EEE340Lecture 071 2-12 Helmholtz’s Theorem Helmholtz’s Theorem: A vector field (vector point function) is determined to within an additive constant if.

Slides:

Advertisements

Similar presentations

The divergence of E If the charge fills a volume, with charge per unit volume . R Where d is an element of volume. For a volume charge:

Advertisements

Two questions: (1) How to find the force, F on the electric charge, Q excreted by the field E and/or B? (2) How fields E and/or B can be created?

Chapter 21 Electric Charge and Electric Field. Charles Allison © 2000 Question An  particle with a charge +2e and a mass of 4m p is on a collision course.

PH0101 UNIT 2 LECTURE 2 Biot Savart law Ampere’s circuital law

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.

ELECTROSTATICS-1 ONLINE TEST Q.NO.ANSWER Q.NO.ANSWER Q.NO.ANSWER

Chapter 2 Electrostatics 2.0 New Notations 2.1 The Electrostatic Field 2.2 Divergence and Curl of Electrostatic Field 2.3 Electric Potential 2.4 Work and.

Electrostatic energy of a charge distribution.

EE3321 ELECTROMAGENTIC FIELD THEORY

PHY 042: Electricity and Magnetism Energy of an E field Prof. Hugo Beauchemin 1.

2.5 Conductors Basic Properties of Conductors Induced Charges The Surface Charge on a Conductor; the Force on a Surface Charge

Electrostatics Electrostatics is the branch of electromagnetics dealing with the effects of electric charges at rest. The fundamental law of electrostatics.

Magnetostatics Magnetostatics is the branch of electromagnetics dealing with the effects of electric charges in steady motion (i.e, steady current or DC).

Ch3 Quiz 1 First name ______________________ Last name ___________________ Section number ______ There is an electric field given by where E 0 is a constant.

2-7 Divergence of a Vector Field

EEE340Lecture 161 Solution 3: (to Example 3-23) Apply Where lower case w is the energy density.

EM & Vector calculus #3 Physical Systems, Tuesday 30 Jan 2007, EJZ Vector Calculus 1.3: Integral Calculus Line, surface, volume integrals Fundamental theorems.

CONDUCTOR – FREE SPACE BOUNDARY CONDITIONS

EEL 3472 Electrostatics. 2Electrostatics Electrostatics An electrostatic field is produced by a static (or time-invariant) charge distribution. A field.

Coulomb’s Law Section 36. Electrostatic field Poisson’s equation.

3. Electrostatics Ruzelita Ngadiran.

Jaypee Institute of Information Technology University, Jaypee Institute of Information Technology University,Noida Department of Physics and materials.

MAGNETOSTATIC FIELD (STEADY MAGNETIC)

Operators. 2 The Curl Operator This operator acts on a vector field to produce another vector field. Let be a vector field. Then the expression for the.

MAGNETOSTATIK Ampere’s Law Of Force; Magnetic Flux Density; Lorentz Force; Biot-savart Law; Applications Of Ampere’s Law In Integral Form; Vector Magnetic.

EEL 3472 Magnetostatics 1. If charges are moving with constant velocity, a static magnetic (or magnetostatic) field is produced. Thus, magnetostatic fields.

Electrostatics Properties of Electric Charges.

Electric Charge and Electric Field

Electricity and Magnetism (I) 電磁學 (I). WeekDateContentRemark 19/16-17 Chapter 1 The Electromagnetic Model Chapter 2 Vector Analysis 29/23-24 Unit Test.

ELEC 3105 Lecture 1 Coulomb. 4. Electrostatics Applied EM by Ulaby, Michielssen and Ravaioli.

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

2). Gauss’ Law and Applications Coulomb’s Law: force on charge i due to charge j is F ij is force on i due to presence of j and acts along line of centres.

Dr. Hugh Blanton ENTC Energy & Potential Dr. Blanton - ENTC Energy & Potential 3 The work done, or energy expended, in moving any object.

EMLAB Chapter 4. Potential and energy 1. EMLAB 2 Solving procedure for EM problems Known charge distribution Coulomb’s law Known boundary condition Gauss’

1 Outline and review Review on Coulomb's Law and electric field. Discussion about electric potential (energy). Coulomb’s Law in electrostatics governs.

The Experimental Law of Coulomb

Electric Charge and Electric Field

Chapter 15 Coulomb’s Law Electrical Force Superposition.

Electric potential §8-5 Electric potential Electrostatic field does work for moving charge --E-field possesses energy 1.Work done by electrostatic force.

UNIVERSITI MALAYSIA PERLIS

Chapter 21 Electric Potential.

