Electric field at the center of a quarter-circle arc of charge

[guyvsdcsniper]

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.

 

[TSny]

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.

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.