Time-dependent fields

Slides:



Advertisements
Similar presentations
EMLAB 1 Introduction to EM theory 2. EMLAB 2 Displacement current With the help of displacement current, magnetic fields are also generated around the.
Advertisements

PH0101 UNIT 2 LECTURE 2 Biot Savart law Ampere’s circuital law
Electromagnetism week 9 Physical Systems, Tuesday 6.Mar. 2007, EJZ Waves and wave equations Electromagnetism & Maxwell’s eqns Derive EM wave equation and.
1 Electromagnetism We want to apply the reaction theory developed in the first few lectures to electronuclear interactions. It is worthwhile reviewing.
Prof. David R. Jackson ECE Dept. Fall 2014 Notes 18 ECE 2317 Applied Electricity and Magnetism 1.
8/5/08Lecture 2 Part 21 Maxwell’s Equations of the Electromagnetic Field Theory Gauss’s Law – charge makes an electric field The magnetic field is solenoidal.
Electromagnetism Giancoli Ch Physics of Astronomy, winter week 7
Electromagnetism and Energy
Phy 213: General Physics III Chapter 30: Induction & Inductance Lecture Notes.
Magnetism Lenz’s Law 1 Examples Using Lenz’s Law.
Chapter 32 Maxwell’s Equations # “Magnetism of Matter” skipped.
TOC 1 Physics 212 Lenz's Law Lenz’s Law Examples Using Lenz’s Law.
Faraday’s Law of Induction II Physics 2415 Lecture 20 Michael Fowler, UVa.
Maxwell’s Equations Maxwell Summarizes all of Physics using Fields.
Chapter 29.
Winter wk 8 – Thus.24.Feb.05 Review Ch.30 – Faraday and Lenz laws Ch.32: Maxwell Equations! Gauss: q  E Ampere: I  B Faraday: dB/dt  E (applications)
Fall 2008Physics 231Lecture 9-1 Electromagnetic Induction.
Board Work What are the directions of the forces on the opposite charges moving with velocity v through magnetic field B? B v +−
Electromagnetism Ch.7 Methods of Math. Physics, Friday 8 April 2011, EJZ Inductors and inductance Waves and wave equations Electromagnetism & Maxwell’s.
Faraday’s Law and Inductance. Faraday’s Law A moving magnet can exert a force on a stationary charge. Faraday’s Law of Induction Induced emf is directly.
Electromagnetic Induction and Faraday’s Law
Lecture 23 Static field Dynamic Field Lecture 23 Faraday’s Law.
Introduction: So far we have These equations are OK for static fields, i.e. those fields independent of time. When fields vary as a function of time the.
Dr. Hugh Blanton ENTC Electrodynamics Dr. Blanton - ENTC Electrodynamics 3 charge ELECTROSTATICS static electric field MAGNETOSTATICS static.
SILVER OAK COLLEGE OF ENGG&TECH NAME:-KURALKAR PRATIK S. EN.NO: SUBJECT:- EEM GUIDED BY:- Ms. REENA PANCHAL THE STEADY STATE OF MAGNETIC.
Faraday’s Law M&I Chapter 23. Maxwell’s Equations (so far…) *Not complete.
Applied Electricity and Magnetism
Lesson 12 Maxwells’ Equations
ELEC 3105 Basic EM and Power Engineering
(i) Divergence Divergence, Curl and Gradient Operations
Electromagnetic Theory
Reading Quiz #17 1) EMF stands for … Electromagnetic force
ELEC 3105 Basic EM and Power Engineering
Induction and Inductance
Flux Faraday’s law Lenz’s law Examples Generator
Time-dependent fields
Lecture 3-5 Faraday’ s Law (pg. 24 – 35)
Ampere’s Law in Magnetostatics
Magnetic Induction Review of Chapter 22.
Electromagnetism.
TIME VARYING FIELDS AND MAXWELL’S EQUATION
Electromagnetics II.
Christopher Crawford PHY
General Review Electrostatics Magnetostatics Electrodynamics
ENE/EIE 325 Electromagnetic Fields and Waves
Electromagnetic Induction
Electric Currents from Magnetism
static magnetic fields
ECE 305 Electromagnetic Theory
§5.2: Formulations of Magnetostatics
C H A P T E R   22 Electromagnetic Induction.
Faraday’s Law of Induction
MAXWELL’S EQUATIONS (TIME VARYING FIELDS) ONLINE TEST Q.NO. ANSWER 1 2
Electromagnetic Induction and Faraday’s Law.
Transforming energy with magnetism
Today’s agenda: Induced emf. Faraday’s Law. Lenz’s Law. Generators.
The “spooky” connection between E and B!
Induction An induced current is produced by a changing magnetic field There is an induced emf associated with the induced current A current can be produced.
Maxwell’s Equations (so far…)
Maxwell’s Equations and Electromagnetic Waves
Applied Electricity and Magnetism
Lect.03 Time Varying Fields and Maxwell’s Equations
E&M I Griffiths Chapter 7.
Maxwell’s equations continued
Lesson 12 Maxwells’ Equations
6. Maxwell’s Equations In Time-Varying Fields
Chapter 13: Electromagnetic Induction
Chapter 23 Faraday’s Law.
Electromagnetic Induction
Chapter 30 Induction and Inductance
Presentation transcript:

