329fall08hw4 - ECE 329 Homework 4 Due: Sept 23, 2008, 5PM...

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Unformatted text preview: ECE 329 Homework 4 Due: Sept 23, 2008, 5PM 1. Curl and divergence exercises: a) On a 25-point 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 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 ....
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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.

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329fall08hw4 - ECE 329 Homework 4 Due: Sept 23, 2008, 5PM...

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