Chapter 29 Magnetic Fields

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Loentz foce law: When a chage q oes with elocity in a agnetic fiel B, the agnetic foce F on the chage is F q B. B E a B E ab a E +q. The static chage oesn t esponse to the agnetic fiel.

1 Chapte 9 Magnetic Fiels electic ipole +e agnetic ipole -e can t fin onopole --> cuent oel Magnetic poles always occu in pais. Thus fa, thee is no conclusie eience that an isolate agnetic onopole eists. 9. Magnetic Fiels an Foces We can efine a agnetic fiel B at soe point in space in tes of the agnetic foce F B. Loentz foce law: When a chage q oes with elocity in a agnetic fiel B, the agnetic foce F on the chage is F q B. B E a B E ab a E +q. The static chage oesn t esponse to the agnetic fiel. Only a oing chage will feel a agnetic-fiel inuce foce.. The agnetic foce is pepenicula to the plane spanne by an B. 3. Unit of the agnetic fiel: tesla (T) N / (C (/s)), T 4 Gauss 4. The agnetic fiel on the eath is.44 G. The aiu of static agnetic fiel

2 at laboatoy is ~ tesla. The peanent agnet pouces the agnetic fiel of ~ T. 5. What s a peanent agnet? Is thee any iffeence between fiels at laboatoy an fo a peanent agnet? in y plane in y plane in yz plane Magnetic Fiel Lines N is like a positie chage an S is like a negatie chage. Insie the agnet the fiel line iection is like that in an electic ipole. 9. Motion of a Chage Paticle in a Unifo Magnetic Fiel. The agnetic foce (Loentz foce) change the iection of the elocity but not the agnitue of the elocity.. Magnetic fiels o not wok on chage paticles an

3 o not change thei kinetic enegy. When the initial elocity is pepenicula to the agnetic fiel, the paticle will o cicula otion. F a FLoentz qb o ( q B qbsin( 9 ) qb (The aius of the paticle s cicula otion epens linealy on its elocity qb an its ass, but inesely on its chage an the agnetic fiel. --> You can use the elation to easue the elocity of chage paticles.) ) The peio of the cycloton otion is The cycloton fequency is Eaple: A poton of ass π π π T. qb qb qb qb f, an the angula spee is ω πf. T π.67 7 kg an chages q e.6 oes in a cicle of aius c pepenicula to a agnetic fiel of B 4 G. Fin (a) the peio of the otion an (b) the spee of the poton. qb T 9 qb (.6 C)(.4T )(.) 6 --> / s.67 kg (.) π π / s 7 s 9 C If the elocity is not pepenicula to the agnetic fiel, the otions can be sepaate to two inepenent pats: along the fiel iection an in the plane pepenicula to the fiel. Motion in nonunifo agnetic fiel: The agnetic fiel is weak at the cente an stong at both ens. The paticles spial aoun the fiel lines an becoe tappe, oscillating back an foth between the two ens. Why? 3

9.3 Applications Inoling Chage Paticles Moing in a Magnetic Fiel The Velocity Selecto Balance of electic an agnetic foce is use fo elocity selection.

4 9.3 Applications Inoling Chage Paticles Moing in a Magnetic Fiel The Velocity Selecto Balance of electic an agnetic foce is use fo elocity selection. F qe + q B When the iections of > E/B qe an q B ae opposite, the paticle unegoes linea otion with the elocity haing the elation qe qb. < E/B Thoson s Measueent of q/ fo Electons The epeients wee pefoe by J. J. Thoson in > The ays of a cathoe-ay tube can be eflecte by electic an agnetic fiels. Thoson s etho: using electic fiel to ben the cathoe-ay an to easue the chage-to-ass atio. Acceleating egion (egion ): qe a y & t --> y at Constant elocity egion (egion ): qe y ayt & t --> qe y qe E y qe + qe q E + 4

The Mass Spectoete Electic fiel acceleating egion: qv The agnetic fiel bening egion: qb --> qb qb --> qv --> q B V If the agnetic fiel an the acceleating oltage ae constant, the aius will epen on the

5 The Mass Spectoete Electic fiel acceleating egion: qv The agnetic fiel bening egion: qb --> qb qb --> qv --> q B V If the agnetic fiel an the acceleating oltage ae constant, the aius will epen on the ass-to-chage atio. ( q / ) Eaple: A 58 6 Ni ion of chage +e an ass 9.6 kg is acceleate though a potential op of 3 kv an eflecte in a agnetic fiel of. T. (a) Fin the aius of cuatue of the obit of the ion. (b) Fin the iffeence in the aii of cuatue of 58 Ni ions an 6 Ni ions. 6 V ( 9.6 )( 3) (a) 9 qb (.6 )(.).5 6 (b) 6 Ni. 5 --> 6 Ni 58 Ni unifo agnetic fiel The Cycloton A chage-paticle acceleato: qb --> π π T --> qb qb π qb ω T etal altenating electic fiel The kinetic enegy of a chage paticle leaing the cycloton is in acuu qb K q B Eaple: A cycloton fo acceleating potons has a agnetic fiel of.5 T an a 5

aiu aius of.5. (a) What s the cycloton fequency? (b) What s the kinetic enegy of the potons when they eege? ω π qb π 9 (.6 )(.5) 7 f.

4 Magnetic Foce Acting on a Cuent-Caying Conucto When a lot of electons ae oing in a confine space of a etal wie, thee is a foce on the wie.

Il B ( Il is calle a cuent eleent.) Use integation to obtain the total foce eete on the cue wie.

