# Electric field problem

1. Jan 22, 2006

### Punchlinegirl

A charge of -4.84 $$\mu C$$ is located at the origin, and a charge of -6.22 $$\mu C$$ is located along the y-axis at 1.361 m. The value of the Coulomb constant is 8.99 x 10^9. At what point along the y-axis is the electric field zero. Answer in units of m.
I know that for the electric field to be zero, the electric field on the charges must equal each other.
I called the distance from the charge at the origin R, and the distance from the second point is d-r.
I used the equation for electric field and set them equal to each other.
$$kQ/r^2= kq/(d-r)^2$$
$$Q/r^2 = q/ (d-r)^2$$
$$Q(d-r)^2 =qr^2$$
$$(d-r)^2 =qr^2/ Q$$
$$(d^2 -2dr + r^2)/ r^2 = q/Q$$
$$d^2/r^2 - 2d/r +1 = q/Q$$
At this point I got stuck on how to solve for r, can someone help me?
Thanks in advance.

2. Jan 22, 2006

### Pyrrhus

Here's some help
$$(d-r)^2 =qr^2/ Q$$
$$d-r = r \sqrt{\frac{q}{Q}}$$

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