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Unformatted text preview: ECE 329 Homework 4 Due: Sept 23, 2008, 5PM 1. Curl and divergence exercises: a) On a 25point graph consisting of x and y coordinates having the integer values { 2 , 1 , , 1 , 2 } sketch the vector field V = x x + y y and find V (curl of V ) and V (divergence of V ). b) Repeat (a) for V = y x + x y . c) Based on above results choose the correct answer in the statements below: i. V = 0 implies the field strength varies ( along or across ) the direction of the field. ii. V = 0 implies the field strength varies ( along or across ) the direction of the field. 2. Verifying vector calculus identities , ( f ) = 0 and ( A ) = 0 : a) The gradient of a scalar field f is defined as f f x x + f y y + f z z . Assuming that the order of differentiation can be switched, show that ( f ) = 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 ....
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This note was uploaded on 04/14/2009 for the course ECE 329 taught by Professor Franke during the Spring '08 term at University of Illinois at Urbana–Champaign.
 Spring '08
 FRANKE

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