# lec5 - d V V V l ECE2112_5 4 ECE 2112 Lecture 5 •...

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Lecture Notes for C-term 2009 Lecture 5 Prof. R. Ludwig Department of Electrical and Computer Engineering Worcester Polytechnic Institute Worcester, MA ECE 2112 Electromagnetic Theory Copyright, 2000 © R. Ludwig

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ECE2112_5 2 Lecture 5 Objectives What is the gradient of a scalar field? How is the divergence applied to a vector field? What is the curl of a vector field?
ECE2112_5 3 ECE 2112 - Lecture 5 Gradient operation Gradient denotes direction of maximum change in scalar field dl dz dy dx d l z y x a u u u l ˆ z y x z y x u u u dl V d V dV l u l ˆ Increase in voltage If gradient is known: 2 1 1 2 P P d V V V

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Unformatted text preview: d V V V l ECE2112_5 4 ECE 2112 Lecture 5 • Divergence V S dV d E S E Flux through surface = charge enclosed ) , , ( z y x z E y E x E z y x E Charge density (C/m 3 ) Point charge ECE2112_5 5 ECE 2112- Lecture 5 • Curl of a vector field C S d S curl ] ˆ [ 1 lim l B n B B Curl specifies the amount of rotational strength a field possesses z y x z y x B B B z y x u u u B Explicit evaluation:...
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