Magnetism. Chapter 21

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1.1 Magnetic Fields Chapte 1 Magnetism The needle f a cmpass is

suth magnetic ple (S) at the the. 1.1 Magnetic Fields 1.

The diectin f the magnetic field at any pint in space is the

1 1.1 Magnetic Fields Chapte 1 Magnetism The needle f a cmpass is pemanent magnet that has a nth magnetic ple (N) at ne end and a suth magnetic ple (S) at the the. 1.1 Magnetic Fields 1.1 Magnetic Fields Suunding a magnet thee is a magnetic field. The diectin f the magnetic field at any pint in space is the diectin indicated by the nth ple f a small cmpass needle placed at that pint. The behavi f magnetic ples is simila t that f like and unlike electic chages. 1.1 Magnetic Fields 1.1 Magnetic Fields The magnetic field lines and patten f in filings in the vicinity f a ba magnet and the magnetic field lines in the gap f a hseshe magnet. 1

1. The Fce That a Magnetic Field Exets n a Chage When a chage is placed in an electic field, it expeiences a fce, accding t F qe 1.

. The velcity f the chage must have a cmpnent that is pependicula t the diectin f the magnetic field. 1.

The palm f the hand then faces in the diectin f the magnetic fce that acts n a psitive chage. If the mving chage is negative, the diectin f the fce is ppsite t that pedicted by RHR-1. 1.

2 1. The Fce That a Magnetic Field Exets n a Chage When a chage is placed in an electic field, it expeiences a fce, accding t F qe 1. The Fce That a Magnetic Field Exets n a Chage The fllwing cnditins must be met f a chage t expeience a magnetic fce when placed in a magnetic field: 1. The chage must be mving.. The velcity f the chage must have a cmpnent that is pependicula t the diectin f the magnetic field. 1. The Fce That a Magnetic Field Exets n a Chage Right Hand Rule N. 1. Extend the ight hand s the finges pint alng the diectin f the magnetic field and the thumb pints alng the velcity f the chage. The palm f the hand then faces in the diectin f the magnetic fce that acts n a psitive chage. If the mving chage is negative, the diectin f the fce is ppsite t that pedicted by RHR The Fce That a Magnetic Field Exets n a Chage DEFINITION OF THE MAGNETIC FIELD The magnitude f the magnetic field at any pint in space is defined as B q F ( vsinθ ) whee the angle (0<θ<180 ) is the angle between the velcity f the chage and the diectin f the magnetic field. newtn secnd culmb mete SI Unit f Magnetic Field: 1 tesla ( T) 1gauss tesla 1. The Fce That a Magnetic Field Exets n a Chage 1. The Fce That a Magnetic Field Exets n a Chage Example 1 Magnetic Fces n Chaged Paticles A ptn in a paticle acceleat has a speed f 5.0x 6 m/s. The ptn encuntes a magnetic field whse magnitude is 0.40 T and whse diectin makes and angle f 30.0 degees with espect t the ptn s velcity (see pat (c) f the figue). Find (a) the magnitude and diectin f the fce n the ptn and (b) the acceleatin f the ptn. (c) What wuld be the fce and acceleatin f the paticle wee an electn? (a) (b) F q vbsinθ 1.6 a F 13 N mp ( 1.60 C)( 5.0 m s)( 0.40T) sin( 30.0 ) N m s kg (c) Magnitude is the same, but diectin is ppsite. a F me 9.11 N m s kg

1.3 The Mtin f a Chaged Paticle in a Magnetic Field 1.3 The Mtin f a Chaged Paticle in a Magnetic Field Cnceptual Example A Velcity Select Chaged paticle in an electic field.

Hw shuld an electic field be applied s that the fce it applies t the paticle can balance the magnetic fce? Chaged paticle in a magnetic field. 1.3 The Mtin f a Chaged Paticle in a Magnetic Field 1.

