Wed., /11 Thus., /1 Fi., /13 Mn., /16 Tues., /17 Wed., /18 Thus., /19 Fi., / 17.7-9 Magnetic Field F Distibutins Lab 5: Bit-Savat B fields f mving chages (n quiz) 17.1-11 Pemanent Magnets 18.1-3 Mic. View f Electic Cicuits 18.4-6 E. Field f Suface Chages, Tansients, Feedback Quiz Ch 17, 18.7-9, Lab 6: E. Field f Suface Chage 18.1-11 Applicatins f the They, Detecting Suface Q RE13, Exp - Exp 3-9 (wk tgethe f magnets) RE14, Lab Ntebk HW17:RQ.31, 3, 34; P.49, 51, 5 RE15 RE16 Exp 18,19,-4 Pepaatin Lab handut Check WebAssign Lad Vpythn Magnets f thse wh haven t gtten them yet (f Thusday set up, dn t fget slenids t) Annuncements Candidates Visiting Next Mnday 11 1: Class 4pm Reseach Talk Opptunity t lean a little abut what physicists d Last Time Bit-Savat f wies. Last time we develped an expessin f the bit f magnetic field geneated by a bit f cuent caying wie. B = I l ˆ Right-Hand Rule f wies. Cnveniently, the ight-hand-ule gets petty simple f a cuent caying wie. Imagine gabbing the wie with yu ight hand such that yu thumb pints alng it in the diectin f cuent flw. Then yu hand waps aund the wie just as the magnetic field des.
Adding Up the Magnetic Field Just as with finding the net electic field due t a chage distibutin, thee s a systematic way t find the net magnetic field due t a cuent distibutin. Geneal Pcess:. Pedict 1. Divide up cuent int pieces and daw B f a epesentative piece. Wite an expessin f B due t ne piece 3. Add (integate) up the cntibutins f all pieces 4. Check the esult Last time, we cnsideed hw t cmputatinally find the field due t a wie. This Time: Magnetic Fields f Cuent Distibutins Nw we ll g n t cnside hw t find the magnetic field f diffeent cuent distibutins. We ll d it analytically. In lab tmw, yu ll d it cmputatinally. Staight Wie. Pedict 1. Divide up cuent int pieces and daw B f a epesentative piece. Wite an expessin f B due t ne piece 3. Add (integate) up the cntibutins f all pieces 4. Check the esult Adding up the Magnetic Field. Staight Line Nw that yu ve gt the expessin f magnetic field due t cuent in a msel f wie, yu can build up any gemety f cuent/wie and find the magnetic field due t it. Examples. Staight. We ll stat simple, with the field alng the cente fm a staight line. Lp. Then we ll ventue t smething me cmplicated the geneal case f a lp But we ll chicken ut at the end, and g f n-axis. Phys 3 Ch 17, Lectue 3 9
Geneal Pcess: Magnetic Field f cuent distibutins same as with the cmpute Divide up cuent int pieces and daw B f a epesentative piece Wite an expessin f B due t ne piece Add (integate) up the cntibutins f all pieces Check the esult 1. Divide up cuent int pieces and daw B f a epesentative piece. Wite an expessin f B due t ne piece = bseatin lcatin suce lcatin = x,,, y, = x, y, + The length f this vect is x + ( y) = x y ˆ = = Phys 3 Ch 17, Lectue 3 9 3 =, s the unit vect is: x, y, ( x + y ) 1 l f the segment is l =, y, = y,1,, s I l ˆ I y,1, I l B = = = 3 x + y x, y, ( ) 3 3. Tanslate this int VPythn Cde and then nest it in a lp t sum ve the length f the wie, fm L/ t L/. Nte: the css pduct can be dne with css(a,b) B = I l ˆ = I y,1, x, y, x + y ( ) 3
