Question

Two particles are fixed to an x axis: particle 1 of charge q1 = 1.73 ¡Ñ 10-8 C at x = 30.0 cm and particle 2 of charge q2 = -4.41q1 at x = 78.0 cm. At what coordinate on the x axis is the electric field produced by the particles equal to zero?

Answer 1

distances from charges
x1 = x-30
x2 = 78-x

q1/x1^2 = q2/x2^2

1/x1^2 = 4.41 /x2^2

1/(x-30)^2 = 4.41/(78-x)^2

6084 - 156 x + x^2 = 4.41(x^2 -60 x + 900)

solve the quadratic