16.360 Lecture 19 Flux in Cartesian Coordinates.

Slides:

Advertisements

Similar presentations

Differential Calculus (revisited):

Advertisements

Electric Flux Density, Gauss’s Law, and Divergence

VEKTORANALYS Kursvecka 6 övningar. PROBLEM 1 SOLUTION A dipole is formed by two point sources with charge +c and -c Calculate the flux of the dipole.

VECTOR CALCULUS 1.10 GRADIENT OF A SCALAR 1.11 DIVERGENCE OF A VECTOR

EEE 340Lecture Curl of a vector It is an axial vector whose magnitude is the maximum circulation of per unit area as the area tends to zero and.

EE3321 ELECTROMAGENTIC FIELD THEORY

EE2030: Electromagnetics (I)

Fundamentals of Applied Electromagnetics

EEE 340Lecture Spherical Coordinates. EEE 340Lecture 042 A vector in spherical coordinates The local base vectors from a right –handed system.

Lecture 2eee3401 Chapter 2 Coordinate Systems 1)Cartesian (rectangular) 2)Circular cylindrical 3)Spherical 4)Others (elliptic cylindrical, conical,…) A.

ARCH 481 3d Modeling and Rendering lecture four: texture maps.

2-7 Divergence of a Vector Field

2006 Fall MATH 100 Lecture 81 MATH 100 Lecture 19 Triple Integral in cylindrical & spherical coordinate Class 19 Triple Integral in cylindrical & spherical.

Lecture 15 Today Transformations between coordinate systems 1.Cartesian to cylindrical transformations 2.Cartesian to spherical transformations.

Lecture 16 Today Gradient of a scalar field

1.1 Vector Algebra 1.2 Differential Calculus 1.3 Integral Calculus 1.4 Curvilinear Coordinate 1.5 The Dirac Delta Function 1.6 The Theory of Vector Fields.

Mathematics Review A.1 Vectors A.1.1 Definitions

Lecture 14 Today Orthogonal coordinate systems 1.The Cartesian (rectangular) coordinate system 2.The cylindrical coordinate system 3.The spherical.

Lecture 18 Today Curl of a vector filed 1.Circulation 2.Definition of Curl operator in Cartesian Coordinate 3.Vector identities involving the curl.

(MTH 250) Lecture 26 Calculus. Previous Lecture’s Summary Recalls Introduction to double integrals Iterated integrals Theorem of Fubini Properties of.

Plasma Dynamics Group Aerospace & Energetics Research Program Boundary Conditions for MHD Resistive MHD equations in weakly conservative form (balance.

Lecture 18: Triple Integrals, Cyclindrical Coordinates, and Spherical Coordinates.

X y z Point can be viewed as intersection of surfaces called coordinate surfaces. Coordinate surfaces are selected from 3 different sets.

MA Day 46 – March 19, 2013 Section 9.7: Spherical Coordinates Section 12.8: Triple Integrals in Spherical Coordinates.

Lecture 13 Basic Laws of Vector Algebra Scalars: e.g. 2 gallons, $1,000, 35ºC Vectors: e.g. velocity: 35mph heading south 3N force toward center.

Lecture 19: Triple Integrals with Cyclindrical Coordinates and Spherical Coordinates, Double Integrals for Surface Area, Vector Fields, and Line Integrals.

Vectors and the Geometry of Space

EED 2008: Electromagnetic Theory Özgür TAMER Vectors Divergence and Stokes Theorem.

UNIVERSITI MALAYSIA PERLIS

Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Double Integrals a. (16.2.1),

Chapter 1 - Vector Analysis. Scalars and Vectors Scalar Fields (temperature) Vector Fields (gravitational, magnetic) Vector Algebra.

Copyright © 2011 Pearson, Inc. P.2 Cartesian Coordinate System.

Triple Integral in Cylindrical Coordinates

INTRODUCTION TO CONDUCTION

10.7 Cylindrical and Spherical Coordinates (Curvilinear Coordinates)

Physics 321 Hour 7 Energy Conservation – Potential Energy in One Dimension.

Notes 13 ECE 2317 Applied Electricity and Magnetism Prof. D. Wilton

ENE 325 Electromagnetic Fields and Waves Lecture 3 Gauss’s law and applications, Divergence, and Point Form of Gauss’s law 1.

Applied Electricity and Magnetism

Divergence and Curl of Electrostatic Fields Field of a point charge arrowsfield lines:

Mathematics Review A.1 Vectors A.1.1 Definitions

Angular Velocity: Sect Overview only. For details, see text! Consider a particle moving on arbitrary path in space: –At a given instant, it can.

1 Vector Calculus. Copyright © 2007 Oxford University Press Elements of Electromagnetics Fourth Edition Sadiku2 Figure 3.1 Differential elements in the.

1 Coordinate Systems and Transformation. Copyright © 2007 Oxford University Press Elements of Electromagnetics Fourth Edition Sadiku2 Figure 2.1 Point.

Pat Arnott, ATMS 749, UNR HOW DO WE TALK ABOUT RADIATION IN THE ATMOSPHERE?

CALCULUS III CHAPTER 5: Orthogonal curvilinear coordinates

Shree Swami Atmanand Saraswati Institute of Technology

University of Utah Introduction to Electromagnetics Lecture 14: Vectors and Coordinate Systems Dr. Cynthia Furse University of Utah Department of Electrical.

Identify the coordinate system that best describes symmetry about the z-axis

Test 2 review Test: 7 pm in 203 MPHY

Vector integration Linear integrals Vector area and surface integrals

Applied Electricity and Magnetism

ECE 305 Electromagnetic Theory

Integration in Vector Fields

Use the Divergence Theorem to calculate the surface integral {image} {image} S is the surface of the box bounded by the planes x = 0, x = 4, y = 0, y =

BRANCH : Electronics & communication Engineering SEM : 3rd BATCH : B-5

Chapter 3 Overview.

EEE 161 Applied Electromagnetics

ENE/EIE 325 Electromagnetic Fields and Waves

Use the Divergence Theorem to calculate the surface integral {image} {image} S is the surface of the box bounded by the planes x = 0, x = 2, y = 0, y =

Vector Calculus for Measurements in Thermofluids

EEE 161 Applied Electromagnetics

課程大綱 OUTLINE Double Integrals（二重積分） Triple Integrals（三重積分）

G L Pollack and D R Stump Electromagnetism

Electrostatic Boundary Value Problems Ref: Elements of Electromagnetics by Matthew N. O. Sadiku.

Lecture 17 Today Divergence of a vector filed

Applied EM by Ulaby, Michielssen and Ravaioli

Fundamentals of Applied Electromagnetics

Chapter 16: Double and Triple Integrals

Lecture 16 Gradient in Cartesian Coordinates

Presentation transcript:

16.360 Lecture 19 Flux in Cartesian Coordinates

16.360 Lecture 19 Flux in Cartesian Coordinates

16.360 Lecture 19 Definition of divergence in Cartesian Coordinates

16.360 Lecture 19 Properties of divergence If No net flux on any closed surface. Divergence theorem

16.360 Lecture 19 Divergence in Cylindrical Coordinates z x y

16.360 Lecture 19 Divergence in Cylindrical Coordinates z x y

16.360 Lecture 19 Divergence in Spherical Coordinates

16.360 Lecture 19 Divergence in Spherical Coordinates

16.360 Lecture 19 Divergence in Spherical Coordinates