A compass needle is not always balanced paralle bv9wh9 8/ f3ms3.wjr8npx jutwe7f+dl to the Earth’s surface, but one end may d383vf.x jr9hpf bwjmt u8/sn9w e7+w dip downward. Explain.

Draw the magnetic field lines arounbc (s5ukgksk, q.d: rtx-z 1)huyhr8+ d a straight section of wire carrying a current horizonc-,:shrgt ky)qhu sbx+ .k85rzd (1kutally to the left.

In what direction are the magnetic field lines surrounding a stra l+ 3s*p*j-bhsauge:night wire carrying a *as:j+n 3 sgl*b ph-eucurrent that is moving directly away from you?

A horseshoe magnet is held vertically with the north p07* kgv+upnss. nxe p9ole on the left and south pole on the right. A wire passing between the poles, equidistant from them, carries a current directly away fromnk +ug7pven0.9*psx s you. In what direction is the force on the wire?

Will a magnet attract any metallc v cv*70:)v - kmg+ 9x9eiz-xmaezineic object, or only those made of iron? (Try it and see. av9g*7)9- mnxezvvk:ci0c e+ zx m-ei) Why is this so?

Two iron bars attract each other no matter which ends are placed cloed e500slk h0zse together. Are both magnets?lzk e hed5000s Explain.

The magnetic field due to currenzll, 2caode 6.t in wires in your home can affect a compass. Discuss the effect in terms of current.6lle,doa2 c zs, including if they are ac or dc.

If a negatively charged particle enters a region of uniform magnequ3 tn spm 6y+re2yp90tic field which is perpendicular to the 2sr eumpty+n6p30q 9y 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.)

In(Fig. Below), charged particles move in the vicinity of a currebm m 4 w*db)c4lmhlx+-nt-carrying wire. For each charged 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 forb4m hdlm4w)b *+c-m lxce due to the magnetic field produced by the wire.

Three particles, a, b, and c, enter a magnetic field as shown in Fig. 20–46.+8yl5lk6; sd o*lau tkk0;et e What cok e8+k*tl0l5 ; ukdyet;as6lan you say about the charge on each particle?

A positively charged particle in a nonuniform magnetic field mvcy+3sj 3+7vxgqgq) x3h dv:follows the trajectory shown hq :)gdmvcgv jx+33v+sx 7qy3 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 hx+x8dxs .cw3k-i /6mx3nzr ya magnet? Can a magnet attract an iron rod? What must you cox xxcs. -3x d +kmrz8ny3ih6/wnsider to answer these questions?

Explain why a strong magnet held near a CRT televisio+fnn*0 xdj,z x m;dve;n screen (Section 17–10) causes the picture to become distorted. Also, explain why the picture sometimes goes completely black where the field is the strongest. [But don’t risk damage to your TV by trying this.][/Butvjd*f;,0xnenzmd x; + don’t risk damage to your TV by trying this.]

Suppose you have thr.)wit l dk;yh1ee iron rods, two of which are magnetized but the third is not. How would yk. yw1; d)lithou determine which two are the magnets without using any additional objects?

Can you set a resting yh;mex ;g+,s uvm;0koelectron into motion with a magnetic field? With an electric fiy ;mu+e x,v0ohkg m;;seld? Explain.

A charged particle is moving in a circleqm:vdnz*9o 3 l under the influence of a uniform magnetic field. If an electric field that points in the same direction9nqzdl*v:m o3 as the magnetic field is turned on, describe the path the charged particle will take.

The force on a particle in a mhlu6d:s0z cdcz2vk 0wsp ./;aagnetic field is the idea behind 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 ac:6w0 a./p2cdzk0sslzvd u h; magnetic field. Explain how ions are caused to move. Do positive and negative ions feel a force in the same direction?

