A compass needle is no+ stmvjlyw;civ;g.o l32e(n 7 t always balanced parallel to the Earth’s surface, but one end may dip downward. i+ ye;to m7 v.v;l(3gl 2cwsnjExplain.

Draw the magnetic field lines around a straight section of wire carrying a cun-l +s ky j.rbe zkl242b-woe,rrent horizontally to tj+ lbnek4-,2r oly2k- bzew.she left.

In what direction are the magnetic field lines surrounding a str:l:zlqsu,, e okpr2 0gaight wire carrying a curpkqrl,z ,:o lsg:2e0urent that is moving directly away from you?

A horseshoe magnet is held vertically with the north pole on the lefs)k* jfu2:ctjav/wzen +g/. wt and south pole on the right. A wiret+/jfz/cs : jwg2.*)n wku eav passing between the poles, equidistant from them, carries a current directly away from you. In what direction is the force on the wire?

Will a magnet attract any metallic object, or only those ,, *8rufkdvvuy ks.(r made of iron? (Try it and see.) W .v,8s,*kuf(yrd vurkhy is this so?

Two iron bars attract each other no matter which ends awuxlwz4a ( f/:re placed close together. Are both magne(a:4uw wxz fl/ts? Explain.

The magnetic field due to current in wires in your home can affect a compan3xica(0 vvr5 mi9 j1rss. Discuss the effect in terms of currents, inc3j i0r5rimv 9avxn c(1luding if they are ac or dc.

If a negatively charged particle enters a regioak pxs83-. u,blw7hhin of uniform magnetic field which is perpendicular to the particle’s velocity, will the kinetic energy of the particle increase, decrease, or stay the si,x h-8u p la.khws3b7ame? Explain your answer. (Neglect gravity and assume there is no electric field.)

In(Fig. Below), charged particles move in the vicinity of a current-casvu 094 xf9 nfuviehvm+ 7wv(,rrying wire. For each charged particle, the arrow indicates the direction of motion of the particle, and the + or - indicates the signxfhv nusmvw9,fe( 70iv 4v+9u 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 fieldbj wvp(.eb(d-s1tcz 7 as shown in Fig. 20–46. What can you say about the charge on eac s-wcbd bzep .1vt((7jh particle?

A positively charged parcxqs2:,*: qv bm; yzlk:omj0rticle in a nonuniform magnetic field follows the trajectrs;2: ,0m*zjly : :qqcxo mkbvory shown 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 att6y 1*l9h u9s o)r9i/wo,(gvr vjeqyijract an iron rod? What must you consider to answer these questiony si/9vy(,)r qujoj9 9hie1l*v6gr ows?

Explain why a strong magnet held near a CRT television screen (Sect6 :izxshu-tmiv l2h8: ion 17–10) causes the picture to become distorted. Also, explain why the picture sometimes goes completely blac8x lzh:6i:-mtishv 2uk 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 n sbqr6i 2p2x;;0a ppvda ya1-magnetized but the third is not. How would you determine which two are the magnets pdq20ap 2 va1;ray b-;in6 xspwithout using any additional objects?

Can you set a resting electron into motion with a +vv7tro4gk ,:ywg wcy 53yzn 1magnetic field? With an electr, zwyo+vc:v 4ktn5wr7gyy g13 ic field? Explain.

A charged particle is moving in a circle xl) mclbm5 g. zib l987:ne ml4voo(,7qna-zdunder the influence of a uniform magnetic field. If an electric field that points in the sal5m74:lzn iadlbe g9 m q-8no)xbc olz7.,m(v me direction as the magnetic field is turned on, describe the path the charged particle will take.

The force on a particle in a magnetilytwt2lx) / r0c field is the idea behind electromagnetic pumping. It is use/0t2l) lwtryx d 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 move. Do positive and negative ions feel a force in the same direction?

A beam of electrons is directed toward a horizontal wirk8cd e .0sj,txe carrying a current from left to right8j. tc ,0xksde
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic s *ay(xlyfxf )+syi(6xx56bkfields that surround a moving electric charge.l66xx(ybsffk5 isx x(*y )+ay

A charged particle moves in a straight line through a particular re mprp71z8 wm-i;5uvfi gion of space. Could there be a nonzero magnetic field in this rprp ;m78wzmui v-f5i1egion? If so, give two possible situations.

