Biot-Savart magnetic force & torque

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

17. N S N S plasma physics

18. plasma physics N S

19. plasma physics magnetic field particle loss

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

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

22. 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

23. 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.

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

25. B z y V x F work

27. aurora borealis

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

29. Lou Frank John Sigwarth

30. I1 dl1 I2 dl2 1 B2 B1

31. current bracing Helmholtz coils

32. lightning arrestor or STAR WARS

33. Magnetic resonance imaging?

34. electric machines rotate about an axis no translation torque

35. I y  (forces) x B Dy Dx z = 0

36. q y x + B q z Dy • q Torque

37. 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

38. 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.

40. 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

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

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

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