Two point charges are placed along a horizontal axis with the following values and positions: +6.0 µC at x = 0 cm and -24.0 µC at x = 60 cm. At what point along the x axis is the electric field zero?

Question

Two point charges are placed along a horizontal axis with the following values and positions:  +6.0 µC at x = 0 cm and -24.0 µC at x = 60 cm.  At what point along the x axis is the electric field zero?

drwls · Accepted Answer

It won't be between the charges, because both charges produce an E-field in the same direction there. Look for it to be along the -X axis, at a point x = -a, where
6/a^2 = 24/(60 + a)^2

(60+a)/a = sqrt(4) = 2
60/a + 1 = 2
a = 60 cm