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Electricity and Magnetism

Electricity and Magnetism. Announcements Review for Quiz #3 Exp EB Force in B-Field on free charge on current Sources of B-Field Biot-Savart Ampere’s Law Exp MF Magnetic Induction Faradays Law Lenz’ Rule. Announcements. Review tonight 7:30 – 9:30 PM Room 1-190 Quiz #3

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Electricity and Magnetism

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  1. Electricity and Magnetism • Announcements • Review for Quiz #3 • Exp EB • Force in B-Field • on free charge • on current • Sources of B-Field • Biot-Savart • Ampere’s Law • Exp MF • Magnetic Induction • Faradays Law • Lenz’ Rule web.mit.edu/8.02x/www

  2. Announcements • Review tonight • 7:30 – 9:30 PM • Room 1-190 • Quiz #3 • Friday, 4-19, Walker Gym • 10AM-11AM • Closed book, no calculators web.mit.edu/8.02x/www

  3. Announcements Reading suggestions: 27-1,2,3,4 27-7,9 28-1,2,3,4,5,6,8 29-1,2,3,5 (eddy currents) web.mit.edu/8.02x/www

  4. Need lot’s of free charges But electrons stuck in potential well of nucleus Need energy DU to jump out of well How to provide this energy? Electrical Breakdown U DU e- web.mit.edu/8.02x/www

  5. Define Vion = DU/q Ionization potential One e- in, two e- out Avalanche? Impact Ionization e- Ukin > DU E E web.mit.edu/8.02x/www

  6. To get avalanche we need: DUkinbetween collisions (1) and (2) > Vion * e Acceleration in uniform Field DUkin = V2 – V1 = e E d12 Avalanche condition then E > Vion /lmfp Impact Ionization (1) (2) lmfp e- lmfp : Mean Free Path E web.mit.edu/8.02x/www

  7. (i) If Density n is big -> lmfp small Impact Ionization How big is Mean Free Path? (ii) If size sof moleculesis big -> lmfp small lmfp = 1/(ns ) Avalanche if E > Vion /lmfp = Vion n s web.mit.edu/8.02x/www

  8. Magnetism • Observed New Force between • two Magnets • Magnet and Iron • Magnet and wire carrying current • Wire carrying current and Magnet • Two wires carrying currents • Currents (moving charges) can be subject to and source of Magnetic Force web.mit.edu/8.02x/www

  9. Magnetic Force • Force between Magnets • Unlike Poles attract F F N N S S • Like Poles repel F F N S N S web.mit.edu/8.02x/www

  10. Magnetic Force • Magnets also attract non-magnets! F Iron nail web.mit.edu/8.02x/www

  11. Current and Magnet N N S S Wire, I = 0 Wire, I > 0 X web.mit.edu/8.02x/www

  12. Magnet and Current F Wire I F • Force on wire if I != 0 • Direction of Force depends on Sign of I • Force perpendicular to I web.mit.edu/8.02x/www

  13. Current and Current I I I I F F F F Attraction Repulsion Experiment MF web.mit.edu/8.02x/www

  14. Force on moving charge FE -q v x B FB E R FL = q E + q v x B R = m v/(q B) Lorentz-Force Cyclotron Radius web.mit.edu/8.02x/www

  15. Work done on moving charge FE -q v x B dW = FB dL = (q v x B) dL = (q dL/dt x B) dL = 0 E FB L W = FE L = q E L Magnetic Field does no Work! web.mit.edu/8.02x/www

  16. Force on Wire carrying current I dFB = dq v x B = dq dL/dt x B = I dL x B x I B Wire dL web.mit.edu/8.02x/www

  17. Sources of the Magnetic Field web.mit.edu/8.02x/www

  18. Current as Source of B Magnetic Field lines are always closed no Magnetic Charge (Monopole) Right Hand Rule Currents and B-Field I web.mit.edu/8.02x/www

  19. Superposition Principle! Currents and B-Field I I web.mit.edu/8.02x/www

  20. Solenoid: Large, uniform B inside Superposition Principle! Currents and B-Field x x x x I web.mit.edu/8.02x/www

  21. Magnetic Field vs Electric Field E B r v +Q +Q B = m0/(4 p) Q/r2 v x r E = 1/(4 pe0) Q/r2 r e0 = 8.85 10-12 C2/(Nm2) m0 = 4 p 10-7 T m /A 1/(m0 e0) = (3 108 m/s)2 = c2 Speed of Light Deep connection between B and E Field web.mit.edu/8.02x/www

