4 03 2002_edited
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This document discusses electricity and magnetism, including the relationship between magnetic force and field, sources of magnetic fields, and the Lorentz force equation. It also examines examples such as the cyclotron radius and relativistic heavy ion collider. Key concepts covered are the magnetic field created by currents and solenoids, forces on moving charges and currents, and the differences between electric and magnetic fields.
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4 03 2002_edited
- 1. Electricity and Magnetism • Today – Charged particles in B-Field – Sources of B-Field Apr 3 2002
- 2. Magnetism • Magnetic Force and Magnetic Field • How are Force and Field related? • What is the Source of the Field? Apr 3 2002
- 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. 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. 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. 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. 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. N Wire, I > 0 N S Apr 3 2002 S X N S Currents and Magnetic Field
- 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. Currents and B-Field I Apr 3 2002 I
- 11. Currents and B-Field I I • Superposition Principle! Apr 3 2002
- 12. Currents and B-Field I Ix x x x • Solenoid: Large, uniform B inside! Apr 3 2002
- 13. Current and Current I F I F Attraction Apr 3 2002 I F I F Repulsion
- 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. Magnetic Field for Current I y dl r φ I z Apr 3 2002 x
- 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