3 1.3 The Mtin f a Chaged Paticle in a Magnetic Field 1.3 The Mtin f a Chaged Paticle in a Magnetic Field Cnceptual Example A Velcity Select Chaged paticle in an electic field. A velcity select is a device f measuing the velcity f a chaged paticle. The device peates by applying electic and magnetic fces t the paticle in such a way that these fces balance. Hw shuld an electic field be applied s that the fce it applies t the paticle can balance the magnetic fce? Chaged paticle in a magnetic field. 1.3 The Mtin f a Chaged Paticle in a Magnetic Field 1.3 The Mtin f a Chaged Paticle in a Magnetic Field The electical fce can d wk n a chaged paticle since thee is displacement in the diectin f the fce. Hence, this wk will incease the kinetic enegy and thus an incease f speed. The magnetic fce always emains pependicula t the velcity and is diected twad the cente f the cicula path. v m F c The magnetic fce cannt d wk n a chaged paticle since mving chage neve has displacement in the diectin f the fce. Hence the kinetic enegy emains cnstant v qvb m mv qb 1.3 The Mtin f a Chaged Paticle in a Magnetic Field 1.4 The Mass Spectmete Cnceptual Example 4 Paticle Tacks in a Bubble Chambe The figue shws the bubble-chambe tacks fm an event that begins at pint A. At this pint a gamma ay tavels in fm the left, spntaneusly tansfms int tw chaged paticles. The paticles mve away fm pint A, pducing tw spial tacks. A thid chaged paticle is kncked ut f a hydgen atm and mves fwad, pducing the lng tack. The magnetic field is diected ut f the pape. Detemine the sign f each paticle and which paticle is mving mst apidly. mv mv 1 mv ev qb eb magnitude f electn chage e m B V KEPE 3

The magnetic fce n the mving chages pushes the wie t the ight. 1.

5 The Fce n a Cuent in a Magnetic Field Example 5 The Fce and Acceleatin in a Ludspeake The vice cil f

The cuent in the vice cil is.0 A. (a) Detemine the magnetic fce that acts n the cil and the cne.

4 1.4 The Mass Spectmete 1.5 The Fce n a Cuent in a Magnetic Field The mass spectum f natually ccuing nen, shwing thee istpes. The magnetic fce n the mving chages pushes the wie t the ight. 1.5 The Fce n a Cuent in a Magnetic Field F qvbsinθ q F ( v t ) t Bsinθ L I 1.5 The Fce n a Cuent in a Magnetic Field Example 5 The Fce and Acceleatin in a Ludspeake The vice cil f a speake has a diamete f m, cntains 55 tuns f wie, and is placed in a 0.-T magnetic field. The cuent in the vice cil is.0 A. (a) Detemine the magnetic fce that acts n the cil and the cne. (b) The vice cil and cne have a cmbined mass f kg. Find thei acceleatin. F ILBsinθ 1.5 The Fce n a Cuent in a Magnetic Field 1.5 The Fce n a Cuent in a Magnetic Field (a) F ILBsinθ (.0 A) [ 55π ( m) ]( 0. T) 0.86 N sin 90 (b) F a m 0.86 N 0.00 kg 43m s 4

The lp tends t tate such that its nmal becmes aligned with the magnetic field.

0x -4 m, cnsists f 0 lps tuns, and cntains a cuent f 0.045 A. The cil is placed in a unifm magnetic field f magnitude 0.15 T.

5 1.6 The Tque n a Cuent-Caying Cil 1.6 The Tque n a Cuent-Caying Cil The tw fces n the lp have equal magnitude but an applicatin f RHR-1 shws that they ae ppsite in diectin. The lp tends t tate such that its nmal becmes aligned with the magnetic field. 1.6 The Tque n a Cuent-Caying Cil 1.6 The Tque n a Cuent-Caying Cil ( 1 1 wsinφ) + ILB( wsinφ) IAB sinφ Net tque τ ILB Example 6 The Tque Exeted n a Cuent-Caying Cil A cil f wie has an aea f.0x -4 m, cnsists f 0 lps tuns, and cntains a cuent f A. The cil is placed in a unifm magnetic field f magnitude 0.15 T. (a) Detemine the magnetic mment f the cil. (b) Find the maximum tque that the magnetic field can exet n the cil. (a) magnetic mment ( )( )( ) NIA A.0 m 9.0 A m τ magnetic mment NIA B sinφ (b) magnetic mment τ NIA B sinφ 9.0 ( A m )( 0.15 T) sin N m numbe f tuns f wie 1.6 The Tque n a Cuent-Caying Cil 1.6 The Tque n a Cuent-Caying Cil The basic cmpnents f a dc mt. 5

1.7 Magnetic Fields Pduced by Cuents 1.7 Magnetic Fields Pduced by Cuents Right-Hand Rule N.. Cul the finges f the ight hand int the shape f a half-cicle.

