Physics 2112 Unit 14

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Malcolm Knight
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1 Physics 2112 Unit 14 Today s Concept: What Causes Magnetic Fields d 0I ds ˆ 2 4 Unit 14, Slide 1

2 You Comments Can you give a summay fo eveything we use the ight hand ule fo? Wasn't too clea on this topic. Will be looking fowad to the lectue in class. Need moe pactice with detemining foce and toque diections. Pobably need to undestand component of the fomula and deivation bette. toque is so cunfusing can we eiteate how to apply RHR fo the F=ILx equation? Maybe i'll come into you office. I'm confused about assigning finges/thumbs to tems in the coss poduct... is it always the same sequence o is it dependent on the specific equation? the integals seem petty complicated. How many will we actually need to do? Unit 14, Slide 2

3 iot-savat Law 4 0 qv ˆ field fom one moving chage ut emembe fom pevious slides I qnav avg d 0I d s ˆ 2 4 field fom tiny ds of cuent caying wie. Unit 14, Slide 3

4 Compae to Electic Fields E 4 1 o ˆ q qv ˆ Tm / A v out of the sceen In the same diection as 12 Pependicula to 12 Unit 14, Slide 4

5 Remembeing Diections: The Right Hand Rule F qv C A C This method always woks! C qv F z x A A A Unit 12, Slide 5

6 Anothe way of looking at it.. Woks when something is going in a cicle Unit 14, Slide 6

7 Example 14.1 (Infinite wie of cuent) What is the magnetic field a distance y o away fom a infinitely long wie of cuent I? Conceptual Plan Use iot-savat Law Stategic Analysis Done in pelectue in detail Integate d 4 0I ds ˆ 2 (Simila to E field fo infinite line of chage) Unit 14, Slide 7

Main Idea y x ds f Q ˆ f ds I d s ˆ 0 4 2 I

8 Main Idea y x ds f Q ˆ f ds I d s ˆ I dx*sin( ) 0 4 ( x 2 y 2 o ) Unit 14, Slide 8

9 Example 14.1 (answe) Magnitude: I 0 2 Cuent I OUT Tm / A Remembe: E 2 o Unit 14, Slide 9

10 Remembeing Diections: The Right Hand Rule F qv F y x F qv z F v v 4 0 qv ˆ Unit 12, Slide 10

11 Question A long staight wie is caying cuent fom left to ight. Two identical chages ae moving with equal speed. Compae the magnitude of the foce on chage a moving diectly to the ight, to the magnitude of the foce on chage b moving up and to the ight at the instant shown (i.e. same distance fom the wie). A) F a > F b ) F a F b C) F a < F b (a) F v (b) Foces ae in diffeent diections (caeful with all the angles!) v F F qv F qvsinq Same q, v, and q (90) I Unit 14, Slide 11

12 Example 14.2 ( field fom hexagon) 120 o b A cuent, I, flows clockwise though a hexagonal loop of wie. The pependicula distance between each side and the cente of the loop is b. What is the magnetic field in the cente of the loop? ds f Q ˆ f ds Unit 14, Slide 12

13 Question Two long wies cay opposite cuent x What is the diection of the magnetic field above, and midway between the two wies caying cuent at the point maked X? A) Left ) Right C) Up D) Down E) Zeo x Unit 14, Slide 13

14 Example 14.3 (Fom Loop) P A cuent, I, flows clockwise though a cicula loop of wie. The loop has a adius a. y o a What is the magnetic field at a point P a distance y o above the plane of the loop in the cente? x Q cosq Q x Unit 14, Slide 14

15 Question P y o When doing this integal, how much of ds is pependicula to? A) all of it ) ds sinq C) ds cosq D) ds/sin ds a x Q cosq Q x Unit 14, Slide 15

16 Foce etween Cuent-Caying Wies X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X F I 1 0I1 2 X X X X X X X X X X I 2 F 12 I 2 L F 12 I 2 L o 2d I 1 Unit 14, Slide 16

17 Foce etween Cuent-Caying Wies I 2 L I towads d us F Anothe I towads us F o F I L I 2d Conclusion: Cuents in same diection attact! I towads us d F Anothe I away fom us Conclusion: Cuents in opposite diection epel! Unit 14, Slide 17

18 Example 14.4 (Two Cuent Caying Wies) 50cm I 2 = 10A 10cm I 1 = 5A Two cuent caying wies a 10cm apat fo a length fo 50cm. Wie 1 caies 5A and Wie 2 caies 10A with both cuent to the left. What is the magnitude and diection of the foce on wie 2 due to wie 1? Unit 14, Slide 18

19 CheckPoint 1A X F What is the diection of the foce on wie 2 due to wie 1? A) Up ) Down C) Into Sceen D) Out of sceen E) Zeo Unit 14, Slide 19

20 What we thought.. X F What is the diection of the foce on wie 2 due to wie 1? A) Up ) Down C) Into Sceen D) Out of sceen E) Zeo A) The cuent though wie 2 ceates a magnetic field pointing out of the sceen at wie 1. Using the RHR, the foce on wie 1 must be up. ) One ight-hand ule shows that the field is into the page, so anothe ight-hand ule shows that the foce points down. Unit 14, Slide 20

21 CheckPoint 1 What is the diection of the toque on wie 2 due to wie 1? A) Up ) Down C) Into Sceen D) Out of sceen E) Zeo Unifom foce at evey segment of wie No toque about any axis Unit 14, Slide 21