6 aiu aius of.5. (a) What s the cycloton fequency? (b) What s the kinetic enegy of the potons when they eege? ω π qb π 9 (.6 )(.5) 7 f.9 Hz 7 ( π )(.67 ) 9 (.6 ) (.5) 7 (.67 ) q B K 9 (.5) 4.3 J 6. MeV 9.4 Magnetic Foce Acting on a Cuent-Caying Conucto When a lot of electons ae oing in a confine space of a etal wie, thee is a foce on the wie. F ( q B)nAL ( J nq & I JA ) --> F IL B F q B : Coulob X Velocity X Magnetic Fiel --> F IL B : (Coulob / Tie) X Length X Magnetic Fiel F l F Il B ( Il is calle a cuent eleent.) Use integation to obtain the total foce eete on the cue wie. --> F I l B Eaple: A wie segent 3 long caies a cuent of 3 A in the + iection. It lies in a agnetic fiel of. T that is in the y plane an akes an angle of 3 o with the + iection. What is the agnetic foce eete on the wie segent? o F IL B kˆ sin 3 9 N ˆ ( )( ) k 6

7 Eaple: A wie bent into a seicicula loop of aius R lies in the y plane. It caies a cuent I fo point a to point b. Thee is a unifo agnetic fiel B B kˆ pepenicula to the plane of the loop. Fin the foce acting on the seicicula loop pat of the wie. Calculate the foce in the +y iection. π π sinθ θ IRB sinθθ IRB ( cosθ ) IRB F y I RB 9.5 Toque on a Cuent Loop in a Unifo Magnetic Fiel A cuent loop epeiences no net foce in a unifo agnetic fiel but it oes epeience a toque. F q B IL B F F IaB b τ F sinθ IabBsinθ τ ( Iabnˆ ) B ( Iab) Bsinθ What s the foce eete on the loop as the fiel is noal to the loop plane? The cuent oel of the agnetic ipole --> the agnetic ipole oent of the cuent loop: µ Iabnˆ IAnˆ o µ NIAnˆ --> τ µ B µ I Copae with the electic ipole: τ p E What s the iffeence of ipole oel between the electic an agnetic ipoles? 7

Eaple: A cicula wie loop of aius R, ass, an cuent I lies on a hoizontal suface. Thee is a hoizontal agnetic fiel B. How lage can the cuent I be befoe one ege of the loop will lift off the suface?

µ Bsinθθ U U µ Bsinθθ µ Bcosθ + U Assue U when o θ 9 --> U & U B µ θ, the wok one is W τθ. U W. Eaple: A squae -tun coil with ege-length 4 c caies a cuent of 3 A.

8 Eaple: A cicula wie loop of aius R, ass, an cuent I lies on a hoizontal suface. Thee is a hoizontal agnetic fiel B. How lage can the cuent I be befoe one ege of the loop will lift off the suface? IA IπR, µ B IπR B gr µ τ --> g I πrb Potential Enegy of a Magnetic Dipole in a Magnetic Fiel When a ipole is otate though an angle of W µ Bsinθθ The wok one on the ipole is stoe in potential enegy, U µ Bsinθθ U U µ Bsinθθ µ Bcosθ + U Assue U when o θ 9 --> U & U B µ θ, the wok one is W τθ. U W. Eaple: A squae -tun coil with ege-length 4 c caies a cuent of 3 A. It lies in the y plane in a unifo agnetic fiel B.3Tiˆ +.4Tkˆ. Fin (a) the agnetic oent of the coil, (b) toque, an (c) the potential enegy. ( 3)(.4) kˆ 5.76kˆ µ A τ µ B, U µ B Eaple: A thin nonconucting isk of ass an aius R has a unifo suface chage pe unit aea σ an otates with angula elocity ω about the ais. Fin the agnetic oent. µ IA --> µ ( IA) ( I )A ω 3 ( π ) ( σ π )( π ) πωσ σ π µ T π R 3 µ πωσ πωσ 4 R 4 8

the caies ae positiely o negatiely chage. the caie concentation n Eaple: A sile slab of thickness an with.5 c caies a cuent of.

9 9.6 The Hall Effect pue Si n-type p-type Si B --> p-type N --> n-type caies ae holes caies ae electons What o you ean a hole? F q B --> E B qe H H The Hall oltage is V E w Bw. H H ( ) I AJ A nq -> V R I B nqt H R H B t V Bw R H / nq is the Hall coefficient. IB n V qt H I IBw Bw nqa nqa H IB nqt By easuing the Hall effect, you can obtain:. the caies ae positiely o negatiely chage. the caie concentation n Eaple: A sile slab of thickness an with.5 c caies a cuent of.5 A in a egion in which thee is a agnetic fiel of agnitue.5 T pepenicula to the slab. The Hall oltage is easue to be.334 µ. Calculate the nube ensity of the chage caies. (.5)(.5) IB 8 n 5.85 electons/ 9 6 tev H (.)(.6 )(.334 ) 3 9

10 Hall-Effect eices ae use to easue the agnetic fiel --> eteine the cuent insie the wie The Quantu Hall Effects VH EH w Bw the Hall esistance: the Hall coefficient: VH Bw B h R I ( nq ) wt nqt n e R H EH JB B ( nq ) B nq

Chapter 28: Magnetic Field and Magnetic Force. Chapter 28: Magnetic Field and Magnetic Force. Chapter 28: Magnetic fields. Chapter 28: Magnetic fields

Chapter 28: Magnetic Field and Magnetic Force. Chapter 28: Magnetic Field and Magnetic Force. Chapter 28: Magnetic fields. Chapter 28: Magnetic fields Chapte 8: Magnetic fiels Histoically, people iscoe a stone (e 3 O 4 ) that attact pieces of ion these stone was calle magnets. two ba magnets can attact o epel epening on thei oientation this is ue to