Classical Electrodynamics Jingbo Zhang Harbin Institute of Technology

Chapter 1 Classical Electrodynamics Section 3 Electrodynamics

Jingbo Zhang Section 3 EletrodynamicsChapter 1 Aug 26, 2004 Classical Electrodynamics Review  In last two sections, we obtained two set vector partial differential equations for electrostatics and magnetostatics, respectively. They seam to be the independent theories.

Jingbo Zhang Section 3 EletrodynamicsChapter 1 Aug 26, 2004 Classical Electrodynamics 1 Electric Charge Conservation Law  Electric charge is conserved and electric current is a transport of electric charge.  The electric charge conservation law can be formulated in the equation of continuity, It means that the time rate of change of electric charge density is balanced by a divergence in the electric current density.

Jingbo Zhang Section 3 EletrodynamicsChapter 1 Aug 26, 2004 Classical Electrodynamics 2 Maxwell’s Displacement Current  In magnetostatics, we got the source equation for magnetic field,  In the case, we used the condition of stationary currents,  However, in general case of non-stationary sources and fields, we must follow the equation of continuity,

Jingbo Zhang Section 3 EletrodynamicsChapter 1 Aug 26, 2004 Classical Electrodynamics  Maxwell’s source equation for time-varying field The second term on the right side, is so-called Maxwell’s displacement current. The real current j(t,x) represent the density of electric current, including conduction current, polarisation current and magnetisation current. The displacement current behaves like a current in vacuum. It predicts the existence of electromagnetic radiation.

Jingbo Zhang Section 3 EletrodynamicsChapter 1 Aug 26, 2004 Classical Electrodynamics  Symmetric Discussion III First time broken ElectrostaticsMagnetostatics

Jingbo Zhang Section 3 EletrodynamicsChapter 1 Aug 26, 2004 Classical Electrodynamics 3 Faraday’s Law of Induction  Ohm’s Law and Electromovtive Force Under certain physical conditions, and for certain materials, there is a linear relationship between the current density and electric Field, where,is the electric conductivity. The electromotive force is defined by Thus, we have

Jingbo Zhang Section 3 EletrodynamicsChapter 1 Aug 26, 2004 Classical Electrodynamics  For static electric field is conservative field, the closed line integral for it is vanished.  Faraday’s Law the non-conservation EMF field is produced in a closed circuit if the magnetic flux through this circuit varies with time.

Jingbo Zhang Section 3 EletrodynamicsChapter 1 Aug 26, 2004 Classical Electrodynamics

Jingbo Zhang Section 3 EletrodynamicsChapter 1 Aug 26, 2004 Classical Electrodynamics 4 Maxwell’s Equations  Microscopic Maxwell’s equations relate ρ and j to the fields. with the initial and boundary conditions, the four vector partial differential Equations completely determine the electric and magnetic fields. In the equations, ρ is the total electric charge density, free and induced charges. And j is the total electric currents, i.e. conduction currents and atomistic currents.

Jingbo Zhang Section 3 EletrodynamicsChapter 1 Aug 26, 2004 Classical Electrodynamics  Macroscopic The microscopic field equtions provide a correct classical picture for fields and source distributions. It is useful to introduce new derived fields for the macroscopic, in which the material properties are already included.