A beam of electrons is directed toward a horizontax ,p0ukx+mp wa6b/ *j4i,tgs(lk p0sml wire carrying a current from lef+ s0l a6ipjx4m0kp,*xwgspk/ ,(t ubmt to right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic g1*xe,s7z:jk g pzus+bs(u*pfields that surround a moving electric charge.pes7*1 u zjuk( ,:sz+ *gpgxbs

A charged particle moves in a straight line through a particula z;q0cqnp ghs0qp7 8;b. xxh8pr region of space. Could .b gcxhp0n ;0hq8 qp78p; qzsxthere be a nonzero magnetic field in this region? If so, give two possible situations.

If a moving charged particle is deflected sidewaysc ff )l)bjm0w9 in some region of space, can we conclude, for cwm)fj0)c9 l fbertain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is a uniform magnetic fiel8b w9bl)xk 3sym9)wug7 gh.wz d $\vec{B}$. 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 whether moving electrons in a certain region of space ar h7i.b wl z8fagf6iep;u j,3ha. tx9rp80ytr2e being deflected by an elecgiu .fpe.68 9jr2afh,ir8 a;h ztl0ptb xy3w7tric field or by a magnetic field (or by both)?

How can you make a compass wfp1w;wrv9 ,g r9emiu 62z4lzke3l f/oithout using iron or other ferromagnetic material?

Two long wires carrying equal currents bbj y8bzgk85a76 z (.jb5axhmI are at right angles to each other, but don’t quite touch. Describe the magnetic force one exerts on the8 zjab6g8j(hmbxkbaz55. by 7 other.

A horizontal current-carrying wire, free to move in Earth’s gravitationalq nrb* w hjo0n*)ngd8gx un 0:1sogn(6souu52 field, is suspended dirn) u*u ghnjxo n 5(b1rgnog 0:6 onsd0w*8s2uqectly 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 of a magnet attract an unmagnetiuvfch4x sj+0r 1u 3at6zed piece of iron?

An unmagnetized nail yw)tt5m ub; d58kue;g will not attract an unmagnetized paper clip. However, if one end of the nail is in contact with a mattdgeu 5yb mw;);u58kgnet, the other end will attract a paper clip. Explain.

Two ions have the same mass, but one v7 c.v-0 unyks sfpse(tf+5a4rrn+f. is singly ionized and the other is doubly ionized. How will their positions on the film of a mass spectrometer (Figve fkssrnf 4 s .ay 7+uf+5-pr.t0nv(c. Below) differ?

What would be the effect on B inside a long sole- t9 nlm,htmh7noid 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 similar to a solenoid is a relay . A relay is an eleow7qk0a1gz (solvn4 a (k04xce 6th4ictromagnet (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 ugk(z l(so7xa eq0aio6wck41 t44 hn 0vsed when you need to switch on a circuit carrying a very large current but you do 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 for5.a2m64o .q1acbwhec7+qad vp 3zwojce per meter of length on a straight wire carrying an 8.40-A cu. coc4av.1+2a7 hqm3eq6w o wjpadzb5rrent 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 for*0z/48ofzncp pe-rs d uo35 jlce on a 160-m length of straight wire stretched be5c zps8*z-de/uor 0f4l3opnjtween two towers carrying a 150-A current. The Earth’s magnetic field of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  Calculate the magnitude of the magnetic force on a 160-m length;o (6z7h cswg-cl)frf of straight wire stretched between two towers carrying a 150-A current.c fsz6-)(;rwgch of7l 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 flowing in a wire 4.80 m long if the maximutn. ere6kh+jt,o +aq1 m force on it is 0.750 N when prtoe.etj,6+ ah n1 kq+laced in a uniform 0.0800-T field?    A

  A 1.5-m length of wire carrao vdtz w4l:/ti0kg/:ying 4.5 A of current is oriented horizontally. At that point on the Earth’s surface, the dip anz:dt/0tl: igk o/4 vawgle of the Earth’s magnetic field makes 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 p 0oi9 4 kiu8,ln7caogv gop078.75 A is a maximum of 1.28 N when placed between the pole faces o4pn0 a o 8v lpi7c7io,o0gkgu9f a magnet. If the pole faces are 55.5 cm in diameter, what is the approximate strength of the magnetic field?    T