Wave Dispersion EM radiation Maxwell’s Equations 1.

Lab 1: Electric Fields and Gauss’s Law Only 11 more labs to go!! When we study electrostatics we talk about stationary charges. Electric charges will be.

Physical principles of nanofiber production 3. Theoretical background of electrospinning (1) Electrostatics D. Lukáš

Electric Potential Electric Potential Energy Work done by Coulomb force when q 1 moves from a to b: b a FEFE r dr ds q 2 (-) q 1 (+) rara rbrb.

Electrostatics Chapter Properties of Physical Objects Mass/Inertial: – Gravity mass: inertia in gravitational interaction – Kinetic mass: inertia.

Chapter 25 Electric Potential. Electrical Potential Energy The electrostatic force is a conservative force, thus It is possible to define an electrical.

Chapter 16 Electric Charge and Electric Field. Units of Chapter 16 Static Electricity; Electric Charge and Its Conservation Electric Charge in the Atom.

REVISION ELECTROSTATICS. The magnitude of the electrostatic force exerted by one point charge (Q1) on another point charge (Q2) is directly proportional.

3/21/20161 ELECTRICITY AND MAGNETISM Phy 220 Chapter2: Gauss’s Law.

ELEN 340 Electromagnetics II Lecture 2: Introduction to Electromagnetic Fields; Maxwell’s Equations; Electromagnetic Fields in Materials; Phasor Concepts;

Electric Forces and Fields AP Physics C. Electrostatic Forces (F) (measured in Newtons) q1q1 q2q2 k = 9 x 10 9 N*m 2 /C 2 This is known as “Coulomb’s.

ELEC 3105 Basic EM and Power Engineering

TOPIC : GAUSS;S LAW AND APPLICATION

ELEC 3105 Lecture 1 Coulomb.

Force as gradient of potential energy

Second Derivatives The gradient, the divergence and the curl are the only first derivatives we can make with , by applying twice we can construct.

Permittivity of free space (or electric constant)

Lecture 2 : Electric charges and fields

The Vector Operator Ñ and The Divergence Theorem

The Experimental Law of Coulomb

Electromagnetics II.

Coulomb’s Law and Electric Field Intensity

Lecture 19 Maxwell equations E: electric field intensity

ELECTROSTATICS - III - Electrostatic Potential and Gauss’s Theorem

Maxwell’s equations.

Electrostatics.

Introduction: A review on static electric and magnetic fields

Griffiths Chapter 2 Electrostatics

Lect.03 Time Varying Fields and Maxwell’s Equations

Presentation transcript:

EEE340Lecture Helmholtz’s Theorem Helmholtz’s Theorem: A vector field (vector point function) is determined to within an additive constant if both its divergence and its curl are specified everywhere.

EEE340Lecture 072 Chapter 3: Static Electric (Electrostatic) Fields 3-1 Introduction An electrostatic field is produced by a static charge distribution. It is time-invariant. There are two fundamental laws governing electrostatic fields: a. Coulomb’s Law (1785 by Charles Augustive de Coulomb) b. Gauss’s Law Throughout this chapter we will assume that the electric field is in a vacuum or free space.

EEE340Lecture 073 The force F between two point charges q 1 and q 2 is and it acts along the line joining them. Here, R is the distance between charges; k is the proportionality constant.  o is known as the permittivity of free space (F/m) (in MKS) (in CGS) or In this book we use only MKS (3.1)

EEE340Lecture 074 The following table is related to chapter 1:

EEE340Lecture Fundamental Postulates of Electrostatics in Free Space Electric field intensity (E-field) Two postulations of electrostatics in free-space: Divergence: Curl: The corresponding integral form (3.4) (3.5) (3-2) (3.7) (3.8)

EEE340Lecture 076 or Zero scalar line integral implies conservation of energy, I.e., the work produced is independent of the path, but depends only on the starting and ending points (states). Electrostatic field is conservative. Eq. (3-7) says that electrostatic field has a source Q

EEE340Lecture Coulomb’s Law Coulomb’s Law states for a point charge at the origin: If the charge is not at the origin, bur at, then (3.12) (3.13) (3.15) (3.14)

EEE340Lecture 078 Note that is a new vector pointing from the source to field point The uni-vector For the convenience in (2-32)-(2-37), (3-61)-(3-63), later sections/chapters, and most EM books and Journals, let us use As a result, the uni-vector

EEE340Lecture 079 You’ll get used to the notation. In case you are not sure whether in a equation is a distance vector or a vector in spherical coordinates, you are free to ask.