1. 16.360 Lecture 23 Static field Dynamic Field

2. 16.360 Lecture 23 Faraday’s Law

3. 16.360 Lecture 23 Electromotive force Stationary Loop in a Time-varying Magnetic field Lenz’s law

4. 16.360 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.

5. 16.360 Lecture 23 Example II Determine the voltage drops across the two resistors

6. 16.360 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:

7. 16.360 Lecture 24 Voltage transformer: Power relations: Why? Current transformer: Impedance transformer:

8. 16.360 Lecture 24 Moving conductor in a static magnetic field:

9. 16.360 Lecture 24 Another way to look at it: Next lecture: The electromagnetic generator Moving conductor in a time varying magnetic field

10. 16.360 Lecture 27 The electromagnetic generator

11. 16.360 Lecture 27 Moving conductor in a time-varying magnetic field Example: I

12. 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

13. 16.360 Lecture 27 Displacement current Ampere’s law in time-varying electric field Example:

14. 16.360 Lecture 28 Boundary conditions for Electromagnetic Maxwell equations boundary conditions

15. 16.360 Lecture 28 Charge-Current continuity Relation charge current continuity equation steady state integral form Kirchhoff’s current law

16. 16.360 Lecture 28 Free-charge dissipation in a conductor

17. 16.360 Lecture 29 Electromagnetic Potentials Electrostatics: Dynamic case:

18. 16.360 Lecture 29 Retard Potentials Electrostatics: Dynamic case:

19. 16.360 Lecture 29 Time-Harmonic Potentials

20. 16.360 Lecture 29 Time-Harmonic Potentials example if no free charge, trans-wave, why? find k?

21. n1 n2 x z