1. Dr. Hugh Blanton ENTC 3331

2. Electrodynamics

3. Dr. Blanton - ENTC 3331 - Electrodynamics 3 charge ELECTROSTATICS static electric field MAGNETOSTATICS static magnetic field static stationary motion accelerated  decelerated motion time-varying electro-magnetic fields ELECTRODYNAMICS

4. Dr. Blanton - ENTC 3331 - Electrodynamics 4 What changes, if charge density and current density are time-dependent? The source of the electric field is still a charge distribution on is time-dependent. Since magnetic monopoles do not exist, the time-dependence is of no consequence

5. Dr. Blanton - ENTC 3331 - Electrodynamics 5 A stationary current has a rotational, static magnetic field A changing electric field generates a magnetic field. Maxwell’s equations must be consistent with the magnetostatic case for. magnetic and electric fields are coupled!

6. Dr. Blanton - ENTC 3331 - Electrodynamics 6 A changing magnetic field induces a rotational electric field. Generator principle Lenz’s law

7. Dr. Blanton - ENTC 3331 - Electrodynamics 7 Four New Things 1.Everything is now time-dependent 2.Displacement current density,. a.Changing current creates a magnetic field. 3. a.A changing magnetic field creates an electric field.

8. Dr. Blanton - ENTC 3331 - Electrodynamics 8 Four New Things 4.Electric and magnetic fields are coupled magneticelectric magnetic

9. Dr. Blanton - ENTC 3331 - Electrodynamics 9 All four aspects are included in the four general Maxwell’s equations of ELECTRODYNAMICS,which contain electrostatic and magnetostatics as special case with. differential form of Maxwell’s equations

10. Dr. Blanton - ENTC 3331 - Electrodynamics 10 A Story Edith, Debbie, Bill and Henry picnicked out in the field. With time, Edith’s comments revolved about the negative aspects of Bill’s personality, but Bill was not to be diverted! Henry felt more and more dizzy, taking in a steady current of beverages and started to appreciate Debbie’s positive side.

11. Dr. Blanton - ENTC 3331 - Electrodynamics 11 However, Debbie was diverted by her charge to teach them Maxwell’s equations of electrodynamics.

12. Dr. Blanton - ENTC 3331 - Electrodynamics 12 Is consistent with experimental experience? Let’s consider a loop, defining the area, S,   very small, loop essentially closed

13. Dr. Blanton - ENTC 3331 - Electrodynamics 13 Integrate on both sides: Apply Stoke’s theorem:   path integral along the edge of the area, S.

14. Dr. Blanton - ENTC 3331 - Electrodynamics 14 Recall that: A change in magnetic field produces a potential difference (voltage).

15. Dr. Blanton - ENTC 3331 - Electrodynamics 15 In this particular case, a current, i, will flow from 2 to 1. Note that this current opposes the direction of a current that would generate. Lenz’s law.    

16. Dr. Blanton - ENTC 3331 - Electrodynamics 16 Since, the magnitude of the current is pro- portional to the area of the loop, S. the magnitude of the change of.  

17. Dr. Blanton - ENTC 3331 - Electrodynamics 17 These conclusions are identical to what was first observed by Faraday and Henry in 1831. Since and

18. Dr. Blanton - ENTC 3331 - Electrodynamics 18 Generalization: EMF is independent of the area S, and EMF is proportional to the number of loops, N. Faraday’s law:

19. Dr. Blanton - ENTC 3331 - Electrodynamics 19

20. Dr. Blanton - ENTC 3331 - Electrodynamics 20 Induction Determine the magnetic flux,, through a single loop. Determine the EMF for N = 10, Bo = 2T, a = 0.1 m,  = 2  sec -1. Draw the EMF as a function of time. What is the polarity of EMF at t = 0? Draw the current, I, as a function of time, t, for R = 1k . a N-turns

21. Dr. Blanton - ENTC 3331 - Electrodynamics 21 independent of x and y

22. Dr. Blanton - ENTC 3331 - Electrodynamics 22 Faraday’s law:

23. Dr. Blanton - ENTC 3331 - Electrodynamics 23

24. Dr. Blanton - ENTC 3331 - Electrodynamics 24 At t = 0, the EMF < 0 (negative). In agreement with Lenz’s law. Since I = V/R  I o = EMF/1k  I o = -1.184/1k  mA

25. Dr. Blanton - ENTC 3331 - Electrodynamics 25

26. Dr. Blanton - ENTC 3331 - Electrodynamics 26 a EMF Induced current, I

27. Dr. Blanton - ENTC 3331 - Electrodynamics 27 It was previously stated that a changing current creates a magnetic field. Take the surface integral of both sides:

28. Dr. Blanton - ENTC 3331 - Electrodynamics 28 Stoke’s theorem converts a surface integral into a line integral. current through an arbitrary surface S C

29. Dr. Blanton - ENTC 3331 - Electrodynamics 29 Ampere’s Circuital Law In magnetostatics: S C

30. Dr. Blanton - ENTC 3331 - Electrodynamics 30 Show that for a transformer where I 1, N 1, I 2, and N 2 are the currents and number of turns on the input and output, respectively.

31. Dr. Blanton - ENTC 3331 - Electrodynamics 31 Faraday’s Law Combine the two equations

32. Dr. Blanton - ENTC 3331 - Electrodynamics 32 If the transformer is free of loses, power in = power out The ratio of currents is inversely proportional to the ratio of turns.

33. Dr. Blanton - ENTC 3331 - Electrodynamics 33 Sliding bar: Determine the EMF between the terminals, if the conducting bar slides to the right with equal to a constant. Use Faraday’s law in your approach.

34. Dr. Blanton - ENTC 3331 - Electrodynamics 34 Faraday’s law: What is the magnetic flux, ?

35. Dr. Blanton - ENTC 3331 - Electrodynamics 35 Differentiating with respect to t: From Lenz’s law, the induced current flows clockwise.