Optical Equations 1 Maxwells equations A historical review for better understanding continued

1
Optical Equations 1 Maxwells equations A
historical review for better understanding
(continued)
2
Acceleration (AC Current)

• If the charge stream is accelerated the
  magnetic flux (swirl) becomes dynamic what makes
  it more important is that an electric field swirl
  will be generated by the dynamic magnetic flux,
  which leads to Faradays law.
• Why would a dynamic magnetic flux generate the
  electric field swirl?
• Implication - the system is attempting to stay
  still once a change is found in magnetic flux,
  an electric field is excited in such a way that
  it tries to cancel out the magnetic flux change
  by generating a new magnetic flux against the
  original one i.e.,

3
Extended Summary beyond Static Fields- A Wrap up
of Experimental Observations

• Stay still charge distribution generates
  divergence driven, swirl free electric field
  (which can be sensed by any charged object, hence
  we have the name electric).
• Charge in static motion generates not only the
  above mentioned electric field, but also swirl
  driven, divergence free magnetic field (which
  differs from the electric field as it can only be
  sensed by the charged moving object, hence we
  have the name magnetic).
• - So far, the fields are static (with spatial
  dependence only, no temporal dependence) and
  non-coupled (between the electric and magnetic
  ones).

4
Extended Summary beyond Static Fields- A Wrap up
of Experimental Observations

• Accelerated charge generates dynamic
  (time-varying) magnetic field, which induces the
  swirl to the electric field.
• Consequently, the electric field will be driven
  by both divergence and curl sources the former
  comes from the stay still or constantly moving
  charges, whereas the latter is induced by the
  time-varying of the magnetic field which comes
  from the charge acceleration. Also, the electric
  and magnetic fields becomes coupled, but still in
  one way (from magnetic to electric only).

5
Extended Summary beyond Static Fields- A Wrap up
of Experimental Observations

• We can express these conclusions mathematically
  to obtain the governing equations for any
  electromagnetic effect in vacuum

Faradays law
Amperes law
Gauss law (E)
Gauss law (M)
6
Maxwells Equations- Power of Logical Thinking
and Math

• Maxwell found inconsistency in the 2nd equation
  if the charge accelerates
• He then mended the 2nd equation by

with Gauss law applied to the last term on the
RHS
7
Maxwells Equations- Power of Logical Thinking
and Math

• Implication of the added term time-varying
  electric field, similar to the current, also
  generates magnetic field.
• Hence we name the time change rate of the
  electric field the displacement current (more
  accurately, the time-derivative of the
  displacement vector), and the conventional
  current the conduction current.

8
Maxwells Equations- Power of Logical Thinking
and Math

• As a consequence
• 1. charge acceleration generates dynamic magnetic
  field in its neighborhood (Amperes law)
• 2. dynamic magnetic field induces dynamic
  electric field (Faradays law)
• 3. dynamic electric field in its neighborhood
  generates dynamic magnetic field (Maxwells
  displacement current equivalence Amperes law),
  such sequence repeats endlessly in a area which
  is not necessarily limited to the location of the
  source where the charge accelerates
• This process describes the electromagnetic wave
  generation and propagation.

9
Maxwells Equations- The Ultimate Form in Vacuum


10
Maxwells Equations- The Ultimate Form in Media


There are 16 scalar variables, but 17
equations. One equation is redundant. Normally,
we dont need the last one (the magneto Gauss
law ), as it is hidden in the 1st equation. The
carrier continuity equation is hidden in the 2nd
equation.
11
Home Work 1 (continued)

• Design a simple electromagnetic wave generation
  and radiation system (antenna system).
• If you move along with the propagation of the
  electromagnetic wave, what do you expect to
  observe? Use equations to describe the
  electromagnetic effect.