22 CheckPoint 3A What is the diection of the foce on wie 2 due to wie 1? A) Up ) Down C) Into Sceen D) Out of sceen E) Zeo Unit 14, Slide 22

23 CheckPoint 3 What is the diection of the toque on wie 2 due to wie 1? A) Up ) Down C) Into Sceen D) Out of sceen E) Zeo LET S DRAW A PICTURE! Unit 14, Slide 23

24 Conside Foce on Symmetic Segments I F out of sceen I F into sceen Net Foce is Zeo! ut the toque is not!!! Electicity & Magnetism Lectue 14, Slide 24

25 CheckPoint 3 What is the diection of the toque on wie 2 due to wie 1? A) Up ) Down C) Into Sceen D) Out of sceen E) Zeo Unit 14, Slide 25

26 Checkpoint 2: Foce on a loop A cuent caying loop of width a and length b is placed nea a cuent caying wie. How does the net foce on the loop compae to the net foce on a single wie segment of length a caying the same amount of cuent placed at the same distance fom the wie? A. the foces ae in opposite diections. the net foces ae the same. C. the net foce on the loop is geate than the net foce on the wie segment D. the net foce on the loop is smalle than the net foce on the wie segment E. thee is no net foce on the loop

27 Checkpoint question Cuent flows in a loop as shown in the diagam at the ight. The diection is such that someone standing at point a and looking towad point b would see the cuent flow clockwise. What is the oientation of the magnetic field poduced by the loop at points a and b on the axis? (A) () (C) (D)

28 on axis fom Cuent Loop I Resulting Field Cuent in Wie Electicity & Magnetism Lectue 14, Slide 28

29 What about Off-Axis? iot-savat Woks, but need to do numeically See Simulation! Unit 14, Slide 29

30 Two Cuent Loops Two identical loops ae hung next to each othe. Cuent flows in the same diection in both. The loops will: A) Attact each othe ) Repel each othe C) Thee is no foce between them Two ways to see this: 1) Like cuents attact 2) Look like ba magnets N S N S Unit 14, Slide 30

F Right Hand Rule Review 1. ANY CROSS PRODUCT qv F d F IL ˆ 0I ds 2 4 2.

31 F Right Hand Rule Review 1. ANY CROSS PRODUCT qv F d F IL ˆ 0I ds Diection of Magnetic Moment Finges: Cuent in Loop Thumb: Magnetic Moment 3. Diection of Magnetic Field fom Wie Finges: Magnetic Field Thumb: Cuent Unit 14, Slide 31

32 Example 14.2 Two paallel hoizontal wies ae located in the vetical (x,y) plane as shown. Each wie caies a cuent of I 1A flowing in the diections shown. y 4cm 4cm I 1 1A I 2 1A x z y. 3cm P What is the field at point P? Font view Side view Conceptual Analysis Each wie ceates a magnetic field at P fom infinite wie: 0 I / 2 Total magnetic field at P obtained fom supeposition Stategic Analysis Calculate at P fom each wie sepaately Total = vecto sum of individual fields Unit 14, Slide 32

33 Question y y What is the diection of at P? 4cm 4cm I 1 1A x z. 3cm P I 2 1A Font view Side view y y y y o. z P z P z P z P A C D Electicity & Magnetism Lectue 14, Slide 33

34 Question Two paallel hoizontal wies ae located in the vetical (x,y) plane as shown. Each wie caies a cuent of I 1A flowing in the diections shown. 0I 2 What is the magnitude of at P poduced by the top cuent I 1? ( 0 4 x 10 7 Tm/A) 4cm 4cm y I 1 1A I 2 1A Font view x z y. 3cm Side view P A) 4.0 x 10 6 T ) 5.0 x 10 6 T C) 6.7 x 10 6 T ỵ What is? distance fom wie axis to P z 4cm 3cm Electicity & Magnetism Lectue 14, Slide 34

35 Example 14.2 Two paallel hoizontal wies ae located in the vetical (x,y) plane as shown. Each wie caies a cuent of I 1A flowing in the diections shown. y I 1 1A 4cm 4cm I 2 1A Font view x y. 3cm z Side view P What is the field at point P? Unit 14, Slide 35

36 Question What is the diection of the magnetic field at point P, which is at the cente of a semicicula loop of wie caying a cuent I as shown? A. Goes in. Goes out C. Goes left D. Goes ight E. Thee is no magnetic field at point P. P

37 Example 14.5 (Cuved Loop of Wie) If I = 6A, what is the magnitude of the magnetic field at point P? 20cm Conceptual Plan Use iot-savat Law P 12cm Stategic Analysis d Integate 4 0I ds ˆ 2 Note staight sections cancel out. both loops

38 Question All of the cuent loops below cay the same cuent I. Rate them accoding to the magnetic field at the ed dot, fom lagest to smallest. A. A>>C. A>C> C. =C>A D. C==A E. C>>A

39 Good News!!!!! Remembe how we used Gauss Law to avoid doing integal in E field? We got simila law fo fields! Unit 14, Slide 39

The Law of Biot-Savart & RHR P θ

The Law of Biot-Savart & RHR P θ The Law of iot-savat & RHR P R dx x Jean-aptiste iot élix Savat Phys 122 Lectue 19 G. Rybka Recall: Potential Enegy of Dipole Wok equied to otate a cuentcaying loop in a magnetic field Potential enegy