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solut56ion4_pdf - Version 097/ABCAB inclasstest 03...

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Version 097/ABCAB – inclasstest 03 – Turner – (56725) 1 This print-out should have 2 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Consider the setup shown in the figure be- low, where the arc is a semicircle with radius of 123 cm. The total chargeon the arc is - 37 . 7 μ C, and distributed uniformly on the semicircle. The Coloumb constant is 8 . 98755 × 10 9 N m 2 / C 2 . x y - - - - - - - - - - - - - - - - - - Δ θ θ r x y I II III IV B A O Determine the magnitude of the electric field at O . 1. 223145.0 2. 1550570.0 3. 113107.0 4. 395715.0 5. 125362.0 6. 371869.0 7. 780225.0 8. 1125790.0 9. 876921.0 10. 142578.0 Correct answer: 1 . 42578 × 10 5 N / C. Explanation: Let : q = - 37 . 7 μ C , r = 123 cm , and k = 8 . 98755 × 10 9 N m 2 / C 2 . x y - - - - - - - - - - - - - - - - - - Δ θ θ r x y I II III IV B A O E By symmetry of the semicircle, the y - component of the electric field at the center is E y = 0 . There we need consider only the x -component of the electric Field. Using ds = r dθ , we have Δ q = λ ds = λ r dθ = q π r r dθ = q π dθ , so Δ E x = k | Δ q | cos θ r 2 = k | q | π r 2 cos θ Δ θ .
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