# Two charged particles

Two point of 2q and -q are situated 1 meter apart on the x axis. find the point or points along the x axis at which the electric field is zero

Suppose the particle 2q is situated on the origin(x =0) and the particle -q at x=1 at the right of the origin. The electric field from the two particles adds as vectors.

$E_{tot}(x) = E1 +E2 = 2q/(4*\pi*\epsilon0*x^2) – q/((4*\pi*\epsilon0*(x-1)^2) =0$, for x >0

$(x-1)^2 -x =0$

$x^2 -4x +2 -x =0$

$x^2 -5x +2 =0$

$x1 =2$ meter , $x2 =1/2$ meter

$E_{tot}(x) = E1 +E2 = 2q/(4*\pi*\epsilon_0*x^2) – q/((4*\pi*\epsilon_0*(x+1)^2) =0$, for x <0

$(x+1)^2 -x =0$

$x^2 +4x +2 -x =0$

$x^2 +3x +2 =0$

It has no real solutions.