A compass needle is not always balanced parallel to the Earth’s sur/ yt::g /dos;rndlh8ib*zbr0face, but one endd*b tg hib0:/z srolyn8:d/;r may dip downward. Explain.

Draw the magnetic field lines around a straight sect eymkl koj w2/w6zd;*xp6x5y 4ion of wire carrying a current horizonypo4dx zm 66e5jxk y/lwk *w2;tally to the left.

In what direction are the magnetic field lines surrounding a straig ntdme/u*q(ly33w r0fht wire carrying a current that is moving directly away from you?weu(mq y3/nflt d*0r 3

A horseshoe magnet is held vertically with the north pole on the left andy s-z*v/tt q)*b/ 0mthuz) ugh south pole on the right. A wire passing between the poles, equidistbthzyu-uv tz /m0t**)qgs /)hant from them, carries a current directly away from you. In what direction is the force on the wire?

Will a magnet attracth36a 0g2 x;dpkcksl.f any metallic object, or only those made of iron? (Try it and seedlh gk;2k. 3as0xfcp6 .) Why is this so?

Two iron bars attract each other no matter j-5le+c:ki6 c5zj xhd which ends are placed close together. Are both magnet6 i5:chkcxdj5-z lje+s? Explain.

The magnetic field due to current in wires in your home can affectk8dh- agv dl1txl)e(1+cupa h9v*r2t a compass. Discuss the effect in terms of +dl8chkahut(gpx1te) 21- v v*9a l drcurrents, including if they are ac or dc.

If a negatively charged particle enters a region o a8wijiy winin3n3rp;m g0h.6 ir5, 9vf uniform magnetic field which is perpendicular to the particle’s velocity, will the kinetic energy of the particle increase, decrease, or stay the same? Explain your answer. (Neglect gravity and assume there is no electric field ;hvip903n3gira ni.5m,yw n iw8ij6r.)

In(Fig. Below), charged particles move in the89hir/az s/uwnwc.o7ppd 2s 7 vicinity of a current-carrying wire. For each chr 2w n/o8z/.s u7ichp7pasw9darged particle, the arrow indicates the direction of motion of the particle, and the + or - indicates the sign of the charge. For each of the particles, indicate the direction of the magnetic force due to the magnetic field produced by the wire.

Three particles, a, b, and c, enter a magnetic field8n qk/dmmc67to4 tdubb7 rq oye4r. 3( as shown in Fig. 20–46. What can you say about the ch8cb yk( m4u./3tmo46bo7trr7dqnd q e arge on each particle?

A positively charged particle in a nonuniform magnetic field f+jv : qws5tm8(zkzzd( ollows the trajectory shown:qzws+(jzmdz k5 v8t( in
(Fig. Below). Indicate the direction of the magnetic field everywhere in space, assuming the path is always in the plane of the page, and indicate the relative magnitudes of the field in each region.

Can an iron rod attract a magnet? Can a magnet attract an iron dkbo 39.jek .xzi9x2grod? What must you considerkbx99o d32.kx z g.jei to answer these questions?

Explain why a strong magnet held near a CRpjwml*nv 2s ln)a ex;ly4916tT television screen (Section 17–10) causes the picture to become distorted. Also, expa6v1jmt lp4 slwy) xlen;* 29nlain why the picture sometimes goes completely black where the field is the strongest. [But don’t risk damage to your TV by trying this.][/But don’t risk damage to your TV by trying this.]

Suppose you have three iron rods, two of which are magnetize6gr9lx carrnd12*c7 co v j*.z7xzqa 1d but the third is not. How would you determine 1c r69*rxrgcn*2z7.ax aj cd loq17vzwhich two are the magnets without using any additional objects?

Can you set a resting electm+ z)zdx+ehopd++c ayc 4 ;v k6wp1.fnron into motion with a magnetic field? With an electric field? Exov+ n +h1 .+;yp6fzm4wk) e+ xcdcdazpplain.

A charged particle is moving in a circle under the influence of a uniform mag jcf2-*5 jed-g ennj5unetic field. If an electric field that points in the same dire5*nn g cjjedf-j-25uection as the magnetic field is turned on, describe the path the charged particle will take.

The force on a particle in a magnetic field is the idea behinvj b5hhgt7q:3d electromagnetic pumping. It is used to pump metallic fluids (such as sodium) and to pump blood in artificial heart machines. The basic design is shown in(Fig. Below). An electric field is applied perpendicular to a blood vessel and to a magnetic field. Explain how ions are caused to:hv 75qbhgt 3j move. Do positive and negative ions feel a force in the same direction?

A beam of electrons is directed toward a horizontal wire carry7x0mrcnb ve(u9: o p-cing a current from left to rig(o9npxrcc 0u vme-b7:ht
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields that surround ah( 8lx5gek(wa moving electric charge.ake5x hw gl(8(

A charged particle moves in a straight line tp v9 bog.aw fjal:w8(*hrough a particular region of space. Could there be a f(wal9gp a.*w8bj :o vnonzero magnetic field in this region? If so, give two possible situations.

If a moving charged particle is deflecte+jca8 kyf,v d,d sideways in some region of space, can we ck,v+dfc ,ayj8onclude, for certain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is a uniform magnetic/ml8*t oa22at0n mh1 hla7wwi field $\vec{B}$. Outside this region, B = 0 Can you inject an electron from outside into the field perpendicularly so that it will move in a closed circular path in the field? What if the electron is injected near the center?

