Electromagnetism Ch.7 Methods of Math. Physics, Friday 8 April 2011, EJZ Inductors and inductance Waves and wave equations Electromagnetism & Maxwell’s.

Slides:

Advertisements

Similar presentations

Electromagnetisme. Electric Fields Coulombs law: Electric potential: Gauss theorem:

Advertisements

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

Maxwell’s Equations and Electromagnetic Waves Setting the Stage - The Displacement Current Maxwell had a crucial “leap of insight”... Will there still.

MAXWELL’S EQUATIONS 1. 2 Maxwell’s Equations in differential form.

Dr. Alexandre Kolomenski

Chapter 34 The Laws of Electromagnetism Maxwell’s Equations Displacement Current Electromagnetic Radiation.

Electromagnetism week 9 Physical Systems, Tuesday 6.Mar. 2007, EJZ Waves and wave equations Electromagnetism & Maxwell’s eqns Derive EM wave equation and.

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? Gauss’s.

1 Electromagnetism We want to apply the reaction theory developed in the first few lectures to electronuclear interactions. It is worthwhile reviewing.

Electromagnetic Waves

Chapter 31 Maxwell’s Equations and Electromagnetic Waves.

So far Geometrical Optics – Reflection and refraction from planar and spherical interfaces –Imaging condition in the paraxial approximation –Apertures.

Week 9 Maxwell’s Equations.  Demonstrated that electricity, magnetism, and light are all manifestations of the same phenomenon: the electromagnetic.

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

The Fundamental Theorem of Calculus

Winter wk 9 – Mon.28.Feb.05 Energy Systems, EJZ. Maxwell Equations in vacuum Faraday: Electric fields circulate around changing B fields Ampere: Magnetic.

G L Pollack and D R Stump Electromagnetism Electromagnetic Induction Faraday’s law If a magnetic field changes in time there is an induced electric.

The Electric and Magnetic fields Maxwell’s equations in free space References: Feynman, Lectures on Physics II Davis & Snyder, Vector Analysis.

Chapter 32 Maxwell’s Equations # “Magnetism of Matter” skipped.

Lecture 28 Last lecture: The electromagnetic generator Moving conductor in a time varying magnetic field Displacement current.

Maxwell’s Equations Maxwell Summarizes all of Physics using Fields.

Physics 2102 Marathon review of the course: 15 weeks in ~60 minutes! Physics 2102 Gabriela González.

Maxwell’s Equations Chapter 32, Sections 9, 10, 11 Maxwell’s Equations Electromagnetic Waves Chapter 34, Sections 1,2,3.

Chapter 24 Electromagnetic waves. So far you have learned 1.Coulomb’s Law – Ch There are no Magnetic Monopoles – Ch Faraday’s Law of Induction.

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)

James Clerk Maxwell. Maxwell’s Equations 1.Gauss’ Law for E-fields –Electric charges are the beginning (source) or end (drain) of field lines 2.Gauss’s.

Lecture 22 James Clerk Maxwell ( ) Physics 2102 Jonathan Dowling Maxwell’s equations the dawn of the 20th century revolution in physics.

Maxwell’s Equations If we combine all the laws we know about electromagnetism, then we obtain Maxwell’s equations. These four equations plus a force law.

Maxwell’s equations the dawn of 20 th century physics James Clerk Maxwell ( ) Physics 2102 Gabriela González.

Electromagnetic Waves. James Clerk Maxwell Scottish theoretical physicist Famous for the Maxwell- Boltzman Distribution and Maxwell’s Equations.

“Significance of Electromagnetic Potentials in the Quantum Theory”

Maxwell’s Equations Faraday Induction (Serway)

Lecture 23 Static field Dynamic Field Lecture 23 Faraday’s Law.

Announcements Change of plans for today: Demos on light and selected review for today.

Chapter 32 Maxwell’s Equations Electromagnetic Waves.

Introduction to materials physics #2 Week 2: Electric and magnetic interaction and electromagnetic wave 1.

Announcements Generalized Ampere’s Law Tested I I Consider a parallel plate capacitor that is being charged Try Ampere’s modified Law on two nearly identical.

Waves from the Sun Electromagnetic Wave Electric field – The electric field E at a point is defined as the force per unit charge experienced by a small.