  The magnetic force per meter on a wire is measured to bea)6/b 6m2hp i3i p*: ieytpcol only 35% of its maximum possible value. Sketch the relationship of the wire and the field if the force had been a maximum, and sketch th*6lp6/i2hc:a3i p yi)bm otpee relationship as it actually is, calculating the angle between the wire and the magnetic field.    $^{\circ}\,$

  The force on a wire b9oh9vzn ou29p qaj4oa 3 sx+,is a maximum 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 could just “float” prm2g2w/c*f k)( n*nifbi( lahorizontally in air because of the/ 2n() niwg rbaki2clf(mp**f force due to the Earth’s magnetic field $\vec{B}$, 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 chbr b ptjc4n*.0arge $q\,=\,+2e$ 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 dir omt pxa e)x0z9gzje(rdeux tu.d6h2-,7g ; r+ection 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 negative cx*q e,5wfg n7vharge for each diagram shown in (Fig. Below), where v75 exqgnwf*,$\vec{v}$ (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 direction o142upa(cbgmoeoc ++q z-p e jwr4 x)*mf $\vec{B}$ 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 upktcg,m r 7ac rmxkfum z2*20bo;2x 8/xward 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)(z;5e( dv2c gvf (ebtk proton enters a 0.20-T field, in a plane perpendicular to the fielkv(c (5;gbz2def ev(td. What is the radius of its path?    m

  An electron experiences the greatest force as it t 5t j9b+whhq9hravels $2.9 \times10^{6 }\;m/s$ 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 bgmx 3 ru2s2mw7eam of electrons that go undeflected when passing through perpendicular electric and magn su23wxmrg 27metic 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 atom wh(u0rt,n ibv mvc /z tdw04zj21ose 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 4p39qptaqz )mx x-7om of charge q moving with constant speed v to make one c-p)q9 a4tmmxx3 opqz7ircular revolution in a uniform magnetic field $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge q moves inv.7 zvl59 :giwz rzr8y a circular path of radius r in a uniform magnetic field Bz9v ivy7z:8.w5 lrgzr. Show that its momentum is p = qBr .

A particle of mass m and charge q moves in a circul eio p+a8 v1ecm1o2,bnar path in a magnetic field B. Show that 1,ao2 nie8o1pvb c+emits kinetic energy is proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momes zz0i1i byjfe3d,/m /ntum 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 16jp3jz r,cm l57gr7n5t 0 m/s perpendicular to the Earth’s magnetic f tjjrn57,35 m rpgclz7ield 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 iue8 yv2y13p,yw kj v+mrc2 5z/mia .hthe equator 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 spe6iacko)jsu2e.us qu x46rz77 ed $\nu=2.0\times10^5\mathrm{~m/s}$ 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 carries a 62 krg ktv0 k.qodq3p(*5yyw :a5-A current. How strong is the magnetic field 6.0 cm away from it? Compare to thwq rko 0dq3.(gkp y2av*tyk:5e 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 at+ -c wi8k-ncf5fzz ioq/ vt:2llowed to produce a magnetic field no larger than that ofzqc vz: 8ct2fk- o/+tiwfin-5 the Earth $(0.55\times10^{-4}\mathrm{~Т})$ 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 7v;dt25ruvho(j /f :-nrdu laout of the page toward you. Indicate, with appropri;nu j27:vahrfo5vt u-l/r d(date 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 aq7oxws g8 g1.2 cj4xoun upward 24-A current exerts an attractive forcw2.4g1jco 8goxsqux7 e per unit length of $8.8\times10^{-4}\mathrm{~N/m}$ 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 magnit nmi8, *1.gjmpoeb jp0ude and direction of the force between two parallel wires 35 m long and 6.0 cm apart, eac1 p .mmj08*g jebip,noh carrying 25 A in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic field is being carried out8 kl7ax4ws kv2nmlbsj 42:+sd 1.00 m from an elect amkkx74d8 l:bjvwn+24slss 2ric cable. 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 current of 95 A along the tops of 8.5-m-high poles. Wha*k rtatcf evwu8:sv(54:o/m rt is the magnitude of the magnetic field produced by this wire at the ground? How does this compare with the Earth’s field of a5w (:ck 8/v* te4tro rfsu:vambout $\frac{1}{2}G$?    $ \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 apart carry 25-A currents)gc0kt n1/uf-p,e1eqykw(vy in the same direction. Determine the magnetic field at point P, 12.0 cm from one wire and 5.0 cm from the othek0u1n-qefwy) eg/cv p1 t(k,yr(Fig. Below).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18 cm duei)x/ bz r,7h (ytr,efo south from a straight vertical wire carrying a 35-A current downward. Inb e() , /z,oixrr7tyhf what direction does the 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 north. What is the net magn bcfa-b v2m8m2sl -/gjetic field 20.0 cm due west of the wire if thev/a -c2lbmsjb8 g -f2m 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 protony+8pa;w zt0vj o(h6vzk)x gh8s passes a given point in space at a rate 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 betwe+7 +dskw9sspeen two long straight wires 2.0 cm apart in terms of the current I ind+ 7 9pe+sksws one when the other carries 15 A. Assume these currents are
(a) in the same direction,
(b) in opposite directions.

