posted by joe .
A charge of 2.4 nC and a charge of 5.0 nC are separated by 33.30 cm. Find the equilibrium position for a -4.1 nC charge.
The distance to the 5.0 nC charge must be sqrt(5.0/2.4)= 1.4434 times the distance to the 2.4 nC charge. That will make the q/r^2 terms equal for both charges. The charge of the object at the equilibrium position does not matter.
33.30 cm, divided in a 1:1.4434 ratio, would put the equilbrium position at 13.63 cm from the smaller charge, and 19.67 cm from the larger charge.