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Unformatted text preview: ECE 329 Homework 5 Due: Thursday, Feb 24, 2009, 5PM 1. Verifying vector calculus identities , ( ) = 0 and ( A ) = 0 : a) The gradient of a scalar field is defined as x x + y y + z z . Assuming that the order of differentiation can be switched, show that ( ) = 0 . Consequently, any curl-free vector field can be expressed as the gradient of some scalar field important in the definition of electrostatic potential studied in Chapter 6. b) Given any differentiable vector field A = xA x + yA y + zA z , show that ( A ) = 0 by first expanding A in terms of partial derivatives (e.g., A x x , A y x etc.) of the components of A . Consequently, any divergence-free vector field can be expressed as the curl of some other vector field important in the definition of vector potential studied in Chapter 6....
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This note was uploaded on 09/16/2011 for the course ECE 329 taught by Professor Kim during the Fall '08 term at University of Illinois, Urbana Champaign.
- Fall '08