physics 101 - magnetic fields

8/18/2019 Physics 101 - magnetic fields

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Magnetic Fields

Chapter 28

Copyright © 2014 John Wiley & Sons, Inc. All rights reserve .


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28-1 !agnetic "iel s an the #e$inition o$ B

28.01 #isting%ish anelectro agnet $ro aper anent agnet.

28.02 I enti$y that a agnetic$iel is a vector '%antity anth%s has (oth agnit% e an

irection.

28.03 )*plain ho+ a agnetic

$iel can (e e$ine in ter so$ +hat happens to a chargeparticle oving thro%gh the$iel .

28.04 "or a charge particleoving thro%gh a %ni$or

agnetic $iel , apply therelationship (et+een the $orceon the charge F B, charge q ,spee v , $iel agnit% e B, anthe angle Φ (et+een the

irections o$ the velocity vector v an the agnetic $iel vector B.

28.05 "or a charge particle sent

thro%gh a %ni$or agnetic $iel ,$in the irection o$ the agnetic$orce F B (y 1- applying the righthan r%le to $in the irection o$the cross pro %ct v ×B an 2-

eter ining +hat e$$ect the© 2014 John Wiley & Sons, Inc. All rights reserve .

Learning Objectives


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28.06 "in the agnetic $orce F B acting on a oving chargeparticle (y eval%ating thecross pro %ct q v ×B - in %nitvector notation an

agnit% e angle notation.

28.07 I enti$y that the agnetic$orce vector F B %st al+ays

(e perpen ic%lar to (oth thevelocity vector v an the

agnetic $iel vector B .

28.08 I enti$y the e$$ect o$ theagnetic $orce on the

particle/s spee an inetic

28.09 I enti$y a agnet as (eing aagnetic ipole.

28.10 I enti$y that oppositeagnetic poles attract each

other an li e agnetic polesrepel each other.

28.11 )*plain agnetic $iel lines,incl% ing +here they originate

an ter inate an +hat theirspacing represents.

Learning Objectives !"ntd.#

© 2014 John Wiley & Sons, Inc. All rights reserve .


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$%e &e'initi"n "' B$%e Field. We can e$ine a agnetic $iel B to (e a vector '%antity that e*ists +hen ite*erts a $orce F B on a charge oving +ith velocity v . We can ne*t eas%re the

agnit% e o$ F B +hen v is irecte perpen ic%lar to that $orce an then e$ine theagnit% e o$ B in ter s o$ that $orce agnit% e

+here q is the charge o$ the particle. We can s% ari e all these res%lts +ith the$ollo+ing vector e'%ation

that is, the $orce F B on the particle (y the $iel B is e'%al to the charge q ti es thecross pro %ct o$ its velocity v an the $iel B all eas%re in the sa e re$erence$ra e-. We can +rite the agnit% e o$ F B as

+here ϕ is the angle (et+een the irections o$ velocity v an agnetic $iel B .© 2014 John Wiley & Sons, Inc. All rights reserve .


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Finding t%e Magnetic F"rce "n a (article

3his e'%ation tells %s the irection o$ F . We no+ the cross pro %ct o$ v an B is a

vector that is perpen ic%lar to these t+o vectors. 3he right han r%le "igs. a c- tells%s that the th% ( o$ the right han points in the irection o$ v B +hen the $ingerss+eep v into B . I$q is positive, then (y the a(ove )'.- the $orce F B has the sa esign as v B an th%s %st (e in the sa e irection5 that is, $or positive q , F B is

irecte along the th% ( "ig. -. I$ q is negative, then the $orce F B an crosspro %ct v B have opposite signs an th%s %st (e in opposite irections. "ornegative q , F is irecte opposite the th% ( "ig. e-.



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Finding t%e Magnetic F"rce "n a (article

Ans+era- to+ar s the

positive a*is(- to+ar s the

negative * a*isc- none cross

pro %ct is ero-© 2014 John Wiley & Sons, Inc. All rights reserve .


