Dr. Hugh Blanton

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ENTC 3331 RF Fundamentals

• Dr. Hugh Blanton
• ENTC 3331

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Electrodynamics
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ELECTROSTATICS static electric field
MAGNETOSTATICS static magnetic field
stationary motion
static
charge
accelerated?decelerated motion
time-varying electro-magnetic
fields ELECTRODYNAMICS
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• What changes, if charge density and current
  density are time-dependent?
• The source of the electric field is still a
  charge distribution on is time-dependent.
• Since magnetic monopoles do not exist, the
  time-dependence is of no consequence

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• A stationary current has a rotational, static
  magnetic field
• A changing electric field generates a magnetic
  field.
• Maxwells equations must be consistent with the
  magnetostatic case for .

magnetic and electric fields are coupled!
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• A changing magnetic field induces a rotational
  electric field.
• Generator principle

Lenzs law
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Four New Things

• Everything is now time-dependent
• Displacement current density, .
• Changing current creates a magnetic field.
• A changing magnetic field creates an electric
  field.

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Four New Things

1. Electric and magnetic fields are coupled

magnetic
electric
magnetic
electric
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• All four aspects are included in the four general
  Maxwells equations of ELECTRODYNAMICS,which
  contain electrostatic and magnetostatics as
  special case with .

differential form of Maxwells equations
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A Story

• Edith, Debbie, Bill and Henry picnicked out in
  the field.
• With time, Ediths comments revolved about the
  negative aspects of Bills personality,
• but Bill was not to be diverted!
• Henry felt more and more dizzy, taking in a
  steady current of beverages and started to
  appreciate Debbies positive side.

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• However, Debbie was diverted by her charge to
  teach them Maxwells equations of electrodynamics.

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• Is consistent with experimental
  experience?
• Lets consider a loop, defining the area, S,

very small, loop essentially closed
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• Integrate on both sides
• Apply Stokes theorem

path integral along the edge of the area, S.
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• Recall that
• A change in magnetic field produces a potential
  difference (voltage).

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• In this particular case, a current, i, will flow
  from 2 to 1.
• Note that this current opposes the direction of a
  current that would generate .
• Lenzs law.

?
?
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• Since , the magnitude of the current
  is pro-portional to
• the area of the loop, S.
• the magnitude of the change of .

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• These conclusions are identical to what was first
  observed by Faraday and Henry in 1831.
• Since
• and

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• Generalization
• EMF is independent of the area S, and
• EMF is proportional to the number of loops, N.
• Faradays law

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• Induction
• Determine the magnetic flux, , through a
  single loop.
• Determine the EMF for N 10, Bo 2T, a 0.1 m,
  w 2p sec-1.
• Draw the EMF as a function of time.
• What is the polarity of EMF at t 0?
• Draw the current, I, as a function of time, t,
  for R 1kW.

a
N-turns
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independent of x and y
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• Faradays law

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• At t 0, the EMF lt 0 (negative).
• In agreement with Lenzs law.
• Since I V/R ? Io EMF/1kW
• Io -1.184/1kW -1.184 mA

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Induced current, I
EMF
a
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• It was previously stated that a changing current
  creates a magnetic field.
• Take the surface integral of both sides

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• Stokes theorem converts a surface integral into
  a line integral.

current through an arbitrary surface
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• Amperes Circuital Law
• In magnetostatics

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• Show that for a transformer
• where I1, N1, I2, and N2 are the currents and
  number of turns on the input and output,
  respectively.

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• Faradays Law
• Combine the two equations

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• If the transformer is free of loses,
• power in power out
• The ratio of currents is inversely proportional
  to the ratio of turns.

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• Sliding bar
• Determine the EMF between the terminals, if the
  conducting bar slides to the right with equal
  to a constant.
• Use Faradays law in your approach.

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• Faradays law
• What is the magnetic flux, ?

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• Differentiating with respect to t
• From Lenzs law, the induced current flows
  clockwise.