1. The problem statement, all variables and given/known data http://www.webassign.net/hrw/W0490-N.jpg The figure above shows three circular arcs centered on the origin of a coordinate system. On each arc, the uniformly distributed charge is given in terms of Q= 2*10-6C. The radii are given in terms of R = 10cm. What is the magnitude of the net electric field at the origin due to the arcs? 2. Relevant equations dE = Kλds / r2 ds=rdθ λ= Charge / Length ⇒ Q/2πr ⇒ Q/(2πr/4) - since only quarter is shown ⇒ 2Q/(πr) 3. The attempt at a solution So i think I got all the steps correct except i cant figure out why i have to multiply sin(45) to get to the right answer at the end. 1. dE = Kλds / r2 - used this formula b/c it's a ring 2. dEcosθ = Kλds / r2 (cosθ) - multiplied cosθ b/c perpendicular component (sinθ) cancels each other. 3. dEcosθ = Kλrdθ / r2 (cosθ) - replaced ds to rdθ b/c cosθ is present and thus want to integrate along 90° to 180° 4. ∫dEcosθ = ∫Kλrdθ / r2 (cosθ) ⇒ E = Kλ/r ∫(cosθ)dθ - r on the numerator and r2 on the denominator cancels to make denominator just r. since r is constant, took out of the integral and just integrate cosθdθ from 90° to 180° 5. E = Kλ/r [-sin(180°)-(-sin(90°)] ⇒ E = Kλ/r - integral just turns out to be 1 and we are left with E = Kλ/r 6. E = Kλ/r - This is 1st arc so to second and third, we just replace r with 2r and 3r respectively. Then we get E1 = Kλ/r ; E2 = Kλ/2r ; E3 = Kλ/3r 7. Replace λ with 2Q/πr (relevant equation section) E1 = K(2Q/πr)/r ; E2 = K(2Q/πr)/2r ; E3 = K(2Q/πr)/3r E1 = K(2Q/πr2) ; E2 = K(Q/πr2) ; E3 = K(2Q/3πr2) 8. Replace Q and r with respective charge and radius E1 = K(2Q/π(R)2) ; E2 = K(-4Q/π(2R)2) ; E3 = K(18Q/3π(3R)2) E1 = K(2Q/π(R)2) ; E2 = K(-4Q/π4R2) ; E3 = K(6Q/π(9R2) 9. Simplify E1 = K(2Q/π(R)2) ; E2 = K(-Q/πR2) ; E3 = K(2Q/π(3R2) E1 = K(6Q/π3(R)2) ; E2 = K(-3Q/π3R2) ; E3 = K(2Q/π(3R2) ※Multiplied E1 and E2 by 3 on both numerator and denominator to simplify E1 + E2 + E3 = Enet Enet = K5Q/π3(R)2 -------------------------------------------------------- crap.... i dont know where I messed up. Originally i got E1 = 2Q/4πr2ε0 + E2 = -4Q/4πr2ε0 + E3 = 6Q/4πr2ε0 Which turned out to be Enet = Q/π2r2ε0 which turned out to be 228974 but the answer is 161903 which is just sin(45) multiplied by 228974. why do you need to multiply sin45?