$\frac{9}{(3-x)^2}=\frac{25}{x^2}$

$\frac{3}{3-x}=\frac{5}{x}$

8x=15

$x=\frac{15}{8}m$ =1.875m

So third charge $q_3$ Put x'=1.875m