If a moving charged particle is deflected sidewaysjj9;bsyke8k/ v; mzz- in some region of space, can we conzmb;s j/8eyjk -kz;v9 clude, for certain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there ;ox eu j1b0hosmi8*4gma 3.huis a uniform magnetic 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 whether moving electrons in a certain region jcr z3v5*f8lt of space are being deflected by an electric field or by a magnetic field (or by both)?l5z * 83cjvrtf

How can you make a compass without using4 umv8o lmaev,i94pn) iron or other ferromagnetic material?

Two long wires carrying e5i 6johb*w feq*qfjq54va*j, qual currents I are at right angles to each other, but don’t quite touch. Describe *q5e5jwaj*q4h b i6* vfqo,jf the magnetic force one exerts on the other.

A horizontal current-carrying wire/ls 8sn) cm/e5rmq06;rknn ifwpiz0- , free to move in Earth’s gravitational field, is suspended directly above a second, parallel, r5ip sk nz eqnn/0;cwi/)0m frls 8-m6current-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 unmagne-1n2xl/p xg l7 yq7xlgtized piece of iron?

An unmagnetized nail will notith /qdsf :/(r attract an unmagnetized paper clip. However, if one end of the nail is in contact with a magnet, the other end will attract a paper clip. Explaiidt:/rqh /(sf n.

Two ions have the same mass, but one is singly b rihc xs+6qzj4ii.33 ionized and the other is doubly ionized. How will their b+ ixh.ic3 4qzri6s3jpositions on the film of a mass spectrometer (Fig. Below) differ?

What would be the effect on B inside a lui79 n pwk7 te:lbb:e(ong 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 similar to a solenoid is a relay . A relay is afk79/ i2(s)da;rasm* sgmf dan 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 onfia(k9)mgf * a/2ddrs7 ;ssma 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 magni 9jop7+dhao-(y2h9zu 2 wn njdtude of the force per meter of length on a straight wire carryip d+2nzunhhj9-a7 owy2 9odj(ng 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 jy5./(rfvc0.ds) xahunj 3xm-m length of straight wire stretched between two towers carrying a 150-A current. The Earth’s magnetic fisa)5 xj(jy .0 crux/d vn3m.fheld of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  Calculate the magnitude of the maim7/.ymnde m8gnetic force on a 160-m length of straight wire stretched between two towers carrying a 150-A current. The Earth’/.i8m mem yn7ds 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 4.803 85qrx-;urequvt 7x d20jxrt m long if the maximum force on it is 0.750 N when placed ind3r ; 2tq8-jx5 exrrx0u7t uqv a uniform 0.0800-T field?    A

  A 1.5-m length of wire carrying 4.5 A of current is orientl dond)/itw)5pve r zw,st67: ed horizontally. At that point on the Earth’s surface, the dip angle of the Earth’s magnetic field makes an angle6 ndvwdoz:/pet ws i5t,7)rl) 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 n/6izbs1 z v0lis a maximum of 1.28 N when placed between the pole faces of a magnet. If the pole faces are 55.5 cm in diamei/61 sznz0l vbter, what is the approximate strength of the magnetic field?    T

  The magnetic force pek:h)gu9 duaxs:c zf271c5 uver meter on a wire is measured to be only 35% of its maximum possible value. Sketch the relationship of the wire and the field if the force had been a maximum, and sketc7z h)2seudvg19fcuk : xa:cu5h the relationship as it actually is, calculating the angle between the wire and the magnetic field.    $^{\circ}\,$

  The force on a wire is a maximum of 0/b-na*ad.whz tp6yd $ 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-uz2( sl9*yo 4vb1 az 9mmh0tzwmm-diameter copper wire could just “float” horizontally in aa02 *1 msy(lz 9w vbot9zm4zhuir because of the 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 charge dba-)j,cjrr 9 $q\,=\,+2e$ 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 direction of the force on an.qana5ej,cz6w x gu/ 7 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 charge for each diag/phn;yg yjd, /a-l)t hram shown in (Fig. Below), whereg ldn-h jp)y/a,/; tyh $\vec{v}$ (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 directionz* okvnpws9/3 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 upwaezeg dud,+jjii74z7:n b * ba/rd 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) proton enters a 0.20-T field, in a plane perpendiculawegu :ax-n5 l6r tlg -una5e:wx6 o the field. What is the radius of its path?    m

