Help finding the Electric field at the center of charged arc

AI Thread Summary
The discussion centers on understanding the calculation of the electric field at the center of a charged arc. The user is confused about the length of the arc being pi/R/2, questioning if it results from dividing the circumference of a circle by four due to evaluating a quarter circle. Confirmation is provided that the charge +Q is indeed spread over this quarter arc length. Additionally, the user seeks a simpler approach to the problem, expressing difficulty in following the teacher's solution. Clarification is offered, inviting further questions on specific confusing parts of the solution.
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Homework Statement
Determine electric field at center of curvature of arc.
Relevant Equations
E=KQ/r^2
I am having trouble understand where area circled in red.

I get that lamda is Q/L. The charge is +Q. Length is pi/R/2.

I am having trouble understanding why the length is pi/R/2? Is it because the circumference of a circle is 2*pi*R and since we have broken this problem down to just evaluating a quarter of the a circle, we divide 2*pi*R by 4 and get pi*R/2 which when we put that under Q we get 2Q/pi*R?

I wasnt sure until I typed out my question about and believe that may be the case, but just looking for some conformation.

Also, is there a simpler approach to this problem? My teacher wrote this out and I found it hard to follow.
 

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quittingthecult said:
I am having trouble understanding why the length is pi/R/2? Is it because the circumference of a circle is 2*pi*R and since we have broken this problem down to just evaluating a quarter of the a circle, we divide 2*pi*R by 4 and get pi*R/2 which when we put that under Q we get 2Q/pi*R?

I wasnt sure until I typed out my question about and believe that may be the case, but just looking for some conformation.
Yes, I think you have correctly answered your own question. The charge +Q is spread out over a length of a quarter of a circle of radius R.
quittingthecult said:
Also, is there a simpler approach to this problem? My teacher wrote this out and I found it hard to follow.
Your teacher's solution looks very good. If there is a specific place in the solution that you are confused about, we can help clarify.
 
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