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Magnetic Field LinesWe can represent agnetic $iel s +ith $iel lines, as +e i $or electric $iel s. Si ilarr%les apply

1- the irection o$ the tangent to a agnetic $iel line at any point gives the irectiono$ B at that point

2- the spacing o$ the lines represents the agnit% e o$ B 6the agnetic $iel is

stronger +here the lines are closer together, an conversely.$)" ("les . 3he close - $iel lines enter one en o$ a agnet an e*itthe other en . 3he en o$ a agnet $ro +hich the $iel lines e erge iscalle the north pole o$ the agnet5 the other en , +here $iel lines enterthe agnet, is calle the so%th pole. 7eca%se a agnet has t+o poles, itis sai to (e a *agnetic di+"le .

a- 3he agnetic $iel lines $or a (ar agnet.(- A co+ agnet9 6 a (ar agnet that is inten e to (e slippe o+n into the r% en o$ a co+

to recover acci entally ingeste (its o$ scrap iron an to prevent the $ro reaching the

co+/s intestines. 3he iron $ilings at its en s reveal the agnetic $iel lines.© 2014 John Wiley & Sons, Inc. All rights reserve .


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28-2 Crosse "iel s #iscovery o$ 3he )lectron

28.12 #escri(e the e*peri ento$ J. J. 3ho son.

28.13 "or a charge particle

oving thro%gh a agnetic$iel an an electric $iel ,eter ine the net $orce on the

particle in (oth agnit% eangle notation an %nit vector

notation.

28.14 In sit%ations +here theagnetic $orce an electric $orce

on a particle are in oppositeirections, eter ine the spee

at +hich these $orces cancel, thespee s at +hich the agnetic$orce o inates, an the spee sat +hich the electric $orce

o inates.

Learning Objectives



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28-2 Crosse "iel s #iscovery o$ 3he )lectron

A o ern version o$ J.J.3ho son/s apparat%s $or

eas%ring the ratio o$ ass tocharge $or the electron. Anelectric $iel E is esta(lishe (yconnecting a (attery across the

e$lecting plate ter inals. 3he

agnetic $iel B is set %p (yeans o$ a c%rrent in a syste o$

coils not sho+n-. 3he agnetic$iel sho+n is into the plane o$ the$ig%re, as represente (y thearray o$ :s +hich rese (le the$eathere en s o$ arro+s-.I$ a charge particle oves thro%gh a region containing (oth an electric $iel an a

agnetic $iel , it can (e a$$ecte (y (oth an electric $orce an a agnetic $orce.When the t+o $iel s are perpen ic%lar to each other, they are sai to (e cr"ssed'ields .I$ the $orces are in opposite irections, one partic%lar spee +ill res%lt in no e$lection

o$ the particle.© 2014 John Wiley & Sons, Inc. All rights reserve .


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28-3 Crosse "iel s 3he ;all )$$ect

28.15 #escri(e the ;all e$$ect $ora etal strip carrying c%rrent,e*plaining ho+ the electric$iel is set %p an +hat li its

its agnit% e.28.16 "or a con %cting strip in a

;all e$$ect sit%ation, ra+ thevectors $or the agnetic $ielan electric $iel . "or thecon %ction electrons, ra+ thevectors $or the velocity,

agnetic $orce, an electric$orce.

28.17 Apply the relationship(et+een the ;all otential

i$$erence V , the electric $ielagnit% e E , an the +i th o$

the strip d .28.18 Apply the relationship

(et+een charge carrier n% (erensity n , agnetic $ielagnit% e B, c%rrent i , an ;all

e$$ect potential i$$erence V .

28.19 Apply the ;all e$$ect res%ltsto a con %cting o(


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As +e ?, ) +in ;. ;all, then a 24 year ol gra %ate st% ent atthe Johns ;op ins @niversity, sho+e that they can.

