Homework02Efield

# Homework02Efield - ECE 3030 Electromagnetic Fields and...

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ECE 3030: Electromagnetic Fields and Waves Fall 2009 Homework 2 SOLUTIONS for GRADER: Electric Fields Reminder: These details are for the students to work out! Date: Tuesday 9/15 Problem 3.3 An inﬁnite line of charge. a. For any arbitrary point (x,y,z) there will be symmetric charges along the z axis at (0,0,z+d) and (0,0,z-d) that are equidistant from (x,y,z). The z components of these two charges will be equal in magnitude but oppositely directed, and hence cancel. So, there can be no z component of the electric ﬁeld. b. By symmetry, any single charge has only radial components in spherical coordinates. By the symmetry argument in part (a), there can be no z component of an inﬁnite line charge in cylindrical coordinates. Hence, there can only be a radial component thereby excluding any ˆ φ component. In fact, no individual charge along the z axis can produce a ˆ φ component of the electric ﬁeld, and hence the superposition of all the charges cannot have a ˆ φ component. c.

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## This note was uploaded on 01/16/2010 for the course ECE 3030 at Cornell.

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Homework02Efield - ECE 3030 Electromagnetic Fields and...

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