How could you tell whe 6 b-h4oc sxzrp,vvn98ther moving electrons in a certain region of space are being deflected by an electric field or by a magnox6 z9c vbnhrpv-4,s8 etic field (or by both)?

How can you make a compass withoutp co*w3x 7x-9/kqhgzene 0n -g using iron or other ferromagnetic material?

Two long wires carrying equal current /;h+xazsi/p qw6qs+n s I are at right angles to each other, but don’t quite touch. Describep nhsi6qqsw/x /+; z+a the magnetic force one exerts on the other.

A horizontal current-carrying wire, free to move in Earth’s gravitational qbn;ckb3tze4 pm,x bl c1/0ea/) ha f5dv8w5j field, i w/c5njbdbqvkxl 4 e ; /p)0ahz5t3 8b1fmca,es suspended directly above a second, parallel, current-carrying wire.
(a) In what direction is the current in the lower wire?
(b) Can the upper wire be held in stable equilibrium due to the magnetic force of the lower wire? Explain.

Why will either pole:bg5 p4mocn3j of a magnet attract an unmagnetized piece of iron?

An unmagnetized nail will not atinh,f , bch(gibl (-8ttract an unmagnetized paper clip. However, if one end of the nail is in contact with a magnet, the ( th ibf8-,giblh, n(cother end will attract a paper clip. Explain.

Two ions have the same mass, but one is singly ionized andpo: aatc*ye z/b5iu9f ) 6l)oz the other is doubly ionized. How will their positions on the tc *5bae 6lozfoyap:z))iu 9/ film of a mass spectrometer (Fig. Below) differ?

What would be the effect on B in2kjs7tt, :9b f lmssxrq)b ,5wside a long solenoid if
(a) the diameter of all the loops was doubled,
(b) the spacing between loops was doubled,
(c) the solenoid’s length was doubled along with a doubling in the total number of loops?

A type of magnetic switch syeo7vn,d-h 1 wimilar to a solenoid is a relay . A relay is an electromagnet (the iron rod inside the coil does not move) which, when activated, attracts a piece of iron on a pivot. Design a relay to close an electrical switch. A relay is used when you need to switch on a circuit carrying a very large current but you dye1-hv7w od,no not want that large current flowing through the main switch. For example, the starter switch of a car is connected to a relay so that the large current needed for the starter doesn’t pass to the dashboard switch.

  (a) What is the magnitude of the force per meter of length on a straight wn9wk4:d/um+az o6 pwfire carryingf uw+wmd ko /n9p:az64 an 8.40-A current when perpendicular to a 0.90-T uniform magnetic field?    N/m
(b) What if the angle between the wire and field is 45.0$^{\circ}\,$?    N/m

  Calculate the magnitude of the magnetic force on a 160-m length of straight wireky 6dnb)iulg;a3 ob;r9 p-zo1 stretched between two towers carrying a 150-A current. The Earth’s magnlbr) ;o zd yk;6n 1g3-aboipu9etic field of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  Calculate the magnitude of the magneti zur5.q7an0ep+0k+,z cn tfx yc force on a 160-m length of straight wire stretched between two towers carrying a 150f p7,0+r zk.at0xznn+e q uy5c-A current. The Earth’s magnetic field of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  How much current is fw2-c)lskyacg l.p-j* g -ri)u; av i*hlowing in a wire 4.80 m long if the maximum force on it is 0.750 N when p2il- pcywi*-sgau -.)h c)*r;lv ag kjlaced in a uniform 0.0800-T field?    A

  A 1.5-m length of wire carrying 4.5 A of current is oriented horizontally. am oony76p 7i6At that point on the Earth’s surface, the dip angle of the Earth’s magnetic field maky a6 m7io6no7pes an angle of 38 $^{\circ}\,$ to the wire. Estimate the magnitude of the magnetic force on the wire due to the Earth’s magnetic field of $ 5.5\times10^{ -5}\;T$ at this point.    $ \times10^{-4 }\;N$

  The force on a wire carrying 8.75 A is a maximum03ek chox5ya xu-qk(3 of 1.28 N when placed between the pole faces of a magneaye c(0-5u khq o3x3xkt. If the pole faces are 55.5 cm in diameter, what is the approximate strength of the magnetic field?    T

  The magnetic force per; j:u gh*ijf(pkle/ 1x.*(uohsw(phy meter on a wire is measured to be only 35% of its maximum possible valjps ((kx1 uhhji* *elh:w ;.puofg/ y(ue. Sketch the relationship of the wire and the field if the force had been a maximum, and sketch the relationship as it actually is, calculating the angle between the wire and the magnetic field.    $^{\circ}\,$

  The force on a wire is a ma475 ( bzu8veah1njvtk ximum of $ 6.50\times10^{-2 }\;N$ when placed between the pole faces of a magnet. The current flows horizontally to the right and the magnetic field is vertical. The wire is observed to “jump” toward the observer when the current is turned on.
(a) What type of magnetic pole is the top pole face?  ----待选择----North PoleSouth pole 
(b) If the pole faces have a diameter of 10.0 cm, estimate the current in the wire if the field is 0.16 T. $\approx$   A(retain one decimal places)
(c) If the wire is tipped so that it makes an angle of 10.0° with the horizontal, what force will it now feel?    N

  Suppose a straight 1.00-mm-diameter copper wire csoyasg-of;l kz 1z;, ,ould just “float” horizontally in air because of the force due to the Earth’s magnetic 1fsk z,sa;oo,;zl - gyfield $\vec{B}$, which is horizontal, perpendicular to the wire, and of magnitude $5.0 \times10^{ -5}\;T$. What current would the wire carry?    A Does the answer seem feasible? Explain briefly.

