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

A quarter circle segment has a uniform linear charge density of λ. Starting with the E-field due to point charges, show that the magnitude of the E-field at the center of curvature(which is distance R away from all points on the quarter circle) is E= (kλ√(2))/R

2. Relevant equations

E= k∫dq/R^2 * r^

r^ is r hat

q=Rλ

k=9x10^9 or in this case just a constant

3. The attempt at a solution

I first approached this as a semi-circle and was going to divide by 2 at the end. With a semi-circle the x unit vectors I can replace r^ with y^*sinθ (didn't get the right answer so this approach is probably wrong).

E= k/R^2∫dq*r^

=((kλ)/R)*y^∫sinθ dθ

=((kλ)/R)*y^[-cos(pi)+cos(0)]

=((2kλ)/R)*y^

=((kλ)/R)*y^

I'm missing a √(2) somehow and I don't know how to get rid of the y hat.

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# Homework Help: Electric Field of a quarter circle segment

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