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Fields and Waves

Study the integral form of Ampere’s Law for time-varying fields. Understand the connection between electric and magnetic fields under varying conditions, illustrated through the example of a Parallel Plate Capacitor. Explore the concept of displacement current and boundary conditions in electromagnetic theory.

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Fields and Waves

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  1. Fields and Waves Lesson 5.1 TIME-VARYING FIELDS Lale T. Ergene

  2. Displacement Current Ampere’s Law Time varying field Static field Integral Form of Ampere’s Law for time varying fields Displacement current Id IC- Conduction Current [A] – Electric Flux Density (Electric Displacement) [in C/unit area] - Current Density (in A/unit area)

  3. Displacement Current Total current Displacement current density • Connection between electric and magnetic fields under time varying conditions

  4. Example: Parallel Plate Capacitor Imaginary surface S1 ++++++++++++++++++++++++++++ + Imaginary surface S2 E-Field - - - - - - - - - - - - - - - - - - - - - - - - - - - - S1=cross section of the wire S2=cross section of the capacitor I1c, I1d : conduction and displacement currents in the wire I2c, I2d : conduction and displacement currents through the capacior

  5. Example: Parallel Plate Capacitor In a perfect conductor I1d=0 From the circuit theory: Total current in the wire:

  6. Example: Parallel Plate Capacitor Electrical charges can’t move physically through a perfect dielectric medium (zero conductivity) I2c=0 no conduction between the plates The electric field between the capacitors d :spacing between the plates

  7. Example : Parallel Plate Capacitor The displacement current I2d • Displacement current doesn’t carry real charge, but behaves like a real current • if wire has a finite conductivity σ then Do Problem 1

  8. Boundary Conditions • Boundary conditions derived for electrostatics and magnetostatics • remain valid for time-varying fields: dielectric-dielectric boundary dielectric-conductor boundary

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