3his ,all e''ect allo+s %s to $in o%t +hether the chargecarriers in a con %ctor are positively or negatively charge .7eyon that, +e can eas%re the n% (er o$ s%ch carriers per%nit vol% e o$ the con %ctor."ig%re a- sho+s a copper strip o$ +i th d , carrying a c%rrent i+hose conventional irection is $ro the top o$ the $ig%re to the(otto . 3he charge carriers are electrons an , as +e no+,they ri$t +ith ri$t spee v d - in the opposite irection, $ro(otto to top.

As ti e goes on, electrons ove to the right, ostly piling %p onthe right e ge o$ the strip, leaving %nco pensate positive

charges in $i*e positions at the le$t e ge as sho+n in $ig%re (-.© 2014 John Wiley & Sons, Inc. All rights reserve .


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When a %ni$or agnetic $iel 7 is applie to a con %cting stripcarrying c%rrent i, +ith the $iel perpen ic%lar to the irection o$the c%rrent, a ;all e$$ect potential i$$erence V is set %p acrossthe strip.3he electric $orce F E on the charge carriers is then (alance (ythe agnetic $orce F B on the .

3he n% (er ensity n o$ the charge carriers can then (eeter ine $ro

in +hich l A/d - is the thic ness o$ the strip. With this e'%ation+e can $in n $ro eas%ra(le '%antities.

When a con %ctor oves thro%gh a %ni$or agnetic $iel B at spee v , the ;all e$$ect potential i$$erence V across it is

Where d is the +i th perpen ic%lar to (oth velocity v an$iel B .



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28-4 A Circ%lating Charge Barticle

28.20 "or a charge particleoving thro%gh a %ni$oragnetic $iel , i enti$y %n er

+hat con itions it +ill travel in a

straight line, in a circ%lar path,an in a helical path.

28.21 "or a charge particle in%ni$or circ%lar otion %e to a

agnetic $orce, start +ith

e+ton/s secon la+ an erivean e*pression $or the or(italra i%s r in ter s o$ the $iel

agnit% e B an the particle/sass m , charge agnit% e q ,

an spee v .

28.22 "or a charge particle ovingalong a circ%lar path in a agnetic$iel , calc%late an relate spee ,centripetal $orce, centripetalacceleration, ra i%s, perio ,

$re'%ency, an ang%lar $re'%ency,an i enti$y +hich o$ the '%antitieso not epen on spee .

28.23 "or a positive particle an anegative particle oving along a

circ%lar path in a %ni$or agnetic$iel , s etch the path an in icatethe agnetic $iel vector, the velocityvector, the res%lt o$ the cross pro %cto$ the velocity an $iel vectors, anthe agnetic $orce vector.

Learning Objectives



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28.24 "or a charge particleoving in a helical path in aagnetic $iel , s etch the path

an in icate the agnetic

$iel , the pitch, the ra i%s o$c%rvat%re, the velocityco ponent parallel to the $iel ,an the velocityco ponent perpen ic%lar tothe $iel

28.25 "or helical otion in aagnetic $iel , apply the

relationship (et+een the ra i%s o$c%rvat%re an one o$ the velocity

co ponents.28.26 "or helical otion in a

agnetic $iel , i enti$y pitch p anrelate it to one o$ the velocityco ponents.




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A (ea o$ electrons is pro


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28-5 Cyclotrons an Synchrotrons

28.27 #escri(e ho+ a cyclotron+or s, an in a s etch,in icate a particle/s path anthe regions +here the ineticenergy is increase .

28.28 I enti$y the resonancecon ition

28.29 "or a cyclotron, apply therelationship (et+een theparticle/s ass an charge, the

agnetic $iel , an the$re'%ency o$ circling.

28.30 #isting%ish (et+een acyclotron an a synchrotron.

