Solving Electric Field Equations: A Case Study

[SteelDirigibl]

Homework Statement

Homework Equations

E=k_e*q/r²

The Attempt at a Solution

See screenshot. The angles are correct, however I can't get the equation right for either part. I understand they should be different since one is force and the other electric field, I thought that should be the electric field solved and simplified.

Not sure how to put in equations on here, so I'll do my best.
before simplification, I had for the i component:
k_e3q/a²+sqrt(2)/2*k_e4q/a²

and for the j component:
k_e5q/a²+sqrt(2)/2*k_e4q/a²


where have I gone wrong? the sqrt(2)/2 is cos(45) and sin(45) to get the components of the Bq in the drawing. Not sure what the problem is. I can do these fine with numbers so maybe I just am not putting it into the computer right. suggestions?

 

[Delphi51]

Ei = ke3q/a²+sqrt(2)/2*ke4q/a² = kq/a²[3 + 2√2]
In the screenshot, you have √2 when you should have 2√2.
Same in the j part.

Use F = q*E to get the force - same expression, just square the q.