pexam1 - Physics 21 Fall 2007 1 2 3 4 5 Total Name...

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Physics 21 Fall, 2007 Practice Hour Exam #1 1 2 3 4 5 Total Name: Recitation Time Recitation Leader 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. 8 3 6 I 3 I 2 I 1 36 V 27 V b a (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 a and b on the dia- gram? Use the calculated values of the currents and show how you get your answer. Problem 2. The circular ring of charge shown in the diagram is in the xy plane centered at the origin and has a radius R . The charge is spread uniformly around the ring with linear density λ . R P (x =0,y=0, z) y z x λ ı φ (a) (4 pts.) Write an expression for the total charge Q on the ring. (b) (3 pts.) Give the components of the vector ( r - r ) from the point on the ring at angle φ (with respect to the x axis) to the point P . (c) (6 pts.) Determine the electric potential dV at the point P due to the element dQ of charge at the point φ on the ring. Express dQ in terms of λ and . (d) (3 pts.) Integrate to find the electric potential V at the point P due to the ring of charge. Your answer should be in terms of λ , R , and z . (e) (4 pts.) Use the expression for V to find the z component of the electric field at the point P .
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