# Help with practice test problem! curved rod with charge density?

1. Feb 21, 2013

### 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 Eλ at P due only to the rod with charge density λ?

Solution:
magnitude = Eλ = λ √(3) / 4∏(ε naught)R
Eλ = (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 dont 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)?

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?

Last edited: Feb 21, 2013
2. Feb 21, 2013

### tms

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

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

And when solving the problem, think of symmetries.