Magnetic Forces, Materials and devices

1. Magnetic Forces, Materials and devices INEL 4151 Dr. Sandra Cruz-Pol Electrical and Computer Engineering Dept. UPRM http://www.treehugger.com/files/2008/10/spintronics-discover-could-lead-to-magnetic-batteries.php

2. Applications Motors Transformers MRI More… http://videos.howstuffworks.com/hsw/18034-electricity-and-magnetism-magnetic-levitation-video.htm

3. Forces due to Magnetic fields Analogous to the electric force: We have magnetic force: The total force is given by: If the charge moving has a mass m, then:

4. Forces on a current element The current element can be expressed as: So we can write: Line current element surface current element volume current element

5. Force between two current elements • Each element produces a field B, which exerts a force on the other element. I1 R21 I2

6. P.E. 8.4 Find the force experienced by the loop if I1=10A, I2=5A, ro=20cm, a=1cm, b=30cm Divide loop into 4 segments. z z I1 F2 F1 b I2 F3 r ro r a F4

7. For segment #1, Force #1 Since I1 is infinite long wire: z I1 I2 b F1 r a ro

8. For segment #2, The B field at segment #2 due to current 1. z F2 I1 I2 b r a ro

9. For segment #3, Force #3 The field at segment 3: z I1 I2 b F3 r a ro

10. For segment #4, The B field at segment #4 due to current 1. z I1 I2 b r a ro F4

11. The total force en the loop is I1=10A, I2=5A, ro=20cm, a=1cm, b=30cm • The sum of all four: • Note that 2 terms cancel out: z F2 F1 F3 r F4

12. Magnetic Torque and Moment Inside a motor/generator we have many loops with currents, and the Magnetic fields from a magnet exert a torque on them. The torque in [N m]is: • Where m is the Magnetic Dipole moment: • Where S is the area of the loop and an is its normal. This applies if B is uniform z B SIDE VIEW B

13. Torque on a Current Loop in a Magnetic Field  CD Motor   

14. Magnetic Dipoles, m Magnet Current loop Where the magnetic moment is:

15. Magnetic Torque and Moment The Magnetic torque can also be expressed as: The torque in [N m]is:

16. Magnetization (similar to Polarization for E) • Atoms have e- orbiting and spinning • Each have a magnetic dipole associated to it • Most materials have random orientation of their magnetic dipolesif NO external B-field is applied. • When a B field is applied, they try to align in the same direction. • The total magnetization [A/m]

17. Magnetization • The magnetization current density [A/m2] • The total magnetic density is: • Magnetic susceptibility is: • The relative permeability is: • Permeability is in [H/m].

18. Classification of Materials according to magnetism Non-magnetic mr=1 Ex. air, free space, many materials in their natural state. Magnetic mr≠1 Diamagnetic mr≤1 Electronic motions of spin and orbit cancel out. lead, copper, Si, diamonds, superconductors. Are weakly affected by B Fields. Paramagnetic mr≥1 Temperature dependent. Not many uses except in masers Ferromagnetic mr>>1 Iron, Ni,Co, alloys Loose properties if heated above Curie T (770C) Nonlinear: mr varies

20. B-H or Magnetization curve • When an H-field is applied to ferromagnetic material, it’s B increases until saturation. • But when H is decreased, B doesn’t follow the same curve.

21. Hysteresis Loop • Some ferrites, have almost rectangular B-H curves, ideal for digital computers for storing information. • The area of the loop gives the energy loss per volume during one cycle in the form of heat. • Tall-narrow loops are desirable for electric generators, motors, transformers to minimize the hysteresis losses.

22. Magnetic B.C. • We’ll use Gauss Law & • Ampere’s Circuit law

23. B.C.: Two magnetic media • Consider the figure below: B1n B1 D S Dh m1 B1t B2n m2 B2 B2t

24. B.C.: Two magnetic media • Consider the figure below: H1n H1 q1 a b K m1 H1t Dh H2n m2 H2 c d H2t D w

25. P.E. 8.8 Find B2 • Region 1 described by 3x+4y≥10, is free space • Region 2 described by 3x+4y≤10 is magnetric material with mr=10 • Assume boundary is current free.

26. P.E. 8.7 B-field in a magnetic material. • In a region with mr=4.6 • Find H and M and susceptability

27. How to make traffic light go Green when driving a bike or motorcycle • Stop directly on top of induction loop on the street • Attach neodymium magnets to the vehicle • Move on top of loop • Push crossing button • Video detectors • http://www.wikihow.com/Trigger-Green-Traffic-Lights • http://www.labreform.org/education/loops.html

28. Inductors • If flux passes thru N turn, the total Flux Linkage is • This is proportional to the current • The energy stored in the inductor is • So we can define the inductance as:

29. When more than 1 inductor *Don’t confuse the Magnetization vector, M, with the mutual inductance!

30. Self -inductance • The total energy in the magnetic field is the sum of the energies: • The positive is taken if currents I1 and I2 flow such that the magnetic fields of the two circuits strengthen each other. See table 8.3 in textbook with formulas for inductance of common elements like coaxial cable, two-wire line, etc.

31. Magnetic Energy • The energy in a magnetostatic filed in a linear medium is: • Similar to E field

32. P.E. 8.10 solenoid A long solenoid with 2x2 cm cross section has iron core (permeability is 1000x ) and 4000 turns per meter. If carries current of .5A, find: • Self inductance per m • Energy per m stored in its field

33. Example: Calculate self-inductance of coaxial cable We’ll find it in two parts:

34. Example: (cont.) coaxial We’ll find it in two parts:

35. Example: Find inductance for a 2-wire transmission line • Linis same as before: • We’ll find Lext from the definition of energy:

36. Magnetic Circuits • Manetomotive force • Reluctance • Like V=IR • Ex: magnetic relays, motors, generators, transformers, toroids • Table 8.4 presents analogy between magnetic and electric circuits

37. 8.42 A cobalt ring (mr=600) has mean radius of 30cm. • If a coil wound on the ring carries 12A, calculate the N required to establish an average magnetic flux density of 1.5 Teslas in the ring.

38. Force on Magnetic materials Relay • N turns, current I • B.C. B1n=B2n(ignore fringing) • Total energy change is used to displace bar a distance dl. • S=cross sectional area of core

39. P.E. 8.16 U-shape electromagnet • Will lift 400kg of mass(including keeper + weight) • Iron yoke has mr=3,000 • Cross section =40cm2 • Air gap are 0.1mm long • Length of iron=50cm • Current is 1A Find number of turns, N Find force across one air gap Esto nos da el B en el air gap.