  An electron experiences the greatest force as iikcy+m0gi9 h j0(r+ ;e6pf6 ohn1 -;vblbzackt 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 /ricccqksyee4 n.t8kk h//27co6 8lx beam of electrons that go undeflected when passing through perpendicular electric and magnetic fields of magnk2i7k 8.ee cs/tkx4cy rcnoc//8 l6hqitude $8.8 \times10^{3 }\;V/m$ 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 atomqm9grn(kme6pa w:moi5 u v0kcpp39sq77 .cd, 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 requi14-j 9w(p hz oeto1fadred for a particle of charge q moving with constant speed v to make o1 9d4 (afjzp ehot-ow1ne circular revolution in a uniform magnetic field $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge q moves in a circular path ofw:n/ jwl 4px5xzty tr3nv6+0y radius r in a uniform magnetic field B. 6yjptwlxz:w nr+ 0/t4x3 5vynShow that its momentum is p = qBr .

A particle of mass m and charge q moves inwu ma kccm8um88 vyqjd83 4*6y a circular path in a magnetic field B. Show that its kinetic energy is propo8ymuk8yc wc68vqdm ma3 8u *4jrtional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momentum of the particle inssbp zadbc0z vr l8r iib,)t mu6pb069//hf3+ 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 Eart,+,pq ixl.lo,k ;hacq +a+u alh’s magnetic field oak c, ,u+hq.xlpalaqo l; ,+i+f $5.00\times10^{-5}\mathrm{~T}$, 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 fi b4 v)t/; of(i6bvywb0bjl+yaeld at the 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 spb:h6rs.h*ez/k 7vhj c jow9ry (k.;zkeed $\nu=2.0\times10^5\mathrm{~m/s}$ 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 65-A curreho. -.s:kpgb 4;vwbjr4hv; bi4ti/uhnt. How strong is the magnetic field 6.0 cm away from it? Compab4v /bi44gsb.phhj .u;vro -: ti;hwk re 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 pro+saz vs05n8e cm0x: epduce a magnetic field no larger than that of th0zn0sepe:cax58 +vs me 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 out of the page to owon9h k7hc/78vk5v nward you. Indicate, with appropriate ar wnvhv89c on/7h ok57krows, the direction of $\vec{\mathbf{B}}$ at each of the points C, D, and E in the plane of the page.

  A vertical straight wi-tezx:sstnm*0u0 ndc0v * c5are carrying an upward 24-A current exerts an attractive forn0ts 0x-v zect*m can 5usd0:*ce 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 magnitude and direction of the force between tw7au(sj 2z 9sygrb u+-(;iq wuro parallel wires 35 m long and 6.0 cm apart, each carrr;-((qyw9guj2r 7 subaz+ i usying 25 A in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic field is being carried out qe zhjrh vaagn/n r.j/b7z7;76 p+m9w1.00 m from an electric cable. What is the maximum allowable current in the cable if thhazq par/.67nm 77h/jbvg9n rwj+;zee experiment is to be accurate to $\pm1.0\%?$    A

  A power line carries a currentx;8 wd5 fcmf6q of 95 A along the tops of 8.5-m-high poles. What is the m8xdcwfq ;6m5 fagnitude of the magnetic field produced by this wire at the ground? How does this compare 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 apart carry 25-m v p.n99ouqfo5a)xwxt/av:2A currents in the same direction. Determine the magnetic field at point P, 12.0 cm from one wire and 5.vt m9 aw)x.q9nfopau5ox:/2v0 cm from the other(Fig. Below).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18 cm d *zesr3bk glknd(m0; 6ue south from a straight vertical wire carrying a 35-A current downward. In what direction does the compass needle point at this location? Assume the horizontal componente m3bkz ds(lgr* ;n60k 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 22.00a /(plabqvq9 A of current due north. What is the net magnetic field 20.0 cm due west of the wire if the Eart0/ba pl9a(qvqh’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 sj0*;7g7 3rrrxrb vw uspace 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 between y6c;w +wb;xp itwo long straight wires 2.0 cm apart in terms of the current I in one when the o wb+ py6wi;cx;ther 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 to, and from, an instr3zfdax (:zpz- n/jj7 yument. If the insulated wires are of negligible diameter but are 2.8 mm (ya f 3z:dn-/7zxzpjjapart, 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 plane of the two wires shown in (Fig. Below)4t9owofn( 2tn, parallel and juswonfo4nt9 t( 2t 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 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 pointkw /faz68dk/qs 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, asa1yow6iu(kw- v 2p+ ky shown in (Fig. Below). There is a current of 2.5 A in both wires. Determine the magnitude an-vwa6+yiky 1pwo (u 2kd 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. A second wire, ma*kq 2 lgp0n-vlde of 2.5-mm-diameter copper wirepv 2q ll-*nkg0 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 oriented so that they are perpendicular to e8 ;)qtpiua5 bt0-t yvaplc z,(ach other. At their closest, they are 20.0 cm apart (Fig. Below). What is the magnitude of the magnetic field at a point midway between them if the top one carries a current oiq(-yt0pvtu z lap,;)8b t 5caf 20.0 A and the bottom one carries 5.0 A?    $ \times10^{-5 }\;T$