  Alpha particles of chardptv-*626 a fkyr9+ an(b,cw rlu4ehige $q\,=\,+2e$ and mass m = $ 6.6\times10^{ -27}\;kg$ are emitted from a radioactive source at a speed of $1.6 \times10^{ 7}\;m/s$. What magnetic field strength would be required to bend them into a circular path of radius r = 0.25 m?    T

  Determine the magnitude and ds o c56 : z,jb3hsec*d*cumar0irection of the force on an electron traveling $ 8.75\times10^{5 }\;m/s$ horizontally to the east in a vertically upward magnetic field of strength 0.75 T.    $ \times10^{-13 }\;N$  ----待选择----NorthSouth 

Find the direction of the force on a negatk*x.ln mk jy9k9kd)7o8wq(ol ive charge for each diagram shown in (Fig. Bd) k .lq79lj n*xm (wyo8kk9okelow), where $\vec{v}$ (green) is the velocity of the charge and $\vec{B}$ (blue) is the direction of the magnetic field. ($\otimes $ means the vector points inward. $\ odot $ means it points outward, toward you.)

Determine the direction5zonbqy7o: c) of $\vec{B}$ for each case in(Fig. Below), where $\vec{F}$ represents the maximum magnetic force on a positively charged particle moving with velocity $\vec{v}$.

  An electron is projected vertically upycs-a6fs:hlth uaf+5ba*) 0u ward with a speed of $1.7 \times10^{6 }\;m/s$ into a uniform magnetic field of 0.350 T that is directed horizontally away from the observer. Describe the electron’s path in this field.    $ \times10^{-5 }\;m$

  A 5.0-MeV (kinetic energy) pfh. j40dl0:vkqo6mv a,ft9e v,uyz9xroton enters a 0.20-T field, in a plane perpendicular to the field0tzj 69exhuqyf: 9k.4m af,,vvvdl o0. What is the radius of its path?    m

  An electron experiences the greatesl9 h9,cq ygo7rt force as it travels $2.9 \times10^{6 }\;m/s$ in a magnetic field when it is moving northward. The force is upward and of magnitude $7.2 \times10^{-13 }\;N$. What are the magnitude and direction of the magnetic field?    T ----待选择----EastWest 

  What is the velocity of a beam o: zroxc-b57xc9l wz ,sf electrons that go undeflected when passing through perpendicular eleczr: czx sb5o-9wcl,7xtric and magnetic fields of magnitude $8.8 \times10^{3 }\;V/m$ and $3.5 \times10^{-3 }\;T$, respectively? What is the radius of the electron orbit if the electric field is turned off? $F_E$    $ \times10^{6 }\;m/s$ $F_{max}$   $ \times10^{ -3}\;m$

  A doubly charged helium atoh9, ab,6f8mz0yt dl1(mwzmvb -ug jm/m whose mass is $6.6 \times10^{-27 }\;kg$ is accelerated by a voltage of 2100 V.
(a) What will be its radius of curvature if it moves in a plane perpendicular to a uniform 0.340-T field?    m
(b) What is its period of revolution?    $ \times10^{ -7}\;s$

  A proton (mass $m_p$), a deuteron $(m=2m_p,Q=e)$, and an alpha particle $(m=4m_p,Q=2e)$ are accelerated by the same potential difference V and then enter a uniform magnetic field $\vec{B}$, where they move in circular paths perpendicular to $\vec{B}$. Determine the radius of the paths for the deuteron and alpha particle in terms of that for the proton. $r_d$ =    $r_p$ $r_{\alpha}$ =    $r_p$

Show that the time T required for a particle :lw- cpgdjfv*(q4 d ,f6)eo nc *l.ddpof charge q moving with constant speed v to make one circular revolution in a uniform magnetic en .pfq:d6v-4, gocj(fdl *pl)dwd*cfield $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of chargel2 hiu sey7b,p-w( l,nm5cp8q q moves in a circular path of radius r in a uniform magnetic field B. Show that its momentum is l8yli-(nhqupw mcp7 b e,s2,5p = qBr .

A particle of mass m and charge q moves in a circulao06xglpmg z+cz)g i ;-r path in a magnetic field B. Show that its kin;-+0x g6gcgzl zpi)o metic energy is proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular q l22p ztp+8dlmomentum of the particle in Problem 21 is $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves with a speed of 160 m/s perpendicular to the Eax utf1el zs:0/ won1zg2zu6-z0b jd;arth’s magneti-o sj xu0t zlg06z1:za2f/zw nu;1ebdc field of $5.00\times10^{-5}\mathrm{~T}$, If the bullet possesses a net charge of $13.5\times10^{-9}\mathrm{~C},$ by what distance will it be deflected from its path due to the Earth’s magnetic field after it has traveled 1.00 km?    $ \times10^{-7 }\;m$

