Question

I need help on this, I already have 2 attempts left!

Point charges q, 7ad 2-21 yC are placed 3.5 m apart. Where must q, 23 yC be placed (on the x-axis, In m) so Point charçes q1 d 3.5 m apart. where must q,-23C be placed (on the x-axis, in m) so that the net force on it is zero? (Assume that q1 is at x 0 and q2 is at x 3.5 m.) x 7.0

Answer 1

The charge q3 must be placed to the right of q2

let the charge q3 be x m to the right of q2

force on q3 by q1 = force on q3 by q2

kq1q3 / r1^2 = kq2q3 / r2^2

47*23 / (3.5 +x)^2 = 21*23 / x^2

47x^2 = 21(3.5 + x)^2

47x^2 = 21x^2 + 257.25 + 147x

26x^2 - 147x - 257.25 = 0

x = 147 + sqrt(147^2 + 4*26*257.25) / 52

= 7.05 m

so the charge q3 should be placed at (3.5 + 7.05) = 10.55 m