What is the resultant vector electric field at the point P?

[Freya]

Homework Statement

There are 3 charges, each denoted q, the first at (0,a), the second at (0,0) and finally one at (b,0). What is the resultant electric field at point P, (b,a)?

Homework Equations

E[/B]=q/(4πεo r²) for a point charge

The Attempt at a Solution

So I know I need to use the superposition principle and sum the fields caused by the individual charges but I'm not sure whether I need to consider the fact that their fields won't necessarily be in the same direction.

My attempt gave me
E= q/(4πεo (1/a² + 1/b² + 1/(a² + b²)) in the direction the same as sqrt(a² + b²).

Thanks for any help, I've been debating this with friends.

 

[BvU]

Hello again,

You really need to make a drawing. $\vec E$ is a vector, as is $\vec F = q\vec E$. Fields add up, so you can calculate the forces separately and then add them up. Vector-wise, as is the habit when dealing with forces !

Oh, and $\sqrt{a^2+b^2}$ has no direction! It's a number, a scalar.

Oh, and E $\propto$ 1/r², not 1/ ( 1/r² )