  Suppose the Earth’s magnetic field at the equaxoa6,v;pf wk( 27 sgkator has magnitude $0.40\times10^{-4}\mathrm{~Т}$ and a northerly direction at all points. Estimate the speed a singly ionized uranium ion $(m=238\mathrm{u},q=e)$ would need to circle the Earth 5.0 km above the equator. Can you ignore gravity? $F_B$    $ \times10^{ 8}\;m/s$ $\frac{F_B}{F_g}$    $ \times10^{8 }\;$

  A proton moving with spc qyr8 -p6, 5ybq7ibqceed $\nu=2.0\times10^5\mathrm{~m/s}$ in a field-free region abruptly enters an essentially uniform magnetic field $B=0.850\mathrm{~T~}(\vec{\mathbf{B}}\perp\vec{\mathbf{v}}).$ If the proton enters the magnetic field region at a $45^{\circ}$ angle as shown in (Fig. Below),
(a) at what angle does it leave, $\theta$    $^{\circ}\,$
(b) at what distance x does it exit the field? x    $ \times10^{-3 }\;m$

  A jumper cable used to start a stalled vehicle)fo+ekc99d sln. z:d-ifxo c n7 zr(z- carries a 65-A current. How strong is the magnetic field 6.fi(n :o. nz czlkxf --s7o)9rdd+e 9zc0 cm away from it? Compare to the Earth’s magnetic field. $B_{cable}$   $ \times10^{-4 }\;T$ the field of the cable is about    times that of the Earth.

  If an electric wire is allowed to produce a magnetic field no larger than that c/mbk j1 )rarsh51ea6 of the Earth16)rb 5/k1sjracmhea $(0.55\times10^{-4}\mathrm{~Т})$ at a distance of 25 cm, what is the maximum current the wire can carry?    A

In (Fig. Below), a long straight wire carries current I out of the paqxs ,licee*zg 17 sa* 9/;twqlge toward you. Indicate, with appropriatsl/*l *cx9,zw t qsqai1ge; e7e arrows, the direction of $\vec{\mathbf{B}}$ at each of the points C, D, and E in the plane of the page.

  A vertical straight wire carrying an u owlaxuwes+nvw486p-g 0 z zt:1l7la/pward 24-A current exerts an attractive force per unit length of -ul z4 61lv+ w ntp g7we:z0ao8xwl/as$8.8\times10^{-4}\mathrm{~N/m}$ on a second parallel wire 7.0 cm away. What current (magnitude and direction) flows in the second wire?    A  ----待选择----upwarddownward 

  Determine the magnitude and direction o4l0p; 3auj; 8t 4ew;rdmkqvcn f the force between two parallel wires 35 m long and 6.0 cm apart, each carrying 0nlv;j uq4w 3dmtc8e4;p; ark 25 A in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s maaa5tz noirrs1g3z yuq(-;q. abmpz624fl )m. gnetic field is being carried out 1.00 m from an electric cable. b3o;p26(f. gizl qsaz m.4 az)5muat1 nyq rr-What is the maximum allowable current in the cable if the experiment is to be accurate to $\pm1.0\%?$    A

  A power line carries a curtrz f. /mg6j p9e6iq.nrent of 95 A along the tops of 8.5-m-high poles. What is the magnitude of the magnetic field produced by this wire at the ground? How does this comparezp .rqje6gi9m fn .6t/ with the Earth’s field of about $\frac{1}{2}G$?    $ \times10^{-6 }\;T$ The field of the cable is about    % that of the Earth.(retain two decimal places)

  Two long thin parallel wires 13.0 cm .f lgf,ahy77s:k+ues 0wosf: apart carry 25-A currents in the same direction. Dete7w efs :syhgfu7:s +o,0fka.lrmine the magnetic field at point P, 12.0 cm from one wire and 5.0 cm from the other(Fig. Below).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18 cm due south zd nrw6q qh;tpw)5 z63from a straight vertical wire carrying a 35-A current downward. In what direction does z6hr3;dn56pw )qqwtzthe compass needle point at this location? Assume the horizontal component of the Earth’s field at this point is $0.45\times10^{-4}\mathrm{~T}$ and the magnetic declination is 0$^{\circ}\,$.    $^{\circ}\,$ N of W

  A long horizontal wire carries 22.0 A of current due n2txd5vw/gbq c951 keiorth. What is the net magnetic field 20.0 cm due west of the wire29dq55x wtkgbvc1/ ei if the Earth’s field there points north but downward, 37$^{\circ}\,$ below the horizontal, and has magnitude $5.0\times10^{-5}\mathrm{~Т}?$
   $ \times10^{-5 }\;T$
$\theta$ =    $^{\circ}\,$ below the horizontal

  A straight stream of protons passes a given point in space at a rag 5c3h 3bwsk(kte of $1.5\times10^9\mathrm{~protons/s~}.$ What magnetic field do they produce 2.0 m from the beam?    $ \times10^{ -17}\;T$

Determine the magnetic field midway between two long straigc f768b srj c01/1ws*fvgf fg, 2qcuktht wires 2.0 cm apart in terms of the current I in one when the other carries 15 A. Assu t1jv f/c86grw7 0cfuq1sf2 ,*gf kbcsme these currents are
(a) in the same direction,
(b) in opposite directions.

