4 03 2002_edited

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4 03 2002_edited

  1. 1. Electricity and Magnetism • Today – Charged particles in B-Field – Sources of B-Field Apr 3 2002
  2. 2. Magnetism • Magnetic Force and Magnetic Field • How are Force and Field related? • What is the Source of the Field? Apr 3 2002
  3. 3. Force on moving charge • Charged particle in a combination of Electric and Magnetic Field: FL = q E + qv x B This we know! Apr 3 2002 Lorentz Force Direction:Right-Hand Rule
  4. 4. Force on moving charge -q FE v E xB FB In B-Field: F= m a |q| v B = m v2/R -> R = m v/(q B) FL = q E + q v x B Apr 3 2002 Cyclotron Radius
  5. 5. Example 1 mile • Why so big? RHIC R = m v/(q B) Momentum p • Large p -> Large R • B ~ 10T (very big!) • Max. B in Lab around 100 T Relativistic Heavy Ion Collider Apr 3 2002
  6. 6. Work done on moving charge -q FE v E xB FB L W = FE L =qEL Apr 3 2002 dW = FB dL = (q v x B) dL =0
  7. 7. Magnet and Current Wire F F I • Force on wire if I != 0 • Direction of Force depends on Sign of I • Force perpendicular to I Apr 3 2002
  8. 8. N Wire, I > 0 N S Apr 3 2002 S X N S Currents and Magnetic Field
  9. 9. Currents and B-Field I • Current as Source of B • Magnetic Field lines are always closed – no Magnetic Charge (Monopole) • Right Hand Rule Apr 3 2002
  10. 10. Currents and B-Field I Apr 3 2002 I
  11. 11. Currents and B-Field I I • Superposition Principle! Apr 3 2002
  12. 12. Currents and B-Field I Ix x x x • Solenoid: Large, uniform B inside! Apr 3 2002
  13. 13. Current and Current I F I F Attraction Apr 3 2002 I F I F Repulsion
  14. 14. Magnetic Field vs Electric Field B r +Q v B ~q ~1/r2 ~v x r azimuthal B = µ0/(4 π) Q/r2 v x r µ0 = 4 π 10-7 T m /A Apr 3 2002 E ~q ~1/r2 / radial E +Q E = 1/(4 π ε0) Q/r2 r ε0 = 8.85 10-12 C2/(Nm2)
  15. 15. Magnetic Field for Current I y dl r φ I z Apr 3 2002 x
  16. 16. Magnetic Field for Current I B = µ0/(4 π) Q/r2 v x r for single charge I = dQ/dt -> dQ v = dQ dl/dt = I dl dB = µ0/(4 π) I dl x r/r2 Law of Biot-Savart: Magnetic Field dB for current through segment dl Apr 3 2002

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