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btpolk
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Homework Statement
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
Homework Equations
E= k∫dq/R^2 * r^
r^ is r hat
q=Rλ
k=9x10^9 or in this case just a constant
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.