Help with practice test problem curved rod with charge density?

[nchin]

help with practice test problem! curved rod with charge density??

Two plastic rods are curved. The left rod is a 120° circular arc of radius
R, and has uniform charge density λ. The rod on the right is a 120° circular
arc of radius 2R, and has uniform charge density -2λ. A point P is located at the center of the circular arcs. Use i (i hat), j (j hat) notation in the following, where i is a unit vector that points in the positive x direction.

a) What is the vector E_λ at P due only to the rod with charge density λ?

Solution:
magnitude = E_λ = λ √(3) / 4∏(ε naught)R
E_λ = (λ (√3) / 4∏(ε naught)R) (√3/2 i hat - 1/2 j hat)


What i got for the magnitude:
λ / 4∏(ε naught)r²)
Im having a hard time visualizing the picture. I know I use the Electric field formula Kq/r². but i don't understand how my teacher got the √3 in the numerator and why its only R instead of R² in the denominator. Also why is the direction (√3/2 i hat - 1/2 j hat)?

Help please!

i think i might have a better idea. i take the integral from 0 to pi/3. charge density lambda = Q / L. L = 2 pi R/4 ---> charge density lambda = 2Q / pi R?

 

[tms]

Two plastic rods are curved. The left rod is a 120° circular arc of radius
R, and has uniform charge density λ. The rod on the right is a 120° circular
arc of radius 2R, and has uniform charge density -2λ. A point P is located at the center of the circular arcs. Use i (i hat), j (j hat) notation in the following, where i is a unit vector that points in the positive x direction.

It would help to know the orientation of the rods with respect to the axes.

And when solving the problem, think of symmetries.