A charge of 5.00 ✕ 10^-9 C and a charge of -3.50 ✕ 10^-9 C are separated by a distance of 60.0 cm. Find the position at which a third charge, of 14.0 ✕ 10^-9 C, can be placed so that the net electrostatic force on it is zero.

Answer 1

F = k Q/r^2
5 at 0 and -3.5 at 60
for 0
k (5)/x^2 + k(-3.5)/(x-60)^2=0

5(x-60)^2 - 3.5 x^2 = 0

5(x^2-120x+3600 ) - 3.5 x^2 = 0

1.5 x^2 - 600 x +18,000 = 0

x = 32.7 or 367
32.7 makes no sense (introduced by squaring)
so
367 cm