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Dr. Hugh Blanton

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The source of the electric field is still a charge distribution on is time-dependent. ... Ampere's Circuital Law. In magnetostatics: S. C. Show that for a transformer ... – PowerPoint PPT presentation

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Title: Dr. Hugh Blanton


1
ENTC 3331 RF Fundamentals
  • Dr. Hugh Blanton
  • ENTC 3331

2
Electrodynamics
3
ELECTROSTATICS static electric field
MAGNETOSTATICS static magnetic field
stationary motion
static
charge
accelerated?decelerated motion
time-varying electro-magnetic
fields ELECTRODYNAMICS
4
  • 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

5
  • 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!
6
  • A changing magnetic field induces a rotational
    electric field.
  • Generator principle

Lenzs law
7
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.

8
Four New Things
  1. Electric and magnetic fields are coupled

magnetic
electric
magnetic
electric
9
  • 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
10
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.

11
  • However, Debbie was diverted by her charge to
    teach them Maxwells equations of electrodynamics.

12
  • Is consistent with experimental
    experience?
  • Lets consider a loop, defining the area, S,

very small, loop essentially closed
13
  • Integrate on both sides
  • Apply Stokes theorem

path integral along the edge of the area, S.
14
  • Recall that
  • A change in magnetic field produces a potential
    difference (voltage).

15
  • 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.

?
?
16
  • Since , the magnitude of the current
    is pro-portional to
  • the area of the loop, S.
  • the magnitude of the change of .

17
  • These conclusions are identical to what was first
    observed by Faraday and Henry in 1831.
  • Since
  • and

18
  • Generalization
  • EMF is independent of the area S, and
  • EMF is proportional to the number of loops, N.
  • Faradays law

19
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20
  • 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
21
independent of x and y
22
  • Faradays law

23
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24
  • 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

25
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26
Induced current, I
EMF
a
27
  • It was previously stated that a changing current
    creates a magnetic field.
  • Take the surface integral of both sides

28
  • Stokes theorem converts a surface integral into
    a line integral.

current through an arbitrary surface
29
  • Amperes Circuital Law
  • In magnetostatics

30
  • Show that for a transformer
  • where I1, N1, I2, and N2 are the currents and
    number of turns on the input and output,
    respectively.

31
  • Faradays Law
  • Combine the two equations

32
  • If the transformer is free of loses,
  • power in power out
  • The ratio of currents is inversely proportional
    to the ratio of turns.

33
  • 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.

34
  • Faradays law
  • What is the magnetic flux, ?

35
  • Differentiating with respect to t
  • From Lenzs law, the induced current flows
    clockwise.
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