Ding this analytically The css pduct is (als use RHR t see diectin): s:,1, x, y, = det 1 ˆ i ˆ j ˆ k x y = x ˆ k =,, x I x y I x y B =,,1 B = y 3 z ( x + y ) ( x ) 3 + 3. Add (integate) up the cntibutins f all pieces B z + L + L dy y = I x x 3 4 = I π ( ) 4 L x y x x y + π + L B z = I x L L 4 π x L x + since nly the distance fm the wie mattes (call it ): If L >>, then: 4. Check the esult The units wk ut: Vey fa away ( >> L ): = ( L ) x x + ( L ) x x + ( ) B wie = 4 π B LI + ( L ) B wie I T m A wie m A = T m LI which is like a small segment f wie f length L., LI Q. Exp 17. Yu wee t have dne Expeiment f tday. What did yu find? (If it s clea that they haven t dne it, have them d it nw.) Shuld find that the field stength dps ff like 1/. Phys 3 Ch 17, Lectue 3 9 4
Shuld find a easnable cuent value. At twice the height, the deflectin deceases by 1/ t abut 1. If the deflectin is, the magnetic field f the wie is B wie = B Eath tanθ = 1 5 T using B wie I. ( ) tan = 7.3 1 6 T. The cuent in the wie is fund Magnetic field f a cicula lp In lab, yu ll simulate the Magnetic field due t a cicula lp. Nw we ll lk at it analytically, natually, the basic set up f the analytical appach will be the same as f the cmputatinal ne that yu ll take tmw, s I encuage yu t take paticulaly gd ntes n the set up. Nw we can lk at the lp centeed n z axis, find field at an abitay lcatin. See PwePint Check the esult The units ae cect (yu can cnfim that). At the cente f the lp, all pints n the wie ae the same distance, s: B z ( z = )= I( πr) R which makes sense because πr is the length (cicumfeence). Alng the z axis, the field is lagest at the cente and deceases fathe away. Vey fa fm the lp ( z >> R): B lp IπR z 3 Phys 3 Ch 17, Lectue 3 9 5
Dem. Let s lk at this thing. 17_B_lp_xy_xz.py Q. Lk familia? Whee have yu seen a field patten like that? A. The electic diple. Cuent Lp = Magnetic Diple. Magnetic diple mment Recall that the electic field alng the axis f an electic diple was Edipleaxis. 3 ε z Nw, the magnetic diple field lks 1 p whee p=qs defined the electic diple mment. B lp IπR n axis. z 3 Define S B diple IA, whee A = πr. 3 A magnetic diple will tend t line up with an extenal magnetic field if it is fee t tate. Exp 17.1 Find the magnetic field f the cils using B cils = B Eath tanθ. Find the cuent with B cils = NIπR, whee R is the adius f a lp and z is the distance fm the z + R 3 cil s cente. ( ) Execises 1. A vey lng wie caying a cnventinal cuent I in the diectin shwn is staight except f a cicula lp f adius R. Calculate the magnitude and diectin f the magnetic field at the cente f the lp. Phys 3 Ch 17, Lectue 3 9 6
. A cnventinal cuent I flws in the diectin shwn belw. Detemine the magnitude and diectin f the magnetic field at pint C. By the RHR, all f the cuved segments pduce magnetic fields int the page at C. The staight segments pduce n (ze) magnetic field at C since d l ˆ f thse. The ute ac (adius R) pduces half the magnetic field f a lp (z=): B ute = 1 πi = πi R R The inne tuns (adius ) pduces 1.5 times the magnetic field f a lp (z=): B inne = 3 πi = 3πI Since the magnetic fields fm the tw pats ae in the same diectin (they ae vects!), the net magnetic field int the page is: B net = B ute + B inne = πi R + 3πI = πi 1 R + 3 Phys 3 Ch 17, Lectue 3 9 7
3. In a huse, the maximum cuent caied by mst wies is 15 ampees (cicuit beakes flip ff the pwe abve that). Suppse tw wies in a hme pwe cd ae abut 3 mm apat as shwn belw and cay cuent in ppsite diectins at any instant (the diectins altenate 6 times pe secnd). (a) Calculate the maximum magnitude f the magnetic field 5 cm away fm the cente f the pwe cd. (b) Explain biefly why twisting the pai f wies int a baid as shwn wuld minimize the magnetic field. Mnday: Pemanent Magnets Phys 3 Ch 17, Lectue 3 9 8