A LONG, STRAIGHT WIRE B I π 4π 7 T m A pemeability f fee space 1.7 Magnetic Fields Pduced by Cuents 1.

5x -6 C and is mving paallel t the wie at a distance f 0.050 m. The speed f the paticle is 80 m/s.

6 1.7 Magnetic Fields Pduced by Cuents 1.7 Magnetic Fields Pduced by Cuents Right-Hand Rule N.. Cul the finges f the ight hand int the shape f a half-cicle. Pint the thumb in the diectin f the cnventinal cuent, and the tips f the finges will pint in the diectin f the magnetic field. A LONG, STRAIGHT WIRE B I π 4π 7 T m A pemeability f fee space 1.7 Magnetic Fields Pduced by Cuents 1.7 Magnetic Fields Pduced by Cuents Example 7 A Cuent Exets a Magnetic Fce n a Mving Chage The lng staight wie caies a cuent f 3.0 A. A paticle has a chage f +6.5x -6 C and is mving paallel t the wie at a distance f m. The speed f the paticle is 80 m/s. Detemine the magnitude and diectin f the magnetic fce n the paticle. sinθ sinθ π I F qvb qv B I π 1.7 Magnetic Fields Pduced by Cuents 1.7 Magnetic Fields Pduced by Cuents Cuent caying wies can exet fces n each the. Cnceptual Example 9 The Net Fce That a Cuent-Caying Wie Exets n a Cuent Caying Cil Is the cil attacted t, epelled by the wie? 6

7 1.7 Magnetic Fields Pduced by Cuents 1.7 Magnetic Fields Pduced by Cuents A LOOP OF WIRE Example Finding the Net Magnetic Field A lng staight wie caies a cuent f 8.0 A and a cicula lp f wie caies a cuent f.0 A and has a adius f m. Find the magnitude and diectin f the magnetic field at the cente f the lp. B I R cente f cicula lp 1.7 Magnetic Fields Pduced by Cuents I1 I I1 I B π R π R 1.7 Magnetic Fields Pduced by Cuents The field lines aund the ba magnet esemble thse aund the lp. 7 ( π T m A) A.0 A 5 B 1.1 T ( m) m π 1.7 Magnetic Fields Pduced by Cuents 1.7 Magnetic Fields Pduced by Cuents A SOLENOID numbe f tuns pe unit length Intei f a slenid B ni 7

AMPERE S LAW FOR STATIC MAGNETIC FIELDS F any cuent

in time, B I net cuent passing thugh suface bunded by

8 Ampee s Law Example 11 An Infinitely Lng, Staight,

electns gives ise t the magnetic ppeties f mateials.

8 1.7 Magnetic Fields Pduced by Cuents 1.8 Ampee s Law A cathde ay tube. AMPERE S LAW FOR STATIC MAGNETIC FIELDS F any cuent gemety that pduces a magnetic field that des nt change in time, B I net cuent passing thugh suface bunded by path 1.8 Ampee s Law Example 11 An Infinitely Lng, Staight, Cuent-Caying Wie Use Ampee s law t btain the magnetic field. B I ( ) I B 1.9 Magnetic Mateials The intinsic spin and bital mtin f electns gives ise t the magnetic ppeties f mateials. In femagnetic mateials gups f neighbing atms, fming magnetic dmains, the spins f electns ae natually aligned with each the. Bπ I B I π 1.9 Magnetic Mateials 1.9 Magnetic Mateials 8

March 15. Induction and Inductance Chapter 31

March 15. Induction and Inductance Chapter 31 Mach 15 Inductin and Inductance Chapte 31 > Fces due t B fields Lentz fce τ On a mving chage F B On a cuent F il B Cuent caying cil feels a tque = µ B Review > Cuents geneate B field Bit-Savat law = qv