Learning Objectives



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$%e ! cl"tr"n 3he $ig%re is a top vie+ o$ the region o$ a cyclotronin +hich the particles protons, say- circ%late. 3he t+o hollo+ #shape o(


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(r"t"n nc%r"tr"n/ 3he agnetic $iel B an the oscillator $re'%ency f osc ,instea o$ having $i*e val%es as in the conventional cyclotron, are a e to vary+ith ti e %ring the accelerating cycle. When this is one properly, 1- the$re'%ency o$ the circ%lating protons re ains in step +ith the oscillator at all ti es,an 2- the protons $ollo+ a circ%lar 6 not a spiral 6 path. 3h%s, the agnetnee e*ten only along that circ%lar path, not over so e 4 10 E 2. 3he circ%larpath, ho+ever, still %st (e large i$ high energies are to (e achieve .



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28-6 !agnetic "orce on C%rrent Carrying Wire

28.31 "or the sit%ation +here ac%rrent is perpen ic%lar to a

agnetic $iel , s etch thec%rrent, the irection o$ the

agnetic $iel , an the irectiono$ the agnetic $orce on thec%rrent or +ire carrying thec%rrent-.

28.32 "or a c%rrent in a agnetic

$iel , apply the relationship(et+een the agnetic $orce

agnit% e F B, the c%rrent i , thelength o$ the +ire L, an theangle f (et+een the length vector

L an the $iel vector B .

28.33 Apply the right han r%le $orcross pro %cts to $in the irectiono$ the agnetic $orce on a c%rrentin a agnetic $iel .

28.34 "or a c%rrent in a agnetic$iel , calc%late the agnetic $orceF B +ith a cross pro %ct o$ thelength vector L an the $iel vectorB , in agnit% e angle an %nitvector notations.

28.35 #escri(e the proce %re $orcalc%lating the $orce on a c%rrentcarrying +ire in a agnetic $iel i$the +ire is not straight or i$ the $ielis not %ni$or .

Learning Objectives



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28-6 !agnetic "orce on a C%rrent Carrying Wire

A $le*i(le +ire passes (et+een thepole $aces o$ a agnet only the$arther pole $ace is sho+n-. a-Witho%t c%rrent in the +ire, the +ireis straight. (- With %p+ar c%rrent,the +ire is e$lecte right+ar . c-With o+n+ar c%rrent, the

e$lection is le$t+ar .

A straight +ire carrying a c%rrent i in a %ni$oragnetic $iel e*periences a si e+ays $orce

;ere L is a length vector that has agnit% e L

an is irecte along the +ire seg ent in theirection o$ the conventional- c%rrent.

!r"" ed ire. I$ a +ire is not straight or the $ielis not %ni$or , +e can i agine the +ire (ro en%p into s all straight seg ents. 3he $orce on the

+ire as a +hole is then the vector s% o$ all the$orces on the seg ents that a e it %p. In thei$$erential li it, +e can +rite

an the irection o$ length vector L or d L is in the

irection o$ i.© 2014 John Wiley & Sons, Inc. All rights reserve .


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28-7 3or'%e on a C%rrent Foop

28.36 S etch a rectang%lar loopo$ c%rrent in a agnetic $iel ,in icating the agnetic $orceson the $o%r si es, the

irection o$ the c%rrent, thenor al vector n , an the

irection in +hich a tor'%e$ro the $orces ten s torotate the loop.

28.37 "or a c%rrent carrying coil ina agnetic $iel , apply therelationship (et+een the tor'%e

agnit% e τ , the n% (er o$t%rns N , the area o$ each t%rn A ,the c%rrent i , the agnetic $iel

agnit% e B, an the angle θ(et+een the nor al vector n an the agnetic $iel vector B .

Learning Objectives



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28-7 3or'%e on a C%rrent Foop

3he ele ents o$ an electric otor Arectang%lar loop o$ +ire, carrying ac%rrent an $ree to rotate a(o%t a $i*e

a*is, is place in a agnetic $iel .!agnetic $orces on the +ire pro %ce ator'%e that rotates it. A co %tator notsho+n- reverses the irection o$ thec%rrent every hal$ revol%tion so that thetor'%e al+ays acts in the sa e

irection.

