Lecture 23 Static field Dynamic Field

Lecture 23 Faraday’s Law

Lecture 23 Electromotive force Stationary Loop in a Time-varying Magnetic field Lenz’s law

Lecture 23 An example: Faraday’s law, differential form (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.

Lecture 23 Example II Determine the voltage drops across the two resistors

Lecture 24 The ideal Transformer properties:  =  I = 0 in the core. The magnetic flux is confined within the core I = ?, with applied voltage of V1and with RL V2, and I2=? Questions:

Lecture 24 Voltage transformer: Power relations: Why? Current transformer: Impedance transformer:

Lecture 24 Moving conductor in a static magnetic field:

Lecture 24 Another way to look at it: Next lecture: The electromagnetic generator Moving conductor in a time varying magnetic field

Lecture 27 The electromagnetic generator

Lecture 27 Moving conductor in a time-varying magnetic field Example: I

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

Lecture 27 Displacement current Ampere’s law in time-varying electric field Example:

Lecture 28 Boundary conditions for Electromagnetic Maxwell equations boundary conditions

Lecture 28 Charge-Current continuity Relation charge current continuity equation steady state integral form Kirchhoff’s current law

Lecture 28 Free-charge dissipation in a conductor

Lecture 29 Electromagnetic Potentials Electrostatics: Dynamic case:

Lecture 29 Retard Potentials Electrostatics: Dynamic case:

Lecture 29 Time-Harmonic Potentials

Lecture 29 Time-Harmonic Potentials example if no free charge, trans-wave, why? find k?

n1 n2 x z