Two particles are fixed to an axis particle 1 of charge q1

Two particles are fixed to an axis: particle 1 of charge q_1 = 2.39 x 10^-8 c at x = 30.0 cm and particle 2 of charge Q_2 = -5.76 Q_1 at x = 62.0 cm. At what coordinates the x - axis is the electric field produced by the particle equal to zero?

Solution

Here the only place where electric field can be zero is to the left of x=30 cm.

E_net=E₁-E₂=0

E₁=E₂

=>K|Q₁|/(0.3-X)² =K|Q₁|/(0.62-X)²

(0.62-X)/(0.3-X) =sqrt[Q₂/Q₁]=sqrt[5.76]

(0.62-X)/(0.3-X) =(+ or -)2.4

Case 1:

0.62-X/(0.3-X) =2.4

0.62-X = 0.72-2.4X

1.4X=0.72-0.62

X=0.0714 m =7.14 cm(left)

Case 2:

0.62-X/(0.3-X) =-2.4

0.62-X =- 0.72+2.4X

3.4X=1.34

X=39.34 cm(right)

SO the answer is

X=7.14 cm( since it is left to x=30 cm)