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exam1andEqn

# exam1andEqn - Physics 21 Fall 2007 Hour Exam#1 1 2 3 4 5...

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Unformatted text preview: Physics 21 Fall, 2007 Hour Exam #1 1 2 3 4 5 Total Name: Recitation Time Recitation Leader October 4, 2007 This exam is closed notes and closed book. You must show enough work on all problems to convince the grader you understand how to solve the problem. You may use a calculator, but you must show a full solution to simultaneous algebraic equations. Give units. There is an equation sheet on the last page. All problems count 20 points. Problem 1. 2 Ω 3 Ω 4 Ω I 1 I 3 I 2 10.0 V 8.0 V a b (a) (10 pts.) Write the loop and junction equations needed to determine the currents I 1 , I 2 , and I 3 in the circuit shown. Indicate clearly the loop used to determine each loop equation. (b) (6 pts.) Determine the currents I 1 , I 2 , and I 3 (including the correct sign) by explicit solution of the equations. You must show your work. (c) (4 pts.) What is the potential difference V b − V a between the points marked b and a on the dia- gram? Use the calculated values of the currents and show how you get your answer. Problem 2. The thin rod shown in the diagram ex- tends along the x axis from x = 0 to x = a . A total charge Q is spread uniformly along the rod. x y P = (0, y ,0) +a x' dQ (a) (3 pts.) Write an expression for the linear charge density λ on the rod. (b) (4 pts.) Give the components of the vector ( r − r ) from the charge dQ shown on the rod at x = x to the point P on the y axis. (c) (4 pts.) Determine the electric field d E at the point P due to the element dQ of charge at the point x on the rod. Express d E in terms of Q , a , x , and y . (d) (6 pts.) Integrate to find ONLY THE y COMPO- NENT E y of the electric field E at the point P due to the rod. Your answer should be in terms of Q , a , and y . (e) (3 pts.) If the point P is a very long distance from the rod along the y axis ( y a ), what should be the limiting form of E ? No calculation is needed. Problem 3. A thin wire with linear charge density λ runs along the central axis of a long hollow conducting...
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exam1andEqn - Physics 21 Fall 2007 Hour Exam#1 1 2 3 4 5...

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