Question

A charge, Q2 = -7.00x10-6 C, is 11.00 cm to the right of charge Q1 = 6.00x10-6 C. Where can a third charge be placed, along the line connecting Q1 and Q2, such that it experiences no net force (other than

Answer 1

Let us assume the third charge is to the left of Q1 and at a distance x from Q1
Let the charge Q3 be Q Coulomb
Force on Q3 due to Q1 = k * -Q * 6.00*10^-6 / x^2
Force on Q3 due to Q2 = k * -Q * -7.00*10^-6/(11+x)^2

For Q3 to experience no net force, the sum of forces must be zero
=> k * -Q * 6.00*10^-6 / x^2 + k * -Q * -7.00*10^-6/(11+x)^2 = 0
6/x^2 - 7/(11+x)^2 = 0
6x^2 + 132x + 726 -7x^2 = 0
x^2 - 132x - 726 = 0
x = [132 +/- sqrt(17424 + 37752)]/2*13 = [132 +/- 234.9]/2 = -51.45 or 183.45

Since we assumed it is left of Q1, the distance is 183.45cm to the left of Q1 or 51.45cm to the right of Q1