Understanding Electric Field Addition for Opposite Charges

[keyfob]

I'm a little confused on how the math is supposed to work out when you are adding an electric field from charges with opposite signs. Looking at the image, both of these situations should yield equivalent electric fields at that point right? I get the right answer for when the situation involves two identical charges, but when the charges are opposite i have an extra negative coefficient from the -q which messes up my calculations. I think the problem is that when I draw triangles to try and split up the components that perhaps my Y should be positive for the -q charge, but I'm not sure if/why that should be the case. Otherwise I'm not really sure what I'm doing wrong...any help would be appreciated.

 

[tiny-tim]

Welcome to PF!

Hi keyfob! Welcome to PF!

… I think the problem is that when I draw triangles to try and split up the components that perhaps my Y should be positive for the -q charge, but I'm not sure if/why that should be the case. Otherwise I'm not really sure what I'm doing wrong...any help would be appreciated.

You seem to be having drawing problems …

just draw the "second" side of the triangle the other way, so that the internal angle is 180º minus the original angle.

 

[keyfob]

Thanks for the help, I'm still a little confused though... I attached an updated picture to this post, is this what you meant? Thanks again

 

[tiny-tim]

I don't understand … what are the 6 triangles at the bottom?

 

[keyfob]

The components of the vectors in the x-y plane

 

[tiny-tim]

But they're all the same.