Electric Field Due to a Point Charge

[tatiana_eggs]

Homework Statement

In below figure, the three particles are fixed in place and have charges q1 = q2 = +e and
q3 = +2e. Distance a = 6.00 μm. What are the magnitude of the
net electric field at point P due to the particles?
http://www.geocities.com/imfrrreal/22-36.jpg

Homework Equations

|E| = k * |q| / r²

The Attempt at a Solution

Well, I've got as far as understanding how to set up my vectors, (blue, above) realizing that E₁ and E₂ cancel. So now I set up my E_net = E₃ = k * 2e / r².

What is r in this case?! I think my real problem here could be geometry, and not physics, but who knows I could be missing something vital from the beginning of the E-fields chapter. I though r would be sqrt 2 * a = 8μm, making r = 4μm. But when I evaluate E_net = k * 2e / (4x10^-6)² I do not get the right answer.

In the solutions manual the final eq. they evaluate is: k * 2e / (a/sqrt 2)²

Where do they get r = a / sqrt 2 ?

Is r not the blue line, but twice as long since the third point charge is twice the charge of the others?

If this ends up being a geometry problem a) slap me b) accept my apologizes and move post.

 

[Doc Al]

I though r would be sqrt 2 * a...

Realize that "a" is the hypotenuse of a right triangle, so it must be the largest side of that triangle.

Where do they get r = a / sqrt 2 ?

Use the pythagorean theorem.

(It's a geometry problem.)