  A long pair of wires conducts 25.0 A of dc current 0: p)np8ihb r0xocva2k kz j9*to, and from, an instrument. If the insulated0v:9bo h0 )xjr8zp*akkc2 np i 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)? Compare 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 pl16 r+ w67kzqz- ,s9zy:z cmzig .ovltcane of the two wires shown in (Fig. Below), parallel and just to the right. If it carries 25.0 A upward, what force per meter of lengzzzsqlz -m17 :r izc6vok9t+.c,ywg 6th does it exert on each of the other two wires? 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 poin-e g:d a;t3(ci9vi ,y u*yeq/ w;jmihzts 23$^{\circ}\,$ 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 straight wire,*nxdm3.slvpp l kk3; 0 as shown in (Fig. Below). There is a current of 2.5 A in bothd.kv 3n;3m0l ppks*lx 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 currens axo0.c:vaoq3w rkt4x95v r7t of 48 A. A second wire, made of 2.5-mm-diama9 v qaoxc5.s30rt4 :kvx o7rweter copper wire and parallel to the first, is kept in suspension magnetically 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 orient scgjf55l3 ox(ed so that they are perpendicular to each other. At their closest, they are 20.0 cm apart (Fig. Below). What5 o (scj35gflx is the magnitude of the magnetic 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 parallelg w;e g/vsu6-g wires are 15 cm apart. Wire A carries 2.0 A current. Wire B’s current is 4.0 A igg/-6 s;ewu vgn 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 along them- 9dktjzy+ b)r, they are at three corners of an equilateral triangle.) The current in each wire is 8.00 A, butt+k 9 z)j-bydr its direction in wire M is opposite to that in wires N and P (Fig. Below). Determine the magnetic force per 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), determine the magnitude and direction of tu n+p/by(l m/pblq+/ihe magnetic field at the midpoint of thelpy(/b mpnub+ /i/+lq side of the triangle between wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires,t8pp tg/i33la i3 2pzz a distance d apart, carry equal currents I in the same direction. One wire iailp 3pi3gpz82 / zt3ts at x = 0, the other is at x = d, (Fig. Below). Determine $\vec{B}$ along the x axis between the wires as a function of x.

