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Magnetostatics

Magnetostatics. EEE 161. Learning Objectives. Students will be able to Apply cross product (right-hand rule) Visualize magnetic field from a straight conductor Calculate the magnetic force On a conductor in an external magnetic field Between two current-carrying conductors

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Magnetostatics

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  1. Magnetostatics EEE 161 EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  2. Learning Objectives • Students will be able to • Apply cross product (right-hand rule) • Visualize magnetic field from a straight conductor • Calculate the magnetic force • On a conductor in an external magnetic field • Between two current-carrying conductors • Explain operation of a simple DC-motor EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  3. EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  4. EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  5. Force on a conductor EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  6. Force on a conductor EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  7. Force on a conductor EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  8. Magnetic Force on a Current Element If the field was coming out of the page EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  9. Right Hand Rule Number of magnetic field lines unit is Weber http://en.wikipedia.org/wiki/File:Manoderecha.svg EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  10. EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  11. Force between two conductors EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  12. Force between two conductors EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  13. Force between two conductors EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  14. Magnetic Force on a Current Element EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  15. Socrative Quiz #1 EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  16. Magnetic Force on a Current Loop EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  17. EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  18. EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  19. EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  20. Socrative Quiz #2 EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  21. EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  22. EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  23. EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  24. EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  25. MS#1 Loop of current is given. It is fixed in the middle of top and bottom wires. Magnetic flux density B. Find the direction of the forces on the loop and CW, CCW? EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  26. How do we find H? Ampere’s law Bio-Savart’s Law How do we find E? Gauss’ Law Coulomb’s Law EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  27. Ampère’s Law EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  28. Guided Example: Magnetic field of an infinite line of current 1. What is the direction of magnetic field? 2.Then we have to pick an appropriate contour (we pick circle because the magnetic field is constant on this circle – all points are the same distance away from the wire) 3. What is the contour piece dl? EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  29. What is the direction of magnetic field? Magnetic field on this circle will be constant (all points are the same distance away from the source (current) EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  30. Why can we take H in front of the integral? Why is H a constant? EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  31. EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  32. Radius of wire a EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  33. Example: Internal Magnetic Field of Long Conductor For r < a EEE 161 Electromagnetics - Magnetostatics Dr. Markovic Cont.

  34. EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  35. MS#2 Find the magnetic field everywhere around an infinite hollow cylindrical conductor shown. J=const (current density). Given: I, a, b. Find H. EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  36. How is B different than H? H – magnetic field B- magnetic flux density Magnetic permeability How is D different than E? E – electric field D- electric flux density electric permittivity EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  37. How can you calculate inductance? EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  38. How can you calculate inductance? Magnetostatic energy Electrostatic energy EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  39. Example: Using Magnetic Energy Density to find Inductance Magnetic field in the insulating material is Current is given EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  40. Example:Magnetic Energy Density Magnetic field in the insulating material is The magnetic energy stored in the coaxial cable is EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  41. Example:Magnetic Energy Density The magnetic energy stored in the coaxial cable is EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  42. EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  43. Graded Quiz MS#3 • Using magnetic energy density equation, find the internal inductance of a wire of circular cross section, with radius of a=1mm. The current is constant throughout the wire. EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  44. Inductance recall • Inductor creates magnetic field • Current in one conductor will cause current in another conductor that’s mutual inductance • J omega L • Inductor resists current changes • Voltage over inductor is inductance x di/dt • Positive VAR EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  45. Conceptual understanding of inductance EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  46. There are circular rings of magnetic-field around all currents EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  47. Right Hand Rule Number of magnetic field lines unit is Weber http://en.wikipedia.org/wiki/File:Manoderecha.svg EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  48. Learning Outcomes • Students will be able to • Describe inductance through flux of magnetic field • Conceptually explain what is inductance • Describe what affects inductance • Estimate inductance EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  49. Resistance • Resistance is defined as • Do we have any such equations for inductance and capacitance? EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

  50. Capacitance and Inductance do not relate directly current and voltage. EEE 161 Electromagnetics - Magnetostatics Dr. Markovic

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