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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 curlfree 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 divergencefree 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 11/16/2009 for the course ECE 329 taught by Professor Franke during the Spring '08 term at University of Illinois at Urbana–Champaign.
 Spring '08
 FRANKE
 Electromagnet

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