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Unformatted text preview: ECE 3030: Electromagnetic Fields and Waves Fall 2008 Your Name: PRELIM 1 September 30 Instructions: Do all problems. Show your work, giving appropriate units with numerical answers. Correct solutions to bonus questions offset lost points. No points will be deducted for wrong answers to bonus questions. Your CIT ID: (e.g., wes5). Exam Number: Academic integrity is expected of all students of Cornell University at all times, whether in the presence or absence of the faculty. Understanding this, I declare I shall not give, use or receive unauthorized aid in this work, nor will I discuss this exam in the presence of anyone who has not yet taken the exam (just in case there is a makeup). Your Signature: 1 CORNELL UNIVERSITY c WES SWARTZ (08/9/20w) EX–1 ECE 3030: Electromagnetic Fields and Waves Fall 2008 Your Name: PRELIM 1 September 30 Reminder: Do your own work! Problem Score Regrade Bonus 1 /30 /30 None 2 /30 /30 10 3 /15 /15 None 4 /25 /25 None Total /100 /100 Table 1: Solutions of Laplace’s Equation Potential Configuration Cartesian Cylindrical Spherical Constant potential Φ( ~ r) = A Φ( ~ r) = A Φ( ~ r) = A Uniform x-directed E-field Φ( ~ r) =- Ax Φ( ~ r) =- Ar cos φ- Uniform y-directed E-field Φ( ~ r) =- Ay Φ( ~ r) =- Ar sin φ- Uniform z-directed E-field Φ( ~ r) =- Az- Φ( ~ r) =- Ar cos θ Charge dipole x-directed- Φ( ~ r) = A cos φ r- Charge dipole y-directed- Φ( ~ r) = A sin φ r- Charge dipole z-directed-- Φ( ~ r) = A cos θ r 2 Cylindrically symmetric- Φ(...
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- Electromagnet, Electric charge, Cornell University, Fundamental physics concepts, Coordinate system, Polar coordinate system, Coordinate systems