ECE309-2008-hw1

# ECE309-2008-hw1 - ECE 309 Electromagnetic Fields University...

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ECE 309 — Electromagnetic Fields University of Virginia Fall 2008 Homework # 1 — Review of Vector Analysis and Electric Fields Due: Wednesday, September 3 Note: The first six problems of this homework are meant as a review of vector analysis and multivariable calculus. If you are “rusty” on this subject, you should review chapter 2 of Cheng or refer to the supplemental text, Div, Grad, Curl and All That by Schey. 1. An unknown vector can be determined if both its scalar product and its vector product with a known vector are given. Assuming that ~ A is a known vector, determine the unknown vector ~ X if both p and ~ B are given, where p = ~ A · ~ X, and ~ B = ~ A × ~ X Suggestion: Use the second vector identity (for ~ A × ( ~ B × ~ C ) ) on the back inside cover of Cheng. 2. Let ~ r be the vector from a fixed origin ( x 0 , y 0 , z 0 ) to the point ( x, y, z ), and let r be its length. Show that (a) ~ ( r 2 ) = 2 ~ r (b) ~ ( 1 r ) = - ˆ r r 2 Note that ˆ r is the unit vector pointing in the direction of ~ r .

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