  A thin 12-cm-long solenoid has a total of 420 turns of wire and carries a currwowor2r- .zea8 l955tm l k,wfent of 2.0 A. Calculatf.r z-tl95k ,or 2ameww 58owle the field inside near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameter is to produce l.2 8an(pdg-lwpb p w17rxt. ya field of 0.385 T at its center. How much current should the solenoid carry if it has 975 turns of tlxdpy2wp tl8br.n(- wp.7 ag1he wire?    A

  A 550-turn solenoid isu,xma5g)j7lqh,q d - yl;nx8 e 15 cm long. The current in it is 33 A. A 3.0-cm-long straight wire cuts through e x8,d;7glmqxqnyau5j),l h - the center of the solenoid, along a diameter. This wire carries a 22-A current 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 cx 79n cvc df4bp1jq(py2-*t al.bplj*opper and want to make a practical solenoid that 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? Consider other variables, such as xvq*(-c1p.2jb9fl 4blcnt*a y pdp7j solenoid diameter, length, and so on.

A toroid is a solenoid in the shape of a circle (Fi e yg:9qb 1b.uansu4wyxj3s(-(rd1gv g. Below). Use Ampère’s law along the circular path, b314 egy9q-ujgsy( (w:v dsun1x.arbshown dashed in (Fig. Below 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 the magnetic field between the conductor0fh;,m y/ami7nhi5 uy s of a coaxial ,a/5f hmhi7y 0;uimyn 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 placed z9mvdh/t/+ :l 4bq;t gdut);k6ouxtz with its face parallel to the magnetic field between the pole pieces of a large magnet. When 6.30 A flows in the coil, the torque on it t4t/9g ok6 dlzxuth/;v)d:umq +zbt ;is $0.325\cdot N$. What is the magnetic field strength?    T

  A galvanometer needle deflect:e2w8 zj-t0ua iz/caw s 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 spring of a galvanometer weqvvr*8,ey.d9v y 5 tygakens by 25% over the years, what current will give full-svy5v yry v,g98d.*etqcale deflection if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by what we, /j*ach tt( /3clckfactor does the output torque change/,kl ae/t 3c*w hct(jc?

Show that the magnetic dipole moment M of an electron orbiting the proton nucle.(2/ nx *lqmaym ltm 20bl5svbus of a hydrogen atom is related to the orbital angular momentum L of the electxq2t *l0mn vsb/y(2 m5l.albmron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter and containing nine loops lies flzf 9*t0d3di3xl2tw kf at on the ground. The Ek xitw9zd33t2flfd *0arth’s magnetic 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 0.56zad)5m +;c.bfdlbjh -6-T magnetic field. What value of electric field could make their paths st)f+ -.acmlz;bd dbh5j raight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atol sla- 7izq08ex6w qq;ms have radii of curvature equal to 21.0, 21.6, 21.9, 22.2, and 22.8 cm. The larglzqlqsq 6wxa708;i e-est radius corresponds to an atomic mass of 76 u. What are the atomic masses of the other isotopes?

  Suppose the electric field between the electric plates in the mass spect;9 xletek2lqioh +y 6lw7 (h7jrometer of (Fig. Belo7+6k2 ;lloe7hhtiey w xlq9j(w) 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 is being used to monitor air pollutants. It is dind g60auh/n 8mfficult, however, to separate molecules with nearly equal mass such as CO (anm0ghu86 nd /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 accelerates ions by a voltage V beforel6ffua*y r8al47 *ejx they enter a magnetic field B. The ions are assumed to start from rest. Show that the mass of yrll**4uf7j68f ea x aan 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 4o3w0ly5 gpyi) 30 loops of wire per meter, and a 25-A current flows through the wire. If the permeability of the iron is 0)y5l iow 3ypg$3000\mu_0$ what is the total field B inside the solenoid?    T

  An iron-core solenoid is 38 cm longf8r +6pqqh*rc and 1.8 cm in diameter, and has 640 turns of wire. The magnetic field inside the solenoid is 2.2 T when 48 A flows in the wire.q*p6 fhqc+rr8 What is the permeability $\mu$ at this high field strength?    $\times10^{-5}\mathrm{T}\bullet\mathrm{m/A}$

  Protons with momentu8cc,s5rfce o a7xhi6) m $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 kinetic energy upon entering a regi(jvpp(fnp2 d.ns9y e6on of constant magnetic field. Whvjeyn (.6n(ppf p sd29at is the ratio of the radii of their circular paths?   

