Question

Two point charges, 5.0 µC and -2.0 µC, are placed 5.0 cm apart on the x axis, such that the -2.0 µC charge is at x = 0 and the 5.0 µC charge is at x = 5.0 cm. At what point(s) along the x axis is the electric field zero?
I'm not exactly sure how i should go by solving this.

Answer 1

First of all, recognize that the point cannot be between x = 0 and x = 5, because the E fields due to the two particles will be in the same direction and cannot cancel each other. In the x > 5 region, the E field due to the -2 uC charge will be less everywhere, so camncellation is not possible. The location will have to be in the x <0 region.

In the x < 0 region,

-2 k/ x^2 + 5k /(5-x)^2 = 0

5/(5-x)^2 = 2/x^2
5x^2 = 50 -20x +2x^2
3x^2 +20x -45 = 0

Take the root x that is < 0. This does not factor easily.