Maxwell’s Equations in Terms of Potentials

Slides:

Advertisements

Similar presentations

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?

Advertisements

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.

MAGNETOSTATICS ONLINE TEST Q.NO.ANSWER Q.NO.ANSWER Q.NO.ANSWER

Chapter 31 Maxwell’s Equations and Electromagnetic Waves.

Lecture 19 Maxwell equations E: electric field intensity

EEE340Lecture : Potential functions Vector potential was introduced because Thus the Faraday’s law becomes i.e., Or (7.55) (7.56)

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.

Lecture 21 Today Magnetic forces and Torques The Biot-Savart Law Magnetic force between two parallel conductors Maxwell’s magnetic potential.

Lecture 19 Exam II Average: Lecture 19 Today Brief review of Electrostatics (I) 1.Maxwell equations 2.Charge and current distributions.

Motors Lecture Hans Christian Oersted (1777 – 1851) Ref:

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.

02/17/2014PHY 712 Spring Lecture 141 PHY 712 Electrodynamics 10-10:50 AM MWF Olin 107 Plan for Lecture 14: Start reading Chapter 6 1.Maxwell’s.

02/16/2015PHY 712 Spring Lecture 141 PHY 712 Electrodynamics 9-9:50 AM MWF Olin 103 Plan for Lecture 14: Start reading Chapter 6 1.Maxwell’s full.

02/19/2014PHY 712 Spring Lecture 151 PHY 712 Electrodynamics 10-10:50 AM MWF Olin 107 Plan for Lecture 15: Finish reading Chapter 6 1.Some details.

02/18/2015PHY 712 Spring Lecture 151 PHY 712 Electrodynamics 9-9:50 AM MWF Olin 103 Plan for Lecture 15: Finish reading Chapter 6 1.Some details.

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.

5.3 Divergence and Curl of B Ampere’s law differential form.

BH Astrophys Ch6.6. The Maxwell equations – how charges produce fields Total of 8 equations, but only 6 independent variables (3 components each for E,B)

“Significance of Electromagnetic Potentials in the Quantum Theory”

Infinitesimal Dipole. Outline Maxwell’s equations – Wave equations for A and for  Power: Poynting Vector Dipole antenna.

Electromagnetism INEL 4152 CH 9 Sandra Cruz-Pol, Ph. D. ECE UPRM Mayag ü ez, PR.

Chapter 10 Potentials and Fields

Classical Electrodynamics Jingbo Zhang Harbin Institute of Technology.

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.

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.

Classical Electrodynamics Jingbo Zhang Harbin Institute of Technology.

Maxwell’s Equations are Lorentz Invariant

The wave equation LL2 Section 46. In vacuum,  = 0 and j = 0. These have non-trivial solutions. Thus, electromagnetic fields can exist without charges.

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

EEE 431 Computational Methods in Electrodynamics Lecture 2 By Rasime Uyguroglu.

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

The retarded potentials LL2 Section 62. Potentials for arbitrarily moving charges 2 nd pair of Maxwell’s equations (30.2) in 4-D.

10. Potentials and Fields Introduction of potential V substantially simplifies finding solutions of problems in Electrostatics. Does such a simplification.

Energy in magnetic fields

ELEC 401 MICROWAVE ELECTRONICS Lecture 1

Department of Electronics

Electromagnetic Waves

Comparison of Magnetostatics and Electrostatics

§7.2 Maxwell Equations the wave equation

The Laws of Electromagnetism Electromagnetic Radiation

The Basis for Electromagnetic and Mechanical Applications

Electromagnetics II.

Christopher Crawford PHY

ELEC 401 MICROWAVE ELECTRONICS Lecture 1

Ampere’s Law (partially correct)

Lecture 19 Maxwell equations E: electric field intensity

Maxwell’s Equations and Electromagnetic Waves

Christopher Crawford PHY

(with Maxwell correction)

Maxwell’s equations.

Chapter IV Gauge Field Lecture 1 Books Recommended:

The “spooky” connection between E and B!

ENE 325 Electromagnetic Fields and Waves

Maxwell’s Equations and Electromagnetic Waves

Maxwell’s Equations (so far…)

AP Physics L17_Maxwell The basis of E&M

Maxwell’s Equations and Electromagnetic Waves

Maxwell’s equations continued

Lesson 12 Maxwells’ Equations

6. Maxwell’s Equations In Time-Varying Fields

Chapter 13: Electromagnetic Induction

Finish reading Chapter 6

Chapter 23 Faraday’s Law.

Electromagnetism in Curved Spacetime

Finish reading Chapter 6

§7.2 Maxwell Equations the wave equation

equation of continuity

Presentation transcript:

Maxwell’s Equations in Terms of Potentials Gauss’s law no magnetic monopoles! Faraday’s law Ampere’s law with Maxwell’s correction We can surely write: Satisfy the homogenous Maxwell’s equations

At this point, we reduced the system of unknowns from 6 to 4 At this point, we reduced the system of unknowns from 6 to 4. Can we simplify even more? and we require that both sets of potentials yield the same fields… can be absorbed in l This Gauge transformation does not affect physical fields! We can choose l as we wish. The actual gauge depends on the problem at hand.

The Coulomb Gauge The Lorentz Gauge The scalar potential is given by the instantaneous charge density! A wave equation with complicated source term The Lorentz Gauge

The Temporal Gauge