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Biot-Savart magnetic force & torque

Biot-Savart magnetic force & torque. Slide through the integral!. Biot-Savart law. j(r’). B(r). +. r’. r. ur’ - r. Biot-Savart law. z. dz’. 2 L. z’. R. B. r. I. z. dz’. 2 L. z’. R. B. r. I. magnetic dipole. B. B. B. j s. A. summary.

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Biot-Savart magnetic force & torque

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  1. Biot-Savart magnetic force & torque

  2. Slide through the integral! Biot-Savart law

  3. j(r’) B(r) + r’ r ur’ - r Biot-Savart law

  4. z dz’ 2 L z’ R B r I

  5. z dz’ 2 L z’ R B r I

  6. magnetic dipole

  7. B B B js A summary Three techniques to find B 1] Ampere’s circuital law - lots of symmetry 2] find vector potential A, then B =  x A 3] Biot - Savart law

  8. Lorentz 1853-1928

  9. B z y F+ V x F- magnetic forces Lorentzforce

  10. v Ma Mb B Larmor radius

  11. Larmor 1857-1942

  12. permanent magnets why? inertia One has to change the magnetic pole of the current-carrying loop.

  13. Please Note: Rocket Sets contain rocket motors that are classified as hazardous materials for shipping purposes. Given this, we must ship Rocket Sets via surface mail through the USPS. model rockets

  14. B B - + C 60 MHD • plasma drift • F = Q (E + v x B) = 0 • 0 = E x + v B x • V  v B x

  15. electric power in space! 12 miles steady state F=0

  16. N S N S plasma physics

  17. plasma physics N S

  18. plasma physics magnetic field particle loss

  19. Example:Charged Particle Orbits in a Tokamakfinite element methodFEMLAB using MATLAB

  20. Tokamak – Problem Definition transformer core poloidal coils primary winding B Ip Icoil Tokamak principle

  21. Tokamak Introduction • A tokamak is a “magnetic bottle” for the confinement of high energy plasmas in Controlled Nuclear Fusion. • The ions and electrons in the plasma travel far between collisions. • collisionless model • particle motion is governed by the EM field • losses are mainly due to collisions with the walls

  22. Tokamak Modeling approach • Coils and plasma current are modeled in FEMLAB and the magnetic field is computed. • plasma current = 2.2 MA • peak toroidal magnetic field = 2 T • Particle orbits are computed using an ODE solver.

  23. Proton orbit - Results banana orbits Results – particle simulation

  24. B z y V x F work

  25. aurora borealis

  26. VIS Dr. Lou Frank & Dr. John Sigwarth

  27. Lou Frank John Sigwarth

  28. I1 dl1 I2 dl2 1 B2 B1

  29. current bracing Helmholtz coils

  30. lightning arrestor or STAR WARS

  31. Magnetic resonance imaging?

  32. electric machines rotate about an axis no translation torque

  33. I y  (forces) x B Dy Dx z = 0

  34. q y x + B q z Dy • q Torque

  35. Never Use Detergent Again! What would you say if I told you that one of the great inventions of the modern age has no moving parts, doesn't have anything to do with the Internet, doesn't even use Microsoft software? What is this wondrous invention... the Euro-Wash Laundry Ball... a collection of rubber and magnets that cleans clothes, even in the hardest of waters without soaps or detergents. Euro-Wash Laundry Ball

  36. MagneForce The first shoe with its own power supply. Comfortable, quality footwear constructed with a lightweight, flexible magnetic insole to generate a deep penetrating magnetic field which increases circulation; reduces foot, leg, and back fatigue; provides natural pain relief and improved energy level. The James Randi Educational Foundation offers $1 million to Florsheim if it can demonstrate its claims for MagneForce Footwear in a formal double-blind scientific test.

  37. Variable Specific Impulse Magnetoplasma Rocket The VASMIR engine has three magnetic cells. 1) Hydrogen is ionized. 2) Microwaves heat the plasma. 3) Magnetic nozzle converts energy into a directed flow. Mars, here we come! cnn 6/2000

  38. 1) Hydrogen is ionized. 2) Microwaves heat the plasma. 3) Magnetic nozzle converts energy into a directed flow.

  39. 1) Hydrogen is ionized. 2) Microwaves heat the plasma. 3) Magnetic nozzle converts energy into a directed flow.

  40. 1) Hydrogen is ionized. 2) Microwaves heat the plasma. 3) Magnetic nozzle converts energy into a directed flow.

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