  A long pair of wires conducts 25.0 A of dc cur ;w/g2piqe6t:etk r , 2jfhksedgh.;(rent to, and from, an instrument. If the insulated wires are of negligible diameter but are 2.8 mm apart, what is the magnetic field 10.00 cm from their midpoint, in their plane (Fig. Below)? /.,j wshid;e:kretpf(g2 tq ;g26 ek hCompare to the magnetic field of the Earth.
   $ \times10^{-6 }\;T$ The field of the wires is about    % that of the Earth.(retain two decimal places)

  A third wire is placed in the plane of the two wir wcw,jrg .v0w(es shown in (Fig. Below), parallel and just to the right. If it carries 25.0 A upward, what force per meter of length does it exert on each of the other two wiw rgvw,w0jc(.res? Assume it is 2.8 mm from the nearest wire, center to center.
$F_{near}$ =    $ \times10^{ -2}\;N/m$  ----待选择----attractrepel 
$F_{far}$ =    $ \times10^{ -2}\;N/m$  ----待选择----attractrepel 

  A compass needle points s2q7 fxq r6vg623$^{\circ}\,$ E of N outdoors. However, when it is placed 12.0 cm to the east of a vertical wire inside a building, it points 55$^{\circ}\,$ E of N. What are the magnitude and direction of the current in the wire? The Earth’s field there is $0.50\times10^{-4}\mathrm{~T}$ and is horizontal.    A  ----待选择----updown 

  A rectangular loop of wire lies in the same plane as a ootilm nhq8 v9k7d4xzm)) . 3/omu/1tzq /qkastraight wire, as shown i)i/z t./lvmhd1m94qqto z7q k namx/o8o3 )ukn (Fig. Below). There is a current of 2.5 A in both wires. Determine the magnitude and direction of the net force on the loop.    $ \times10^{ -6}\;N$  ----待选择----away from wiretowards wire 

  A long horizontal wire carries a current of 48 A.6h7j 7xfzpx-d 3tuqrbkbp 6d/gpn 2e(:o o+i . A second wire, made of 2.5-mm-diameter copper wire and parallel to the first, is kept in suspension magnetical o+xrid fn (hgdjxp3ze:-7 7 bo2bkt6 q6ppu/.ly 15 cm below (Fig. Below).
(a) Determine the magnitude and direction of the current in the lower wire.    A the current is to the  ----待选择----leftright 
(b) Is the lower wire in stable equilibrium?  ----待选择----not in stable equilibrium in stable equilibrium 
(c) Repeat parts (a) and (b) if the second wire is suspended 15 cm above the first due to the latter’s field.

  Two long wires are oriented so that they areud/yh1vu.x - d perpendicular to each other. At their closest, they are 20.0 cm apart (Fig. Below). What is the magnitude of the magndyu vdx/uh1-. etic field at a point midway between them if the top one carries a current of 20.0 A and the bottom one carries 5.0 A?    $ \times10^{-5 }\;T$

  Two long straight parallel wires are 15 cm apart. Wire A carries 2.0 i-nc 8p b.c,wz s4i8dsA current. Wire B’s current is 4.0 di ns4 iw-p.cbcz8 ,s8A in the same direction.
(a) Determine the magnetic field magnitude due to wire A at the position of wire B. $\approx$    $ \times10^{-6 }\;T$(retain one decimal places)
(b) Determine the magnetic field due to wire B at the position of wire A. $\approx$    $ \times10^{-6 }\;T$(retain one decimal places)
(c) Are these two magnetic fields equal and opposite? Why or why not?
(d) Determine the force on wire A due to wire B, and the force on wire B due to wire A. Are these two forces equal and opposite? Why or why not? $\approx$    $ \times10^{-5 }\;N/m$(retain one decimal places)

  Three long parallel wires are 3.8 cm from one another. (Looking algnms8a3fi )e5ong them, they are at three corners of an equilateral triangle.) The current in each wire is 8.00 A, but its direction in wire M is opposite to that in wires N and P (Fig. Below). Determine the magnetic force g58)3esnmaf iper unit length on each wire due to the other two.
$\frac{F_\text{M net y}}{l_\mathrm{M}}$ =    $ \times10^{ -4}\;N/m$ =    $^{\circ}\,$
$F_{N\,net}$ =    $ \times10^{-4 }\;N/m$ $\theta$ =    $^{\circ}\,$
$F_{P\,net}$ =    $ \times10^{ -4}\;N/m$ $\theta$ =    $^{\circ}\,$

  In (Fig. Below), determ 9lal+zlz, qq(ine the magnitude and direction of the magnetic field at the midpoint of the side of the tl(9 q a,qll+zzriangle between wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a distance d apart, carry e-*zqd d hkul fs-u81j;qual currents I in the same direction. One wire is at x = 0, the other is at x = d, (Fig. Below). Determlf*udj qk1;-d zh-8 suine $\vec{B}$ along the x axis between the wires as a function of x.

  A thin 12-cm-long soleno(gvyhrky zr ,56p8xl3zj ;3rcid has a total of 420 turns of wire and carries a current of 2.0 A. Calculate the field inside near the cente3 ,vh5yp(3 8z jrl g6;rzycrxkr.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameter is )wy. 1yjl0pm u7au-a 7fdir1b to produce a field of 0.385 T at its center. How much current should the solenoid carry if ityw ay-1 ia1 p7)7.uf drjbulm0 has 975 turns of the wire?    A

  A 550-turn solenoid is 15 cm long. The current in it isxp*y4//uoz8l kk*2yu ).lelbt/ucf i 33 A. A 3.0-cm-long straight wire cuts through the center of the solenoid, along a diameter. This wire carries a 22-A curl i l8ytp)c e2xzuku4*f/*uyolb //k.rent downward (and is connected by other wires that don’t concern us). What is the force on this wire assuming the solenoid’s field points due east?    N

You have 1.0 kg of copper and want to make a practical solenoid thoy:d we8n0km: at produces the greatest possible magnetic field for a given voltage. Should you make your copper wire long and thin, short and fat, or something else? k:0 eywod m8:nConsider other variables, such as solenoid diameter, length, and so on.

