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16.360 Lecture 23. Static field. Dynamic Field. 16.360 Lecture 23. Faraday’s Law. 16.360 Lecture 23. Electromotive force. Stationary Loop in a Time-varying Magnetic field. Lenz’s law. 16.360 Lecture 23. Faraday’s law, differential form. An example:.

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16.360 Lecture 23

Static field

Dynamic Field

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16.360 Lecture 23

Faraday’s Law

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16.360 Lecture 23

Electromotive force

Stationary Loop in a Time-varying Magnetic field

Lenz’s law

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16.360 Lecture 23

Faraday’s law, differential form

An example:

(a) The magnetic flux link of a single turn

of the inductor.

(b) The transformer emf,.

(c) The polarity of the emf.

(d) The induced current.

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16.360 Lecture 23

Example II

Determine the voltage drops across the

two resistors

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16.360 Lecture 24

The ideal Transformer properties:

  •  = 
  • I = 0 in the core.
  • The magnetic flux is confined within the core

Questions:

  • I = ?, with applied voltage of V1and with RL
  • V2, and I2=?
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16.360 Lecture 24

Voltage transformer:

Power relations:

Why?

Current transformer:

Impedance transformer:

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16.360 Lecture 24

Moving conductor in a static magnetic field:

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16.360 Lecture 24

Another way to look at it:

Next lecture:

  • The electromagnetic generator
  • Moving conductor in a time varying magnetic field
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16.360 Lecture 27

The electromagnetic generator

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16.360 Lecture 27

Moving conductor in a time-varying magnetic field

Example:

I

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16.360 Lecture 27

Displacement current

  • Ampere’s law in static electric field
  • Ampere’s law in time-varying electric field
  • proof of Ampere’s law:

Displacement current density

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16.360 Lecture 27

Displacement current

  • Ampere’s law in time-varying electric field

Example:

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16.360 Lecture 28

  • Boundary conditions for Electromagnetic

Maxwell equations

boundary conditions

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16.360 Lecture 28

  • Charge-Current continuity Relation

charge current continuity equation

steady state integral form

Kirchhoff’s current law

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16.360 Lecture 28

  • Free-charge dissipation in a conductor
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16.360 Lecture 29

  • Electromagnetic Potentials

Electrostatics:

Dynamic case:

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16.360 Lecture 29

  • Retard Potentials

Electrostatics:

Dynamic case:

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16.360 Lecture 29

  • Time-Harmonic Potentials
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16.360 Lecture 29

  • Time-Harmonic Potentials

if no free charge, trans-wave, why?

  • example

find k?

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n1

x

n2

z