Where Is the Electric Field Zero Between Two Negative Charges?

[tuggler]

Homework Statement

Two points are resting on a string. The first point is resting at x = 6.0 m and has charge q1 =−7.1 µC. The second point is resting at x = −4.0 m and has charge q2 = −4.3 µC.
At what location is the total electric field zero from the two points(other than infinity)?

Homework Equations

$$E =\frac{KQ}{r^2}$$

$$\frac{q_1}{r_1^2} = \frac{q_2}{r_2^2}$$

The Attempt at a Solution

I divided away the constant K from my second equation because they cancel out when you set them equal to each other.

I don't know what my $$r_1,r_2$$ should be here?

 

[LeonhardEu]

Why don't you set the distance from the first charge x and define the distance from the other with x and the distance between the two charges? Thus you introduce only one variable in one equation.

 

[Chestermiller]

Don't forget that the contribution to the electric field from each charge has direction, so, if the point is between the two charges, the contribution from the charge at x = 6 is pointing in the negative x-direction, and the contribution from the charge at x = -4 is pointing in the positive x-direction.

 

[tuggler]

I am not following can you guys elaborate more please?