A toroid is a solenoid in the shape of a circle (Figka0s0t9z( qnd hiu 9+qlmk slxlp0 ,)1. Below). Use Ampère’s law along the circular path, shown dashed in (Fig. Below uhtml0)d ssqn xikp (,zl0190 kqal9+a), to determine that the magnetic field
(a) inside the toroid is $B=\mu_0NI/2\pi r$ where N is the total number of turns, and
(b) outside the toroid is B = 0 .
(c) Is the field inside a toroid uniform like a solenoid’s? If not, how does it vary?

(a) Use Ampère’s law to show that thetw/hrp48 n n)x magnetic field between the conductors of a c)tp /rn8 xhw4noaxial cable (Fig. Below) is $B=\mu_0I/2\pi r$ if r is greater than the radius of the inner wire and less than the radius of the outer cylindrical braid.
(b) Show that B = 0 outside the coaxial cable.

  A single square loop of wire 22.0 cm on a side is plac*:7 j aj:kgm5ymonp v6ds af*3ed with its face parallel to the magnetic field between the pnga* :mmd5:37vjyo s6j*pakfole pieces of a large magnet. When 6.30 A flows in the coil, the torque on it is $0.325\cdot N$. What is the magnetic field strength?    T

  A galvanometer needle deflectsq f+c n9o: v89t2f (sly40e4vcde ldxi full scale for a $53.0 -\mu A$ current. What current will give full-scale deflection if the magnetic field weakens to 0.860 of its original value?    $\mu A$

  If the restoring sprb:mfx+ b g;oh6ing of a galvanometer weakens by 25% over the years, what current will give full-scale deflm boh 6fgx+:;bection if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor dro89(otx*ux2a7wbh zfwfe 5p2hps by 12%, by what factor does the output torque chx7z bw8t(fe52fu w9x hp o*h2aange?

Show that the magnetic dipo,wu76 wlktcqh-0dl.0q+ b hiale moment M of an electron orbiting the proton nucleus of a hydrogen atom is related to ta l6qicq,t.wuh0blh+ 70kw -dhe orbital angular momentum L of the electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0i +xmg/ng0avfo6f. 8d cm in diameter and containing nine loops lies flat on the ground. The Earth’s mag 6dggi vo8a+xmf/. fn0netic field at this location has magnitude $5.50\times10^{-5}\mathrm{~Т}$ and points into the Earth at an angle of 56.0$^{\circ}\,$ below a line pointing due north. If a 7.20-A clockwise current passes through the coil,
(a) determine the torque on the coil,   $\times10^{-5}\mathrm{m}•\mathrm{N}$
(b) which edge of the coil rises up: north, east, south, or west?

  Protons move in a circle of radius 5.10 cm in a 0.566-T,c r+d4io),mz ylbf9y magnetic field. What value of electric field could make their paths straight? In what direction must it poin+ 4lbydcifm 9r,y,)o zt?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, ge cj5c/oos.s :ermanium atoms have radii of curvature equal to 21.0, 21.6, 21.9.soecs/ c:5 jo, 22.2, and 22.8 cm. The largest radius corresponds to an atomic mass of 76 u. What are the atomic masses of the other isotopes?

  Suppose the electric field between thfuhv pf 0k1*m0 k33m0ot2fr yxe electric plates in the mass spectrometer of (Fig. Belf3mpho0 x0k 2 fyuk m13*v0tfrow) is $2.48\times10^4\mathrm{~V/m}$ and the magnetic fields $B=B^{\prime}=0.68\mathrm{~Т}.$ The source contains carbon isotopes of mass numbers 12, 13, and 14 from a long-dead piece of a tree. (To estimate atomic masses, multiply by $1.67\times10^{-27}\mathrm{~kg.}$)
How far apart are the lines formed by the singly charged ions of each type on the photographic film?
$2r_{13}$ - $2r_{12}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)
$2r_{14}$ - $2r_{13}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)
What if the ions were doubly charged?
$2r_{13}$ - $2r_{12}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)
$2r_{14}$ - $2r_{13}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)

A mass spectrometer 4zh 2 cln92 o8weonlk;is being used to monitor air pollutants. It is difficult, however, to separate molecules with nearly equ ; w84oh9eon2nkzlcl2al mass such as CO (28.0106 u) and $N_2(28.0134u)$. How large a radius of curvature must a spectrometer have if these two molecules are to be separated on the film by 0.50 mm?

One form of mass spectrometer accelerate/c:cg.b.tz 6rheh ;dcs ions by a voltage V before they enter a magnetic fiel.;.hc g:chertd zb6/cd B. The ions are assumed to start from rest. Show that the mass of an ion is $m=qB^2R^2/2V,$ where R is the radius of the ions’ path in the magnetic field and q is their charge.

