Fields and Waves Lesson 5 1 TIMEVARYING FIELDS

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Fields and Waves Lesson 5. 1 TIME-VARYING FIELDS Lale T. Ergene

Fields and Waves Lesson 5. 1 TIME-VARYING FIELDS Lale T. Ergene

Displacement Current Ampere’s Law Static field Time varying field Integral Form of Ampere’s Law

Displacement Current Ampere’s Law Static field Time varying 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)

Displacement Current Total current Displacement current density • Connection between electric and magnetic fields

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

Example: Parallel Plate Capacitor + - Imaginary surface S 1 Imaginary surface S 2

Example: Parallel Plate Capacitor + - Imaginary surface S 1 Imaginary surface S 2 S 1=cross section of the wire ++++++++++++++ -------------- E-Field S 2=cross section of the capacitor I 1 c, I 1 d : conduction and displacement currents in the wire I 2 c, I 2 d : conduction and displacement currents through the capacior

Example: Parallel Plate Capacitor In a perfect conductor From the circuit theory: Total current

Example: Parallel Plate Capacitor In a perfect conductor From the circuit theory: Total current in the wire: I 1 d=0

Example: Parallel Plate Capacitor Electrical charges can’t move physically through a perfect dielectric medium

Example: Parallel Plate Capacitor Electrical charges can’t move physically through a perfect dielectric medium (zero conductivity) I 2 c=0 no conduction between the plates The electric field between the capacitors d : spacing between the plates

Example : Parallel Plate Capacitor The displacement current I 2 d • Displacement current

Example : Parallel Plate Capacitor The displacement current I 2 d • Displacement current doesn’t carry real charge, but behaves like a real current • if wire has a finite conductivity σ then Do Problem 1

Boundary Conditions • Boundary conditions derived for electrostatics and magnetostatics remain valid for time-varying

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