Mon. Tues. 6.2 Field of a Magnetized Object 6.3, 6.4 Auxiliary Field & Linear Media HW9

Size: px

Start display at page:

Download "Mon. Tues. 6.2 Field of a Magnetized Object 6.3, 6.4 Auxiliary Field & Linear Media HW9"

Darcy Heath
5 years ago
Views:

1 Fi. on. Tus. 6. Fild of a agntid Ojct 6.3, 6.4 uxiliay Fild & Lina dia HW9

2 Dipol t fo a loop Osvation location x y agntic Dipol ont Ia... ) ( 4 o I I... ) ( 4 I o... sin 4 I o Sa diction as cunt B ) ( - B o dip sin cos 4 ) ( 3 B o dip (ys, sa fo as E fo p) Gnally ( s not ncssaily at oigin o pointing up)

3 agntic Fild Effcts on toic Dipols Poto-Quantu Divation Consid a chagd paticl oving in th psnc of a agntic fild. Th ontu in th paticl + fild syst: p p p p kin H * p q Hailtonian pkin syst v kin fild 1 q 1 1 p p q p p Fo an lcton, =, q = - agntic fild unifo and in th diction givs H H p p B p B Poduct ul B B L p L B 8 8 Bs Bs B Poduct uls 1 & and dfin B in diction, s in x-y plan, ducs to B Bs Bs So if dh db L 4 Paaagntic Diaagntic Oits oint to inii ngy- What kind of ato is pdoinatly Opposs fild add to fild diaagntic? *not ally how you uild a Hailtonian, ut happns to wok in this cas Bs

4 Osvation location agntiation d dnsity of agntic dipol onts Consid patch of atial covd in agntic dipols If diffntially sall ( ) o 4 i i i o d 4 i o 4 If th s an, what dos that say aout cunts? Each agntic dipol is a cunt loop, so d d o 4 with constant, opposit cunts wh two loops t cancl, laving only dg cunt Consid a lock of so thicknss di dia sid K K dl dl a sid sid sid dia loop d n n d n

5 agntiation d Consid patch of atial covd in diffntially-sall agntic dipols If not qual agntiations / cunts, inn cunt cossings only patially cancl, giving cunt acoss ody Th cunt down on stip is th diffnc twn that aound two adjacnt loops: Iy y Iy I y y I y I y y xy I y xy di Iy y Iy x xy xy x x da y y y Iy yanc Iyanc y y y x x x y y y So, if th agntiation, which h point s, vais acoss y, th s a nt cunt in x Looks a lot lik on t in a coss poduct.

6 d o d 4 agntiation K n Osvation location It ay failia (without th -suscipts) that o 4 d o 4 K da (Divation alost idntical to that fo polaiation s scala potntial)

7 K n agntiation Exapl: n infinitly long cicula cylind cais a unifo agntiation paalll to its axis. Find th agntic fild insid and outsid th cylind. o 4 d o 4 K da d 0 and K n ẑ ŝ B B o Bfo th ath, think aout th aangnt of icoscopic cunt loops that would giv this. B dl oi ncl Lik a solnoid (can you say a agnt ) pian loop and agunt fo (copaativly) unifo and 0 outsid BL ol B o B 0ẑ 0 s, 0 s.

8 K n agntiation Excis: n infinitly long cicula cylind cais a unifo, cicufntial agntiation. Find th agntic fild insid and outsid th cylind. o 4 d o 4 K da d B B o Bfo th ath, think aout th aangnt of icoscopic cunt loops that would giv this. Waning: th ath of is a littl sutl.

9 K Ex. 6.1: What s th agntic potntial of a sph with constant agntiation in th diction? x n y o 4 K agntiation d o 4 K da sin d Giffiths points out that this has th sa fo as xapl 5.11: unifo sufac chag dnsity, s, otating with angula spd w. K sv s w sin swsin So you can jup to th conclusion and sustitut in plac of sw o sw 3 o 4 s w 3 3 cos B B o o 3 o 3 3 3

10 K n agntiation d o o 4 4 K da d B B o Excis: n ion od of lngth L and squa coss sction (sid a) is givn a unifo longitudinal agntiation, thn is nt aound into a cicl. Find th agntic fild vywh. a a

11 K n agntiation d o o 4 4 K da d B B o Exapl: n ion od of lngth L and squa coss sction (sid a) is givn a unifo longitudinal agntiation, thn is nt aound into a cicl. with a naow gap (width w). Find th agntic fild at th cnt of th gap, assuing w<<a<<l. a a

12 d K n agntiation d o o 4 4 K da B B o Exapl: Lik ound chag, total ound cunt ust 0 fo any shapd ojct. n K t l Stoks I I I I I da K t dl da n t dl Poduct ul 1 n t dl dl dl a c a c dl n t dl dl n t l I 0

13 Fi. on. Tus. 6. Fild of a agntid Ojct 6.3, 6.4 uxiliay Fild & Lina dia HW9

Physics 202, Lecture 5. Today s Topics. Announcements: Homework #3 on WebAssign by tonight Due (with Homework #2) on 9/24, 10 PM

Physics 202, Lecture 5. Today s Topics. Announcements: Homework #3 on WebAssign by tonight Due (with Homework #2) on 9/24, 10 PM Physics 0, Lctu 5 Today s Topics nnouncmnts: Homwok #3 on Wbssign by tonight Du (with Homwok #) on 9/4, 10 PM Rviw: (Ch. 5Pat I) Elctic Potntial Engy, Elctic Potntial Elctic Potntial (Ch. 5Pat II) Elctic