Time-dependent fields

Static fields decoupled .D = r  x E = 0 .B = 0  x H = J D = eE B = mH Electric fields have zero curl Caused by Static Charges Magnetic fields have zero divergence Caused by Static Currents Asymmetry in E and B field properties

Maxwell’s equations for Electromagnetism Dynamic fields coupled .D = r  x E = - ∂B/∂t .B = 0  x H = J + ∂D/∂t D = eE B = mH Maxwell’s equations for Electromagnetism Field equations more symmetric (fields resemble each other)

Deriving Circuit Theory ! .D = r  x E = - ∂B/∂t .B = 0  x H = J + ∂D/∂t Kirchhoff’s Law V=LdI/dt

Gauss’ Law for electrostatics (Flux prop. to enclosed charge) The 4 Maxwell equations .D = r Gauss’ Law for electrostatics (Flux prop. to enclosed charge)

Gauss’ Law for magnetostatics (There is no magnetic charge) The 4 Maxwell equations .B = 0 Gauss’ Law for magnetostatics (There is no magnetic charge)

Faraday’s law of induction (Changing magnetic flux The 4 Maxwell equations  x E = - ∂B/∂t Faraday’s law of induction (Changing magnetic flux creates voltage)

(Changing electric flux creates magnetic field) The 4 Maxwell equations  x H = J + ∂D/∂t Ampere’s law (Changing electric flux creates magnetic field)

The 4 Maxwell’s equations .D = r  x E = - ∂B/∂t .B = 0  x H = J + ∂D/∂t Not just E,B but D,H and also inputs r, J = sE B = mH D = eE Constitutive equations (Maxwell’s eqns don’t give e, m, s, r Need quantum mechanics/solid state/statistical physics for this!) We treat them as external inputs

The 4 Maxwell’s equations .D = r  x E = - ∂B/∂t .B = 0  x H = J + ∂D/∂t Most important consequence: Electromagnetic Waves (Chapter 7) Here we’ll learn the two new equations (Faraday’s Law and Ampere’s Law)

Changing magnetic flux Faraday’s Law  x E = - ∂B/∂t Since  x E ≠ 0 , can’t have E = -U Changing magnetic flux creates voltage

Faraday’s Law  x E .dA = - ∂B.dA/∂t Integrate both sides

Faraday’s Law E .dl = - ∂FB/∂t Stokes Theorem

Changing magnetic flux Faraday’s Law E .dl = - ∂FB/∂t Changing magnetic flux creates voltage

Faraday’s Law Vemf = - ∂FB/∂t Definition: FB/I = L Vemf = - LdI/dt (Solenoid) Vemf = - LdI/dt

Changing magnetic flux Faraday’s Law  x E = - ∂B/∂t Changing magnetic flux creates voltage (and thus current)

How to change magnetic flux? http://hyperphysics.phy-astr.gsu.edu/hbase/electric/farlaw.html

Lenz’s Law Induced current opposes any change in flux (Nature Prefers Inertia) opposing induced flux Increasing flux

Lenz’s Law Induced current opposes any change in flux (Nature Prefers Inertia) opposing induced flux Decreasing flux

Force argument for Lenz’s Law Lorentz Force -e(v x B) downwards on el Wire motion Current flows upward in slider Current flows upward in slider Current flows upward in slider Decreasing B Flux towards you  induced B also towards you Increasing B Flux towards you  induced B away from you

No matter which way you see it, the current in the slider flows the same way !!

http://micro.magnet.fsu.edu/electromag/java/faraday/ /faraday2 /lenzlaw/ /transformer /detector