(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A charge Q is distributed evenly on a wire bent into an arc of radius R, as shown in

the figure below.What is the mathematical expression that describes the electric field

at the center of the arc (point P indicated) as a function of the angle θ? Sketch

a graph of the electric field as a function of θ for 0 < θ < 180.

I added the figure for the question as an attachment.

3. The attempt at a solution

lambda=Q/pi R

dE= kdQ/R^2

dE= (kdQ/R^2) cos θ

dQ=lambda dl

dl= Rd theta

dQ=lambda R dθ

dE=(k[lambda R d θ]/R^2)cos θ

E=(k lambda R cos θ/R^2)d θ(from pi/2 to -pi/2)

E=k lambda/R cos θ dθ

E=k lambda/Rsin θ

E=k lambda/R[sin(pi/2)-sin(-pi/2)]

E=k lambda/2R

E=k(Q/piR)/2R=2kQ/piR^2

E= 2kq/piR^2

Is this right? I used K for 1/4pi(E) to make it easier to type.

Also i am kind of lost on what is expected for the sketch.

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# Homework Help: Charge Distrubution evenly on Arc (Radius R)

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