  The power cable for an electric trolley (Fig. Below) carries a horizontal c, k+m6ezhqc(jurrent of 330 A toward the east. The Earthjqkz ,h(6 +ecm’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 w: r g.-y9cw,7kglpfhq hich has acquired a net 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 Earth’s magnetqujquux bpb.p c(pdae/35e0c (t)/ 5uic field points almost horizontally to the north up0x d eju b( utu()a5.pep 3/cbq5qc/and 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 mf g4dka0o,c(wfvf* 45g3xxme ass is $6.6\times10^{-27}\mathrm{~kg},$ 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 latrc2fe wv;8azm0*w//2d qvtiuncher” is shown in (Fig. Below). A large current moves in a closed 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 restwam f* t8/q0 ew2t/zvvc2;rid 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-m-ra3v wr/c1f ce db tb/-a4xa8m-diameter copper wire and is suspended in air due to the two magnetic forces from the bottom two wires. The current flow through the two bottom wires is 95 A in each. Calculate thb 3dtb-xc//ac- vrw 4 8faaer1e required current flow in the suspended wire.    A

Two stiff parallel wires a 5u8jy*qubp5*f9 zsz8x c kdr2distance l apart in a horizontal plane act as rails to support a light metal rod of mass m (perpendicular to each rail), (Fig. Below). A magnetic field b8u5*c jyfzk*8 pu59rdx q 2zs$\vec{B}$, 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 deqqa(z*+f0 :bxxul k t:flection of the electron beam near the center of a TV screen due to t:q(x*u f0a:zx tlk+bq he 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 u9qkv8 azznuj go- 3q8p,,crd*sed to accelerate 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 electvo,8d3u-jn zzck*r89 qag q ,pric field E. (There is no electric 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, located at the corners of a orxcop *o, 0l*/5xagssquare of side l, carrr*lgo, x/50a ospx*c oy equal 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 useful in p1xeh,8 pemsx;article accelerators for “beam steering”; that is, the magnetic fields can be used to change the beam’s direction without 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 e , hx1pe8m;xswhat angle will a beam of protons traveling at $ 1.0\times10^{7 }\,m/s;$ be bent?    $^{\circ}\,$

  The magnetic field B at the center of a circular coil of wire carrying a ry6lv ctuj;,s3d2g)ccurrent I (as in Fig. Below) it2cs6g,lv ;3yurjcd )s
$B=\frac{\mu_{0} N I}{2 r},$
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 the magnetic field is aboq17u+8cc2 v h1jwptm sut 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 magnitude o. 8ma q;gfrlyh17;x .yu6avblf magnetic fields produced by overhead power 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’sg6 y78.xllhaqrf av; .um1yb; 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 field would make a beam of electrons, travecwqiepb-cl)j ix8lo-k 3o.21ling to the right at a speed o)olc joxii k-8.cepb -3qw 1l2f $4.8 \times10^{ 6}\;m/s$ 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 spiral path through a gas in a magnetic field of 0.0o*x, )sf-yvj+, f nent10 T, perpendicular to the plane of the spiral, as shown in (Fig. Below). In two successive loops, at points P a)o,ynsx ev ,tfn *+jf-nd 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 4:tl,50yc9 /tqfw )cktrr ajw0.30-T magnetic field at its cen: qa5f 4ttr09wtjw c,/)ly kcrter. 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 diameterisx323ggg4c fap b i- .(c1oby 0.50 mm, carry the same current but in opposite directions. They are suspended by 0.50-m- c 1 gb-o4i 23cay3.bisxfgp(glong 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 j 17u45bi bvqj6h.foc 45$^{\circ}\,$ 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$