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Workshop02Efield

# Workshop02Efield - Hint Apply the Divergence Theorem and...

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ECE 3030: Electromagnetic Fields and Waves Fall 2009 WORKSHOP 2 INSTRUCTOR NOTES: Electric Fields from Charges Reminder: You can verify student work with these solutions. Date: Thursday 9/10 1. At start of session give the hints indicated for each problem. 2. Problem 3.13 Hint: Use superposition – adding solutions. The stu- dents have seen solutions for the potential and electric field of charged spheres. This problem superimposes two of those solutions, one for a large positively charged sphere and one for a small negatively charged sphere. Note the solutions are only for points on the x axis! a. The big sphere does not contribute, so ~ E = 4 3 πb 3 ( - ρ ) 4 πε 0 c 2 ˆx b. ~ E = 4 3 πa 3 ρ 4 πε 0 d 2 ˆx + 4 3 πb 3 ( - ρ ) 4 πε 0 ( d + c ) 2 ˆx = ρ 3 ε 0 a 3 d 2 - b 3 ( d + c ) 2 ) ˆx 3. Problem 3.16
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Unformatted text preview: Hint: Apply the Divergence Theorem and the integral form of Gauss’ Law. We could compute the electric ﬁeld and evaluate surface integrals over the 6 sides of the cube. (A tedious task in this case.) But we know the requested integral is equal to charge inclosed (Gauss’ Law), so we just evaluate the volume integral: L Z L Z L Z ρ xyz L 3 d x d y d z = ρ L 3 8 ε 4. There should be lots of time to start the homework problems. Encourage the students to get each of the three problems at least set up. Note 3.19 requires MatLab plots. 5. Homework 2: Problems 3.3, 3.4, 3.19 CORNELL UNIVERSITY c ± WES SWARTZ (09/8/10) 2–1...
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