Finish EM Ch.5: Magnetostatics Methods of Math. Physics, Thus. 10 March 2011, E.J. Zita Lorentz Force Ampere’s Law Maxwell’s equations (d/dt=0) Preview:

Maxwell’s Equations in Free Space IntegralDifferential.

1 Discussion about the mid-term 4. A high voltage generator is made of a metal sphere with a radius of 6 cm sits on an insulating post. A wire connects.

Chapter 24 Electromagnetic waves Lecture 11 April 26, 2005.

Maxwell’s Equations are Lorentz Invariant

Maxwell’s Equations BY: HARIYANI MITUL ( )

Lecture 21-1 Maxwell’s Equations (so far) Gauss’s law Gauss’ law for magnetism Faraday’s lawAmpere’s law *

Electromagnetism Faraday & Maxwell. Maxwell James Clerk Faraday ( ) was an Scottish scientist. He was a gifted mathematician and one of the first.

Maxwell’s Equations. Four equations, known as Maxwell’s equations, are regarded as the basis of all electrical and magnetic phenomena. These equations.

Last Time Faraday's Law Inductance and RL (RLC) circuit.

Lesson 12 Maxwells’ Equations

Reading Quiz #17 1) EMF stands for … Electromagnetic force

Electromagnetic Waves

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?

Time-dependent fields

The Laws of Electromagnetism Electromagnetic Radiation

Electromagnetic Radiation

PHY 114 A General Physics II 11 AM-12:15 PM TR Olin 101

Maxwell’s equations.

Natural Optics KM Geise Ampère’s Law.

Faraday’s law Accelerated electron creates time-varying current, time-varying current creates time-varying magnetic field, time-varying magnetic field.

Maxwell’s Equations and Electromagnetic Waves

Maxwell’s Equations (so far…)

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?

Maxwell’s Equations and Electromagnetic Waves

Electromagnetic Waves

Lesson 12 Maxwells’ Equations

Lecture 31: MON 30 MAR Ch.32.1–3: Maxwell’s equations

Electromagnetism in Curved Spacetime

Electromagnetic Waves

Presentation transcript:

Electromagnetism Ch.7 Methods of Math. Physics, Friday 8 April 2011, EJZ Inductors and inductance Waves and wave equations Electromagnetism & Maxwell’s eqns Derive EM wave equation and speed of light

Faraday’s Law

Break time…

Waves

Wave equation 1. Differentiate d D/ d t  d 2 D/ d t 2 2. Differentiate d D/ d x  d 2 D/ d x 2 3. Find the speed from

Causes and effects of E Gauss: E fields diverge from charges Lorentz force: E fields can move charges F = q E

Causes and effects of B Ampere: B fields curl around currents Lorentz force: B fields can bend moving charges F = q v x B = IL x B

Changing fields create new fields! Faraday: Changing magnetic flux induces circulating electric field Guess what a changing E field induces?

Changing E field creates B field! Current piles charge onto capacitor Magnetic field doesn’t stop Changing electric flux →“displacement current” → magnetic circulation

Partial Maxwell’s equations Charge → E fieldCurrent → B field Faraday Changing B → E Ampere Changing E → B

Maxwell eqns → electromagnetic waves Consider waves traveling in the x direction with frequency f =   and wavelength =  /k E(x,t)=E 0 sin (kx-  t) and B(x,t)=B 0 sin (kx-  t) Do these solve Faraday and Ampere’s laws?

Faraday + Ampere

Sub in: E=E 0 sin (kx-  t) and B=B 0 sin (kx-  t)

Speed of Maxwellian waves? Faraday:   = k E 0 Ampere:      E 0 =kB 0 Eliminate B 0 /E 0 and solve for v=  /k    x Tm/A   = 8.85 x C 2 N/m 2

Maxwell equations → Light E(x,t)=E 0 sin (kx-  t) and B(x,t)=B 0 sin (kx-  t) solve Faraday’s and Ampere’s laws. Electromagnetic waves in vacuum have speed c and energy/volume = 1/2  0 E 2 = B 2 /(2  0 )

Full Maxwell equations in integral form

Integral to differential form Gauss’ Law: apply Divergence Thm: and the Definition of charge density: to find the Differential form:

Integral to differential form Ampere’s Law: apply Curl Thm: and the Definition of current density: to find the Differential form:

Integral to differential form Faraday’s Law: apply Curl Thm: to find the Differential form:

Finish integral to differential form…

Maxwell eqns in differential form