Why Do the X Components of the Electric Field Cancel Out?

[FocusedWolf]

I have this standard homework problem to find the electrical field at a point.

I figured out most of the math like the x and y components of the E Field from the two charges acting on the point. I also have the correct answer and i don't understand why the x components of the electrical charge cancel and all that's left is the sum of the two y components.

Here's drawing of problem and me figuring out direction of e fields: http://focusedwolf.googlepages.com/work2.bmp

It just looks to me like the y components should cancel and it's the sum of the x components.

 

[neutrino]

If the charges are equal in magnitude, the y-components should cancel, and the resulting field would be twice the x-component (in magnitude) of the field of anyone charge.

 

[FocusedWolf]

So your agreeing with my intrepration?

Here is the problem... with "work". they skpped a lot of steps, but notices at end says the x components cancel due to symmetry, and not the y. zzz

http://focusedwolf.googlepages.com/problem.jpg

 

[neutrino]

Although not specified, I think they may have defined \theta with respect to the y-axis. In that case, what they've stated is correct. cos\theta components, and not the "x-components", do cancel out due to symmetry.

 

[FocusedWolf]

Hmm i think i get it...so its its not x = Ecos(theta) and y = Esin(theta) but instead, cause theta is "looking down", x = Esin(theta) and y = Ecos(theta)... so the x's do sum and the y's do cancel... just backwards

So if theta was defined from between x-axis and P, the "normal" way could be used with x = Ecos(theta)... and get same answer?

 

[neutrino]

The answer would be the same, but your new theta would be pi/2 - old theta.

Remember, the direction of the field does NOT depend upon what coordiante system or the angle convention you use. If you're in doubt, think of it in physical terms.

 

[FocusedWolf]

Yep it worked

http://focusedwolf.googlepages.com/answer.jpg