Classical Electrodynamics

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Classical Electrodynamics

• Jingbo Zhang
• Harbin Institute of Technology

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Chapter 1Classical Electrodynamics

• Section 3
• Electrodynamics

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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.
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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.
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2 Maxwells 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,

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• Maxwells source equation for time-varying field

The second term on the right side, is so-called
Maxwells 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.
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• Symmetric Discussion III
• First time broken

Electrostatics
Magnetostatics
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3 Faradays Law of Induction

• Ohms 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
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• For static electric field is conservative field,
• the closed line integral for it is vanished.

• Faradays Law
• the non-conservation EMF field is produced in
  a closed circuit if the magnetic flux through
  this circuit varies with time.

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4 Maxwells Equations
Maxwells equations relate ? and j to the fields.
with the initial and boundary conditions, the
four vector partial differential Equations
completely determine the electric and magnetic
fields.

• Microscopic

In the equations, ? is the total electric charge
density, free and induced charges. And j is the
total electric currents, i.e. conduction currents
and atomistic currents.
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• 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.