The charges and coordinates of two charged particles held fixed along the x -axi

Question

The charges and coordinates of two charged particles held fixed along the x-axis are
Q1 = +7 C, x1 = 2 cm, Q2 = -3 C, x2 = 5 cm. At what position on x-axis should a third particle of charge Q3 = +4 C be placed such that the net electrostatic force on particle 3 due to the other two particles is zero?

The charges and coordinates of two charged particles held fixed along the x-axis are
Q1 = +7 C, x1 = 2 cm, Q2 = -3 C, x2 = 5 cm. At what position on x-axis should a third particle of charge Q3 = +4 C be placed such that the net electrostatic force on particle 3 due to the other two particles is zero?

Explanation / Answer

here Q1 > Q2

so, the third must be placed close to Q2 and it is right of Q2.

let x is the distance from Q2 where Q3 should be placed.

Apply, F13 = F23

k*Q1*Q3/r13^2 = k*Q2*Q3/r23^2

Q1/(3+x)^2 = Q2/x^2

x^2/(3+x)^2 = Q2/Q1

x/(3+x) = sqrt(3/7)

x = (3+x)*0.6546

x = 1.964 + 0.6546*x

x*(1 - 0.6546) = 1.964

x*0.3454 = 1.964

x = 1.964/0.3454

= 5.7 cm

so, at x = 5 + 5.7

= 10.7 cm Q3 must be placed

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