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nchin
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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 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?
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 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?
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