  A long thin solenoid has 430 loops of wire per meter, and a 25-A c1xo r4 9jeomael/ 2m1uurrent flows through the wie r1la12u/m4oxme9jo re. If the permeability of the iron is $3000\mu_0$ what is the total field B inside the solenoid?    T

  An iron-core solenoid is 38 cm long an9 mk68 1lmxmnrspr19fd 1.8 cm in diameter, and has 640 turns of wire. The magnetic field inside the solenoid r1p81rmsn9mk9 l mxf6is 2.2 T when 48 A flows in the wire. What is the permeability $\mu$ at this high field strength?    $\times10^{-5}\mathrm{T}\bullet\mathrm{m/A}$

  Protons with momentumw )yclszoe+t6d- ev3; $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ are magnetically steered clockwise in a circular path 2.0 km in diameter at Fermi National Accelerator Laboratory in Illinois. Determine the magnitude and direction of the field in the magnets surrounding the beam pipe.    T

  A proton and an electron have the same kin d-uqi,:bmd kxh-pk v96p49 pdetic energy upon entering a region of constant mp,pk x9d 4-i-u d6kb:hv dqm9pagnetic field. What is the ratio of the radii of their circular paths?   

  The power cable for anzle18 qe4sx pkr00 .vzp v79av electric trolley (Fig. Below) carries a horizontal current of 330 A toward the east. The Easl. 718p9k ve e rv0azqpzxv04rth’s magnetic field has a strength $5.0\times10^{-5}\mathrm{~T}$ and makes an angle of dip of 22$^{\circ}\,$ at this location. Calculate the magnitude and direction of the magnetic force on a 15-m length of this cable.    N the force on the wire is  ----待选择----southerlynortherly  and   $^{\circ}\,$ above the horizontal .

  Calculate the force on an airplane which has acquired a oby 7p6di* ip sfm2ed:skl6-6net charge of $1550\mu C$ and moves with a speed of 120 m/s perpendicular to the Earth’s magnetic field of $5.0\times10^{-5}\mathrm{~T}$.    $ \times10^{-6 }\;N$

  Near the equator, the Eart9t2sx+m2r; fve 5 zzxeh’s magnetic field points almost horizontally to the north anx; tfvz+92 2e r5emszxd has magnitude $B=0.50\times10^{-4}\mathrm{~T.}$ What should be the magnitude and direction for the velocity of an electron if its weight is to be exactly balanced by the magnetic force?    $ \times10^{-6 }\;m/s$  ----待选择----eastwest 

  A doubly charged helium atom, whose mass is rv7-ygfd36xsivumuo 3::kw 48)szp 5/h zcwp$6.6\times10^{-27}\mathrm{~kg},$ is accelerated by a voltage of 2400 V.
(a) What will be its radius of curvature in a uniform 0.240-T field? $\approx$    m (retain three decimal places)
(b) What is its period of revolution?    $ \times10^{-7 }\;s$

  A sort of “projectile launcher” isxd8j4g, qmns49, awsv shown in (Fig. Below). A large current moves in a mga,sjqn 89d44x,ws vclosed loop composed of fixed rails, a power supply, and a very light, almost frictionless bar touching the rails. A magnetic field is perpendicular to the plane of the circuit. If the bar has a length L = 22cm, a mass of 1.5 g, and is placed in a field of 1.7 T, what constant current flow is needed to accelerate the bar from rest to 28m/s in a distance of 1.0 m? In what direction must the magnetic field point?
   A
the magnetic field must be ----待选择----updown 

  In (Fig. Below) the top wire is 1.00-mm-diameter copper i06etd .ur+poe:8d yr wire and is suspended in air due to the 0ui+ r68:proded eyt.two magnetic forces from the bottom two wires. The current flow through the two bottom wires is 95 A in each. Calculate the required current flow in the suspended wire.    A

Two stiff parallel wires a distance l apart g /yt.e;ax0 zvin a horizontal plane act as rails to support a light metal rod of mass m (perpendicular to each railyagx zv0/ .;te), (Fig. Below). A magnetic field $\vec{B}$, directed vertically upward (outward in the diagram), acts throughout. At t = 0, wires connected to the rails are connected to a constant current source and a current I begins to flow through the system. Determine the speed of the rod, which starts from rest at t = 0, as a function of time
(a) assuming no friction between the rod and the rails,
(b) if the coefficient of friction is $\mu_k$.
(c) Does the rod move east or west if the current through it heads north?

  Estimate the approximate maximum deflection of the electx *be*uby*1xn ron beam near the center of a nx1y*ux * *ebbTV screen due to the Earth’s $5.0\times10^{-5}\mathrm{~T}$ field. Assume the CRT screen is 22 cm from the electron gun, where the electrons are accelerated
(a) by 2.0 kV,    mm(Round to the nearest integer)
(b) by 30 kV. Note that in color TV sets, the CRT beam must be directed accurately to within less than 1 mm in order to strike the correct phosphor. Because the Earth’s field is significant here, mu-metal shields are used to reduce the Earth’s field in the CRT.    mm(Round to the nearest integer)

The cyclotron (Fig. Below) is a device used to accemd5 4z*ecng1r3gjz y( +pv;ndlerate elementary particles such as protons to high speeds. Particles starting at point A with some initial velocity travel in circular orbits in the magnetic field B. The particles are accelerated to higher speeds each time they pass through the gap between the metal “dees,” where there is an electric field E. (There is no el4+zv jdc5 zd ergmyn;3p1n *(gectric field inside the hollow metal dees.) The electric field changes direction each half-cycle, owing to an ac voltage $V=V_0\sin2\pi ft,$ so that the particles are increased in speed at each passage through the gap.
(a) Show that the frequency f of the voltage must be $f\,=\,Bq/2/pi m,$ where q is the charge on the particles and m their mass.
(b) Show that the kinetic energy of the particles increases by $2qV_0$ each revolution, assuming that the gap is small.
(c) If the radius of the cyclotron is 2.0 m and the magnetic field strength is 0.50 T, what will be the maximum kinetic energy of accelerated protons in MeV?

