I\'m stuck on an easy problem, I know the answer just not how to get it. Two cha

Question

I'm stuck on an easy problem, I know the answer just not how to get it. Two charges are placed on the x-axis as shown in the figure. A charge of -Q is placed at the origin and a charge of +4Q is placed at x = -a. Referring to the figure, where on the x-axis is the electric field zero? a) at a point to the right of the origin b) at a point between x=-a and x=0 c) at a point to the left of x=-a I know the answer is a, but why can it not be c? I don't know how to approach this problem or which equations I should be using.

Explanation / Answer

charge -q is at (0,0)

charge +4q is at (-a,0)

let p be a point between +4q and -q where the electric field due to the charges is zero

let the distance of point p from charge -q be d

electric field due to -q at p is

E1 = k x (-q/d^2)

where k = (1/4pi x e_o) = 9 x 10^9 Nm^2/C^2

electric field due to +4q at p is

E2 = k x (+4q/(-a - d)^2)

as the electric field is zero at point p therefore

E1 = E2

or k x (-q/d^2) = k x (+4q/(-a - d)^2)

solving the above equation for d

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