Course Updates. Reminders: 1) Assignment #8 available. 2) Chapter 28 this week.

Transcription

1 Couse Updtes Remindes: 1) Assignment #8 vilble ) Chpte 8 this week

2 Lectue 3 iot-svt s Lw (Continued) θ d θ P R R θ R d θ d

3 Mgnetic Fields fom long wie An infinitely long wie long the y-is with the cuent moving y. Wht is the mgnetic field t position on the -is? y symmety we gue the field must be in the diection only. μ dl ˆ μ sinφ dl( ˆ ) 4 π 4 π ˆ μ sinφ Since, sin(φ) dy; 4π sin(π φ), we hve sinφ dy sin ( π φ) dy 3 dy 1 ( ) y 3/ dy Lectue 3 1 y y μ π ˆ ( ) 3

4 Mgnetic Fields fom long wie Mgnetic fields t points,b, nd c loop ound Lectue 3 μ π c c b b 4

5 Lectue 3 5 Mgnetic Fields fom wie segment Hee the poblem is the sme ecept wie not infinitely long! ; sin 4 ˆ ˆ 4 dy dl φ π μ π μ ( ) ( ) sin sin 3 / b b y y dy dy dy b b y φ π φ ( ) { }( ) b b b ˆ sin sin 4 ˆ 4 θ θ π μ π μ P -b y dl ˆ y θ θ b ut must be ceful of signs. o

6 Putting it ll togethe We know tht cuent-cying wie cn epeience foce fom -field. We know tht cuent-cying wie poduces - field. Theefoe: We epect one cuent-cying wie to eet foce on nothe cuent-cying wie: d F F b Lectue 3 Cuent goes togethe wies come togethe Cuent goes opposite wies go opposite 6

7 Foce between two pllel long wies (1 st deived by M. Ampee) Lectue 3 Suppose we hve two // wies with Cuents nd which e distnce pt. The bottom wie will poduce mgnetic field of μ π on the top wie. The foce on length L on the top wie will be F L μ ' L π ' The foce is downwd in the diection of the othe wie. Foce/unit length is F L μ π ' 7

8 Question 1: Two slck wies e cying cuent in opposite diections. Wht will hppen to the wies? They will: ) ttct b) epel c) twist due to toque Lectue 3 8

9 Question 1: Two slck wies e cying cuent in opposite diections. Wht will hppen to the wies? They will: ) ttct b) epel c) twist due to toque Lectue 3 9

10 Question : Lectue 3 Now, two slck wies e cying cuent in the sme diection. Wht will hppen to the wies? They will: ) ttct b) epel c) twist due to toque 1

11 Question : Lectue 3 Now, two slck wies e cying cuent in the sme diection. Wht will hppen to the wies? They will: ) ttct b) epel c) twist due to toque 11

12 Lectue 3 ) Find due v to one wie t the position of the othe wie b) Use F L to find the diection of F in ech cse F F : Point you thumb down, you finges wp in the diection of ound the wie: The diection of due to the left wie t the position of the ight wie is out of the sceen. b: is up, is out of the sceen, so F is to the ight. the foce is epulsive. 1

13 Question 3 A cuent flows in the y diection in n infinite wie; cuent lso flows in the loop s shown in the digm. Wht is F, the net foce on the loop in the -diection? () F < (b) F (c) F > y F left F top X Lectue 3 F ight F bottom 13

14 Question 3 A cuent flows in the y diection in n infinite wie; cuent lso flows in the loop s shown in the digm. Wht is F, the net foce on the loop in the -diection? () F < (b) F (c) F > Foces cncel on the top nd bottom of the loop. Foces do not cncel on the left nd ight sides of the loop. y F left F top X F bottom Lectue 3 F ight The left segment is in lge mgnetic field thn the ight Theefoe, F left > F ight 14

15 Mgnetic Field of wie loop Suppose wie loop is centeed t the oigin in the y- plne. Wht is the field long the cente line is (-is)? y symmety, the net field must be only long the -is s the y nd components will cncel. μ dl ˆ d 4π d d cosθ d μdl 4π d R μ 4π μ 4π ( )( ) π Fo >> : dl μ 4π μ 3 μ μ 33 Lectue 3 dl 15

16 Cicul Loop, nywhee on is Lectue 3 μ R ( R ) 3 >> R ( ) μr 3 Epessed in tems of the mgnetic moment μ πr >> R ( ) μ μ 3 π Note the typicl 1/ 3 dipole field behvio! R 16

17 Question 4 Equl cuents flow in identicl cicul loops s shown in the digm. The loop on the ight (left) cies cuent in the ccw (cw) diection s seen looking long the diection. Wht is the mgnetic field (A) t point A, the midpoint between the two loops? () (A) < (b) (A) (c) (A) > o A o Lectue 3 17

18 Question 4 Equl cuents flow in identicl cicul loops s shown in the digm. The loop on the ight (left) cies cuent in the ccw (cw) diection s seen looking long the diection. Wht is the mgnetic field (A) t point A, the midpoint between the two loops? () (A) < (b) (A) (c) (A) > o A o Lectue 3 The ight cuent loop gives ise to < t point A. The left cuent loop gives ise to > t point A. Fom symmety, the mgnitudes of the fields must be equl. Theefoe, (A) 18

19 Question 5 Equl cuents flow in identicl cicul loops s shown in the digm. The loop on the ight (left) cies cuent in the ccw (cw) diection s seen looking long the diection. o A Lectue 3 o Wht is the mgnetic field () t point, just to the ight of the ight loop? () () < (b) () (c) () > 19

20 Question 5 Equl cuents flow in identicl cicul loops s shown in the digm. The loop on the ight (left) cies cuent in the ccw (cw) diection s seen looking long the diection. o A Lectue 3 o () () < (b) () (c) () > The signs of the fields fom ech loop e the sme t s they e t A Howeve, point is close to the ight loop, so its field wins!

21 4 moe lectues until Sping ek Lectue 3 HW #8 need mgnetic equivlent of Guss Lw, net time Office Hous immeditely fte this clss (9:3 1:) in WAT14 (1:3-/1-1:3 M/WF) Lst dy to dop soon gde feedbck on webpge 1