Four very long straight parallel wires, locatedbkj4sc 3;wxs40yy bvs::9wwf at the corners of a square of side l, carry equal cs 3ybssb; kj xwwv:y9f4w40:currents $I_0$ perpendicular to the page as shown in (Fig. Below). Determine the magnitude and direction of $\vec{B}$ at the center C of the square.

  Magnetic fields are very ubaw w(fb e1jh64f7pdtgl w m06vk1)a(seful in particle accelerators for “beam steering”; that is, the magnetic fields can be used to change the beam’s direction withoutth64ea7v 1kmf1pd 6ww b0(f)j(wa lbg altering its speed (Fig. Below). Show how this works with a beam of protons. What happens to protons that are not moving with the speed that the magnetic field is designed for? If the field extends over a region 5.0 cm wide and has a magnitude of 0.33 T, by approximately what angle will a beam of protons traveling at $ 1.0\times10^{7 }\,m/s;$ be bent?    $^{\circ}\,$

  The magnetic field B at the c*h-tmam0ck3p enter of a circular coil of wire carrying a current I (as itm-mh30a* cpk n Fig. Below) is
$B=\frac{\mu_{0} N I}{2 r},$
where N is the number of loops in the coil and r is its radius. Suppose that an electromagnet uses a coil 1.2 m in diameter made from square copper wire 1.6 mm on a side. The power supply produces 120 V at a maximum power output of 4.0 kW.
(a) How many turns are needed to run the power supply at maximum power?    turns
(b) What is the magnetic field strength at the center of the coil?    $ \times10^{-4 }\;T$
(c) If you use a greater number of turns and this same power supply (so the voltage remains at 120 V), will a greater magnetic field strength result? Explain

  Near the Earth’s poles ty7g)g qo53-g cie8jcd he magnetic field is about 1G($ 1\times10^{ 4}\;T$) Imagine a simple model in which the Earth’s field is produced by a single current loop around the equator. Roughly estimate the current this loop would carry. [Hint: Use the formula given in Problem 80.]    $ \times10^{ 9}\;A$

  You want to get an idea of the z .adx:e.ms7/f vm9kso6 v/hdy e k1y6magnitude of magnetic fields produced by overhead yy. hf9ds6 :x7ksk .z/e mvo6ad1e/vmpower lines. You estimate that the two wires are each about 30 m above the ground and are about 3 m apart. The local power company tells you that the lines operate at 10 kV and provide a maximum of 40 MW to the local area. Estimate the maximum magnetic field you might experience walking under these power lines, and compare to the Earth’s field. [For an ac current, values are rms, and the magnetic field will be changing.] $B_{net}$ $\approx$    $ \times10^{ -5}\;T$(Round to the nearest integer)

  (a) What value of magnetic fiel/,3q7i )zghrr z k3v6ra.zy l:2 zntmid would make a beam of electrons, traveling to the right at a spha : v 6)z3z3lnrtmyi7kqgrz/,i.r2zeed of $4.8 \times10^{ 6}\;m/s$ go undeflected through a region where there is a uniform electric field of 10,000V/m pointing vertically up?    $ \times10^{ -3}\;T$(retain one decimal places)
(b) What is the direction of the magnetic field if it is known to be perpendicular to the electric field?
(c) What is the frequency of the circular orbit of the electrons if the electric field is turned off?    $ \times10^{7 }\;Hz$

  A proton follows a spiralg-.h :fimfiimt u+ 5,q path through a gas in a magnetic field of 0.010 T, perpendicular to the plane of the spiral, as shown in (Fig. Below). In two successive loops, at points P and-ii hmiut +:5f,.qmfg Q, the radii are 10.0 mm and 8.5 mm, respectively. Calculate the change in the kinetic energy of the proton as it travels from P to Q.    $ \times10^{-20 }\;J$

  A 32-cm-long solenoid, 1.8 cm in diameter, is to produce a 0.pl dd( klwd(;530-T magnetic field at its;dp ll dkd(w5( center. If the maximum current is 5.7 A, how many turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, each of diameter 0.50 mm+s4( ,m bqv4czc-8 x4cstsuqp, carry the same current but in opposite dis -+ c(48 qsbvuspcxqz4tm4,crections. They are suspended by 0.50-m-long strings as shown in (Fig. Below). If the suspension strings make an angle of 3.0$^{\circ}\,$ with the vertical, what is the current in the wires?    A

  An electron enters a uniform magnetic field B = 0.23 T at a 45o+1 o0yyd zbj1$^{\circ}\,$ angle to $\vec{B}$. Determine the radius r and pitch p (distance between loops) of the electron’s helical path assuming its speed is $3.0 \times10^{6 }\;m/s$. See (Fig. Below).
r $\approx$    $ \times10^{-5 }\;m$ (retain one decimal places)
p =    $ \times10^{-4 }\;m$