  22. Magnetic Field for Current I dB = m0/(4 p) dQ/r2 v x r for charge dQ I = dQ/dt -> dQ v = dQ dl/dt = I dl Law of Biot-Savart dB = m0/(4 p) I dl x r/r2 Magnetic Field dB for current through segment dl For total B-Field: Integrate over all segments dl web.mit.edu/8.02x/www

  23. Magnetic Field for Current I y +L dl r dl f x r n I -L z web.mit.edu/8.02x/www

  24. Magnetic Field for Current I • For quiz: • No long calculations • But need to understand how to use Biot-Savart to find direction of B web.mit.edu/8.02x/www

  25. Remember: Gauss’ Law Electric Flux fE Integral over any closed surface Electric Charge is the Source of Electric Field web.mit.edu/8.02x/www

  26. Gauss’ Law for Magnetic Fields • Magnetic Flux through closed surface is 0 • This says: There are no magnetic monopoles • Important Law – one of Maxwell’s equations • Unfortunately of limited practical use web.mit.edu/8.02x/www

  27. Ampere’s Law I • Ampere’s idea: Relate Field B to its Source: I Closed Line instead of closed surface! B web.mit.edu/8.02x/www

  28. Ampere’s Law I Ampere’s Law helps because we can choose integration path! B Right-Hand rule for relating sign of dl and I web.mit.edu/8.02x/www

  29. Ampere’s Law I Ampere’s Law helps because we can choose integration path! B web.mit.edu/8.02x/www

  30. Field of a Solenoid x x x x x x x x • Current I • n turns per unit length • (infinite length) B a b h B = m0 I n Loop C c d L web.mit.edu/8.02x/www

  31. Coaxial Cable Conductor I2 I1 Insulator Outside field vanishes for I2 = I1 web.mit.edu/8.02x/www

  32. Cylindrical Conductor I • Uniform Current-Density J • Radius R • Uniform Current-Density J • Radius R • J = I/(p R2) r R web.mit.edu/8.02x/www

  33. Magnetic Induction • Currents give rise to B-Field • Q: Can B-Field give rise to current? • A: Only if Magnetic Flux changes with time! • Took a very long time to realize... web.mit.edu/8.02x/www

  34. Faradays Law Magnetic Flux (usually, A not closed surface) Faradays Law web.mit.edu/8.02x/www

  35. Faradays Law • FB can change because • |B| changes • Angle between B and A changes • |A| (size of circuit in B) changes web.mit.edu/8.02x/www

  36. Faradays Law B x Moving circuit: Induced EMF is consequence of force on moving charges v F +q web.mit.edu/8.02x/www

  37. Lenz’ Rule Lenz’ Rule: Sign of Iind such that it opposes the flux change that generated it web.mit.edu/8.02x/www

  38. Use of Faradays Law • To find Iind: • Calculate FB • Find, what makes FB change • Find sign of Iind using Lenz’ rule B x v web.mit.edu/8.02x/www

  39. Use of Faradays Law • To find Iind: • Calculate FB • Find, what makes FB change • Find sign of Iind using Lenz’ rule B x v web.mit.edu/8.02x/www

  40. Use of Faradays Law • To find Iind: • Calculate FB • Find, what makes FB change • Find sign of Iind using Lenz’ rule B x v web.mit.edu/8.02x/www

  41. Use of Faradays Law B x • Sign of current: • Opposing change of FB • -> Reducing B v web.mit.edu/8.02x/www

  42. Use of Faradays Law B x • Sign of current: • Opposing change of FB • -> Reducing B v Iind web.mit.edu/8.02x/www

  43. Use of Faradays Law B x • Sign of current: • Opposing change of FB • -> Reducing B v Iind Lenz’ Rule: Effect of Iind current opposing dFB/dt is like ‘drag’ or ‘inertia’ web.mit.edu/8.02x/www

  44. My favorite Demo Falling Al disk B • Falling Al ring is slowed down in B-Field • Induced Eddy-currents • Energy converted to heat web.mit.edu/8.02x/www

  45. Faradays Law B x Moving circuit: Induced EMF is consequence of force on moving charges What about changing B? v F +q web.mit.edu/8.02x/www

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