As sho+n in the $ig%reright- the net $orce on theloop is the vector s% o$the $orces acting on its $o%rsi es an co es o%t to (e

ero. 3he net tor'%e acting

on the coil has aagnit% e given (y

+here N is the n% (er o$ t%rns in the coil, Ais the area o$ each t%rn, i is the c%rrent, B isthe $iel agnit% e, an θ is the angle(et+een the agnetic $iel B an the nor alvector to the coil n .



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28-8 3he !agnetic #ipole !o ent

28.38 I enti$y that a c%rrentcarrying coil is a agnetic ipole+ith a agnetic ipole o ent

μ that has the irection o$ the

nor al vector n , as given (y aright han r%le.

28.39 "or a c%rrent carrying coil,apply the relationship (et+eenthe agnit% e μ o$ the agnetic

ipole o ent, the n% (er o$t%rns N , the area A o$ each t%rn,an the c%rrent i .

28.40 Gn a s etch o$ a c%rrentcarrying coil, ra+ the irection

o$ the c%rrent, an then %se a

right han r%le to eter ine theirection o$ the agnetic ipoleo ent vector μ .

28.41 "or a agnetic ipole in an

e*ternal agnetic $iel , apply therelationship (et+een the tor'%e

agnit% e τ , the ipole o entagnit% e μ , the agnetic $ielagnit% e B , an the angle θ

(et+een the ipole o ent vector μ an the agnetic $iel vector B .

28.42 I enti$y the convention o$assigning a pl%s or in%s sign to ator'%e accor ing to the irection o$

rotation.

Learning Objectives



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28.43 Calc%late the tor'%e on aagnetic ipole (y eval%ating a

cross pro %ct o$ the ipoleo ent vector μ an the e*ternal

agnetic $iel vector B , inagnit% e angle notation an%nit vector notation.

28.44 "or a agnetic ipole in ane*ternal agnetic $iel , i enti$y the

ipole orientations at +hich thetor'%e agnit% e is ini % an

a*i % .

28.45 "or a agnetic ipole in ane*ternal agnetic $iel , apply therelationship (et+een the

orientation energy U , the ipoleo ent agnit% e μ , the

e*ternal agnetic $ielagnit% e B , an the angle θ

(et+een the ipole o entvector μ an the agnetic $ielvector B .

28.46 Calc%late the orientationenergy U (y ta ing a ot pro %ct

o$ the ipole o ent vector μan the e*ternal agnetic $ielvector B , in agnit% e angle an%nit vector notations.





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28.47 I enti$y the orientations o$ aagnetic ipole in an e*ternalagnetic $iel that give theini % an a*i %

orientation energies.

28.48 "or a agnetic ipole in aagnetic $iel , relate the

orientation energy U to the +orW one (y an e*ternal tor'%e as

the ipole rotates in the agnetic$iel .





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A coil o$ area A an N t%rns, carrying c%rrent i - in a %ni$or agnetic $iel B +ill e*perience a tor'%e τ given (y

+here μ is the *agnetic di+"le *"*ent o$ the coil, +ith agnit% e μ = NiA

an irection given (y the right han r%le.

3he orientation energy o$ a agnetic ipole in a agnetic $iel is

I$ an e*ternal agent rotates a agnetic ipole$ro an initial orientation θ i to so e otherorientation θ f an the ipole is stationary (othinitially an $inally, the +or W one on the

ipole (y the agent is



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28 S% ary

$%e Magnetic Field BH #e$ine in ter s o$ the $orce F B acting on a test particle +ith chargeq oving thro%gh the $iel +ithvelocity v

. 28-2

. 28-15

Magnetic F"rce "n a ! rrent!arr ing )ireH A straight +ire carrying a c%rrent i in

a %ni$or agnetic $iele*periences a si e+ays $orce

H 3he $orce acting on a c%rrentele ent i F in a agnetic $iel is

. 28-26

. 28-16

$"r e "n a ! rrent !arr ing!"ilH A coil o$ area A an N t%rns,

carrying c%rrent i - in a %ni$oragnetic $iel B +ill e*perience a

tor'%e τ given (y. 28-37

!%arge (article !irc lating ina Magnetic FieldH Applying e+ton/s secon la+ to the

circ%lar otion yiel s

H $ro +hich +e $in the ra i%s r o$the or(it circle to (e

. 28-28



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28 S% ary

$%e ,all ''ectH When a con %cting strip carrying ac%rrent i is place in a %ni$or

agnetic $iel B , so e chargecarriers +ith charge ! - (%il %p onone si e o$ the con %ctor, creating

a potential i$$erence V across thestrip. 3he polarities o$ the si esin icate the sign o$ the chargecarriers.

