Answer to Question #240771 in Electric Circuits for sda

Question #240771

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?



1
Expert's answer
2021-09-23T08:40:27-0400

Gives

q1=9μcq2=25μcx=3mthirdcharge=q3q_1=9\mu c\\q_2=25\mu c\\x=3m\\third charge=q_3

Equilibrium condition


F13=F23F_{13}=F_{23}

k×9×106×q3(3x)2=k×25×106×q3x2\frac{k\times9\times10^{-6}\times q_3}{(3-x)^2}=\frac{k\times 25\times10^{-6}\times q_3}{x^2}

9(3x)2=25x2\frac{9}{(3-x)^2}=\frac{25}{x^2}

33x=5x\frac{3}{3-x}=\frac{5}{x}

8x=15

x=158mx=\frac{15}{8}m =1.875m

So third charge q3q_3 Put x'=1.875m


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