Module 18: Outline. Magnetic Dipoles Magnetic Torques

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1 Module 18: Magnetic Dipoles 1

2 Module 18: Outline Magnetic Dipoles Magnetic Toques 2

3 IA nˆ I A Magnetic Dipole Moment μ 3

4 Toque on a Cuent Loop in a Unifom Magnetic Field 4

5 Poblem: Cuent Loop Place ectangula cuent loop in unifom B field ĵ 1) What is the net foce on this loop? 2) What is the net toque on this loop? 3) Descibe the motion the loop makes ˆk î 5

6 Toque on Rectangula Loop τ= IABĵ j ĵj x kˆ îi A= An ˆ = abnˆ: aea vecto nˆ =+ kˆ, B= Bˆi τ = IA B Familia? No net foce but thee is a toque 6

7 Magnetic Dipole Moment Define Magnetic Dipole Moment: Then: τ IA ˆn IA τ= μ B Analogous to τ = p E τ tends to align μ with B 7

8 Animation: Anothe Way To Look At Toque Link to animation Extenal field connects to field of magnet and pulls the dipole into alignment 8

9 Demonstation: Galvanomete 9

10 Concept Question Question: Foce on Magnetic Dipole 10

11 Concept Question: Dipole in Field μ Fom est, the coil above will: 1. otate clockwise, not move 2. otate counteclockwise, not move 3. move to the ight, not otate 4. move to the left, not otate 5. move in anothe diection, without otating 6. both move and otate 7. neithe otate t no move 8. I don t know 11

12 Enegy of Magnetic Dipole U = - μ B Dipole This equation gives you a geneal way to think about what dipoles will do in B fields 12

13 Expeiment 6: Magnetic Foces on Dipoles This is a little ticky. We will lead you though with lots of Concept Question questions

14 Fist: Set up cuent supply Open cicuit (disconnect a lead) Tun cuent knob full CCW (off) Incease voltage to ~12 V This will act as a potection: V<12 V Reconnect leads in Helmholtz lt mode Incease cuent to ~1 A

15 Field Pofiles: B vs. Height VERY UNIFORM! Single Coil Helmholtz Anti-Helmholtz ZERO FIELD!

16 Concept Question: Dipole in Helmholtz A andomly aligned dipole at the cente of a Helmholtz coil will feel: 1. a foce but not a toque 2. a toque but not a foce 3. both a toque and a foce 4. neithe foce no toque

17 Next: Dipole in Helmholtz (Q1-2) Set in Helmholtz Mode (~1 A) Tun off cuent Put dipole in cente (0 on scale) Randomly align using ba magnet Tun on cuent What happens?

18 Concept Question: Moving in Helmholtz When moving though the above field pofile, a dipole will: 1. Neve otate t 2. Rotate once 3. Rotate twice P19-18

19 Fields: Gav., Electic, Magnetic Ceate: Feel: Mass m Chage q (±) No m g = G ˆ q E = k 2 e F = m g F = q E g E ˆ 2 Magnetic Monopoles! Ceate: Dipole p E Dipole μ B Feel: τ = p E τ=μ B 19

20 Appendix: Foce on a Dipole in a Non-Unifom Field 20

21 Dipoles don t move??? This dipole otates but doesn t feel a net foce But dipoles CAN feel foce due to B. What s up? 21

22 Something New Dipoles in Non-Unifom Fields: Foce 22

23 Foce on Magnetic Dipole? We Want to Know: What is the foce on this dipole? 23

24 Concept Question Question: Foce on Magnetic Dipole 24

25 Concept Question: Field Stength A B C Whee is the pictued field the stongest? 1. A 2. B 3. C 4. I don t know 25

26 Concept Question: Dipole in Field The cuent caying coil above will feel a net foce 1. upwads 2. downwads 3. of zeo 4. I don t know 26

27 Can just sum I ds x B foces Is thee anothe way? 27

28 Foce on Magnetic Dipole Altenate Thought #1 Whee does the dipole want to be? 28

29 Think Using Enegy U = Dipole - μ B Whee does dipole go to educe its enegy? Aligned dipoles seek high fields! Æ Foce hee is down 29

30 Foce on Magnetic Dipole Altenate Thought #2 What makes the field pictued? 30

31 Foce on Magnetic Dipole N μ S N S Ba magnet below dipole, with N pole on top It is aligned with the dipole pictued, they attact! 31

32 Concept Question Questions: Foce on Dipole 32

33 Concept Question: Dipole in Field The cuent caying coil above will feel a net foce 1. upwads 2. downwads 3. of zeo 4. I don t know 33

34 Concept Question: Fee Dipoles If a numbe of dipoles ae andomly scatteed though space, afte a while they 1. Attact (move togethe) 2. Repel (move apat) 3. Basically stay put 4. I don t know 34

35 MIT OpenCouseWae SC Physics II: Electicity and Magnetism Fall 2010 Fo infomation about citing these mateials o ou Tems of Use, visit:

Magnetic Dipoles Challenge Problem Solutions

Magnetic Dipoles Challenge Problem Solutions Magnetic Dipoles Challenge Poblem Solutions Poblem 1: Cicle the coect answe. Conside a tiangula loop of wie with sides a and b. The loop caies a cuent I in the diection shown, and is placed in a unifom