Orientati"n nerg "' aMagnetic &i+"leH 3he orientation energy o$ a

agnetic ipole in a agnetic $ielis

H I$ an e*ternal agent rotates aagnetic ipole $ro an initial

orientation θ i to so e otherorientation θ f an the ipole isstationary (oth initially an $inally,

the +or W one on the ipole (ythe agent is

. 28-38

. 28-39



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28 10 A proton travels thro%gh %ni$or agnetic


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28.10- A proton travels thro%gh %ni$or agnetican electric $iel s. 3he agnetic $iel is .

At one instant the velocity o$ the proton is . At that instant an in %nit vector notation, +hat is the

net $orce acting on the proton i$ the electric $iel isa- , (- , an c- = N k i

N k N k 19

1918

10)ˆ01.8ˆ41.6(

ˆ106.1,ˆ1044.1−

−−

×+

××−

28 18 In "ig 28 E a particle oves along a circle in a region o$ %ni$or


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28.18- In ig. 28 E, a particle oves along a circle in a region o$ %ni$oragnetic $iel o$ agnit% e 7 4 3 . 3he particle is either a proton or an

electron yo% %st eci e +hich-. It e*periences a agnetic $orce o$agnit% e .2 * 10 1 . What are a- the particleLs spee , (- the ra i%s o$ the

circle, an c- the perio o$ the otion= v 4.?? * 10 E Ks, r 0.00>1 ,% 8.? *10 M? s

28 2?- An electron $ollo+s a helical path in a %ni$or agnetic $iel o$


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28.2?- An electron $ollo+s a helical path in a %ni$or agnetic $iel o$agnit% e 0. 3 . 3he pitch o$ the path is E µ , an the agnit% e o$ theagnetic $orce on the electron is 2 * 10 1 . What is the electronLs

spee = v E . Ks


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28.4E- In "ig. 28 44, a etal +ire o$ ass m 24.1 g can sli e+ith negligi(le $riction on t+o hori ontal parallel rails separate(y istance 2. E c . 3he trac lies in a vertical %ni$or

agnetic $iel o$ agnit% e E. 3 . At ti e t 0 , evice & is

connecte to the rails, pro %cing a constant c%rrent i ?.1 Ain the +ire an rails even as the +ire oves-. At t E1.1 s ,+hat are the +ireLs a- spee an (- irection o$ otion le$t orright-=

. 4 * 10 2 Ks, le$t


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28. - 3+o concentric, circ%lar +ire loops, o$ ra iir 1 20 c an r 2 0 c , are locate in an xy plane5each carries a cloc +ise c%rrent o$ > A "ig. 28 48-.

a- "in the agnit% e o$ the net agnetic ipoleo ent o$ the syste . (- Nepeat $or reversec%rrent in the inner loop.

2.8E A. 2, 1.1 A. 2

28 2 A ( $ l h i i i ' $ hi $ il


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28.>2- A (ea o$ electrons +hose inetic energy is ' e erges $ro a thin $oil+in o+9 at the en o$ an accelerator t%(e. A etal plate at istance d $ro

this +in o+ is perpen ic%lar to the irection o$ the e erging (ea "ig. 28-. a- Sho+ that +e can prevent the (ea $ro hitting the plate i$ +e apply

a %ni$or agnetic $iel s%ch that in +hich m an ! are theelectron ass an charge. (- ;o+ sho%l (e oriente =

physics 101 - magnetic fields

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