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Unformatted text preview: / r aw DO NOT BEGIN THIS EXAM UNTIL TOLD TO START Name:
Student Number:
Instructor:
ECE 2317 I
Applied Electricity and Magnetism
Exam 2 November 18, 2000 1. This exam is closed book and closed notes. A calculator and one crib
sheet (one 8.5” X 11" piece of paper) are allowed. 2. Show all of your work. No credit will be given if the work required to
obtain the solutions is not shown. 3. Perform all your work On the paper provided. 4. Write neatly. You will not be given credit for work that is noteasily
legible. 5. Leave answers in terms of the parameters given in the problem.
6. Show units in all of your ﬁnal answers. 7. Circle your ﬁnal answers. 8. if you have any questions, ask the instructors. You will not be given
credit for work that is based on a wrong assumption. 9. You will have a total of 90 minutes to work the entire exam. [25 Prob. 1' 125 Prob. 3 [25 Prob. 2 [25 Prob. 4 ...._...._._........ _ Problem 1 (25 pts) A inﬁnitely long cylindrical shell of uniform charge density ps0 [C/mz] is shown below. a) Calculate the potential inside the shell, by integrating the electric ﬁeld. Assume that the potential is zero on the z axis. ‘. f, P)
 t a; 1)) Calculate the potential outside the shell, by integrating the electric ﬁeld. Assume again that
the potential is zero on the z axis. 0) Modify your answers to the above two parts to obtain the solutions if the potential on the z
axis is 10 [V]. 41/ / \4 Problem 2 (25 pts) A metal sphere of radius a is in air. The dielectric breakdown of the air is E: [Wm]. a) What is the maximum total charge QM: that can be placed on the sphere before the air will
break down? b) Assuming that this charge is placed on the sphere, what is the stored energy of the system?
Use the potential formula for your calculation, and express your answer in terms of EC. c) Repeat the calculation to ﬁnd the stored energy in terms of E6, using the electric—ﬁeld
formula {W x. "W" 'Z.\\‘ “ “2 a H Eff—(FM; O 5 Rig 1 ~ 5.. 2
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3r Froblem 3 (25 pts) A parallelplate capacitor is shown below. The top plate is at a voltage of V2 [V], while the
bottom plate is assumed to be at a voltage of V; [V], with V2 > V1. a) Solve the Laplace equation to obtain the solution for the potential function inside the
capacitor. b) Using your answer to part (a), ﬁnd the electric ﬁeld inside the capacitor. c) Using your answer to part (b), along with boundary conditions, determine the charge density
and the total charge Q [C] on the top plate. d) Using your answer from part (c), determine the capacitance of the parallel—plate capacitor. A [1112] [plate area) Problem 4 (25 pts) A conducting sphere of radius a is above the ground, which may be considered to be a perfect
conductor. Assume that the sphere is far enough above the ground so that the charge density on
the sphere may be assumed to be uniform. The total charge on the sphere is Q [C]. Find the voltage drop between the sphere and the ground, VAB (where the A conductor is the sphere and the B conductor is the ground). Do this by integrating the electric ﬁeld between the
two conductors. ' ...
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 Spring '08
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