Electromagnetic waves

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  • 1. Electromagnetic Waves
    Presented by :
    Anup Kr Bordoloi
    ECE Department ,Tezpur University
    11/11/2008
  • 2. Electromagnetic Waves in homogeneous medium:
    The following field equation must be satisfied for solution of electromagnetic problem
    there are three constitutional relation which determines
    characteristic of the medium in which the fields exist.
    Solution for free space condition:
    in particular case of e.m. phenomena in free space or in a perfect dielectric containing no
    charge an no conduction current
    Differentiating 1st
  • 3. Also since and are independent of time
    Now the 1st equation becomes on differentiating it
    Taking curl of 2nd equation
    (But )
    this is the law that E must obey
    lly for H
    these are wave equation so E and H satisfy wave equation.
  • 4. For charge free region
    for uniform plane wave
    There is no component in X direction be either zero, constant in
    time or increasing uniformly with time .similar analysis holds for H
    Uniform plane electromagnetic waves are transverse and have components in E and H only in the direction perpendicular to direction of propagation
    Relation between E and H in a uniform plane wave:
    For a plane uniform wave travelling in x direction
    a)E and H are both independent of y and z
    b)E and H have no x component
    From Maxwell’s 1st equation
    From Maxwell’s 2nd equation
  • 5. Comparing y and z terms from the above equations
    on solving finally we get
    lly
    Since
    The ratio has the dimension of impedance or ohms , called characteristic impedance or intrinsic impedance
    of the (non conducting) medium. For space
  • 6. The relativeorientation of E and H may be determined by taking their dot product and using above relation
    In a uniform plane wave ,E and H are at right angles to each other.
    electric field vector crossed into the magnetic field vector gives the direction in which the wave travels.
  • 7. The wave equation for conducting medium:
    From Maxwell’s equation if the medium has conductivity
    Taking curl of 2nd eq. ( )
    For any homogeneous medium in which is constant
    But there is no net charge within a conductor
    Hence wave equation for E.
    lly , wave equation for H.
    Sinusoidal time variations:
    where is the frequency of variation.
    time factor may be suppressed through the use phasor
    notation.
    Time varying field may be expressed in terms of corresponding phasor quan
    -tity
  • 8. as
    Phasor is defined by
    real
    Phase is determined by of the
    complex number ,time varying
    field quantity may be expressed as
    Maxwell’s equation in phasor form:
    for sinusoidal steady state we may substitute the phasor
    relation as
    Imaginary axis
    Real axis
  • 9. which is the differential equation in phasor form.
    Observation point:
    Time varying quantity is replaced by phasor quantity
    Time derivative is replaced with a factor
    Maxwell’s equation becomes
    The above equations contain the equation of continuity
    The constitutive relation retain their forms
    For sinusoidal time variations the wave equation for electric field in lossless medium
  • 10. becomes
    In a conducting medium the wave equation becomes
    Wave propagation in lossless medium:
    For uniform plane wave there is no variation w.r.t. Y or Z.
    For Ey component solution may be written as
    The time varying field is
    real
  • 11. When c1 and c2 are real,
    if c1 = c2 the two travelling waves combine to form standing wave which does not
    progress.
    Wave velocity: if velocity is given by
    or
    phase –shift constant.
    From fig.
    Again
  • 12. Thank you