A +5.0 µC charge is placed at the origin and a -3.9 µC charge is placed at x = 25 cm. At what coordinates can a third charge be placed so that it experiences no net force?

Answer 1

E1=k•q1/(x+ Δx)² (to the right)
E2= k•q2/(Δx)² (to the left)
E1= E2
k•q1/(x+ Δx)² = k•q2/(Δx)²
q1•(Δx)² = q2• (x+ Δx)²= q2• (x²+ 2•x•Δx + Δx²)
5• Δx²=3.9(0.0625+0.5 Δx + Δx²)
1.1 Δx² -1.95• Δx -0.24375 =0
Δx = {1.95±√(1.95²+4•1.1•0.24375)}/2.2=
=(1.95±2.21)/2.2= 1.89 m and -0.12m (extraneous root)
Δx =1.89 m