Determine the electric field on the y axis

[LANS]

Homework Statement

Two 2.04 µC point charges are located on the x axis. One is at x = 1.02 m, and the other is at x = -1.02 m. Determine the electric field on the y-axis at y = 0.470 m.

Homework Equations

E = k*q/r^2

The Attempt at a Solution

First I find the distance from one of the charges to the point on the y-axis.
$$\sqrt(1.02^2 + 0.47^2) = 1.123m$$

I also find the angle between this line and the y-axis.
$$tan^1 \frac{1.02}{0.47} = 65.26$$

Then I found the component of the electric field at the point on the axis which lies along the y-axis.

$$E = k_e*\frac{q}{r^2}$$
$$E = 8.99e9 * \frac{2.04\mu C}{1.123m}*cos(65.26)$$

As this only accounts for one charge, and the other charge is equal in magnitude and position, I double this number to get the answer.

Howerver, this gives me the wrong answer. Any help would be appreciated.

 

[Apteronotus]

The E field due to one of the charges (the one at x=1.02) on the y-axis is given by your equation E=k*q/r^2.
if you draw a line from your charge to the point on the y-axis, this E vector points in this direction. If your other charge (at x=-1.02) has opposite sign, then the y components of the E vectors cancel each other out and the x-components add. Else, the x-components cancel and the y-components add.

In either case break the E vector that you found into its x and y components using SOH CAH TOA. Then do the simple algebra depending on the signs of your charges.