  Two long straight pak:ykl6fs c93o 2ui g 1*vsx3murallel wires are 15 cm apart. Wire A carries 2.0 A current. Wire B’s current is 4.0 A in the same ux:3c3l of iyvk1kus9m6sg2 *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. (Lookin8:* (zh)yj jzalvc4png along 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 per unit length on each wire due to the other tw4p j h8n (lvzzay:c*)jo.
$\frac{F_\text{M net y}}{l_\mathrm{M}}$ =    $ \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 dijqp/*w z (e9aorection of the magnetic field at the midpoint of thojw(/ ep9*za qe side of the triangle between wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a distance d aq-b .ygbbe w,6tcz czdi: *u7/part, carry equal currents I in the same direction. One wire is at x = 0, the other is7,.b-cd e bwc:/y 6i*zqbzutg 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)eabb lsl .(i7 5 +4kewx6yxaf and carries a current of 2.0 A. Calculate th(b +.ase 5xl 4ablyef)kw ix76e field inside near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameter is to produce a field of8x:3gldqz ss )o)hcc . 0.385 T at its center. How muc:q .hgzsd3)so8x) cl ch current should the solenoid carry if it has 975 turns of the wire?    A

  A 550-turn solenoid is 15 cm long. The currz.l3+xxbrj )5-nvnqatj h6 e nd-,a 9eent in it is 33 A. A 3.0-cm-long straight wire cuts through the center of the solenoid, along a diameter. This-z-nj,j.6ntbx +nerh xl59 )3ved qa a 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 copper and want to make a practical soleno7pvvc+up d hct 6p)l1 3ud9) 8oduwi9eid that produces the greatest possib w uc)p7 piud168ch9pl vu9o)d3etd+vle 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 solenoid diameter, length, and so on.

A toroid is a solenoid in the shape of a circle (Fig. Below). Use Ampère’s ls;3 5ubvdm;y /-yqb8ydr0vf naw along the circular path, shown dashed in (Fig. Below a), to determine that the magnetic fddfb y ;yvn 0ms /vqyb385-ru;ield
(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 conduc3) -t,beag/qmn ms6tdlsv-0qtors of a coaxial cg/l t-ntq6,qdv -mss ae 0b3)mable (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 2q wtx8xl8mh :v6cl-4z2.0 cm on a side is placed with its face parallel to the magnetic field between t6t4 w-8xv8hm:lclx qz he pole 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 d cngt:83ttr5z4be0n3zuy )atr i. 5ueeflects 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 galvanomete/d0g-bygrji2 5kkus +c8* xigtz8qr 3r weakens by 25% over the years, what current will give full-scale deflection if+krydiu0* tg/8 2-83r gbxgj5cq kizs it originally required $36-\mu A$ ?    $\mu A$

If the current to a mo+q)a hyur ov/)tor drops by 12%, by what factor does the output torque chanuao+qhr)yv /)ge?

Show that the magnetic dipole moment M of an electron orbit 7. se788uy1oruo( vl adb6onning the proton nucleus(nu7 dos8r uav.86lye 7 onbo1 of a hydrogen atom is related to the orbital angular momentum L of the electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter and containing nine loops lie+fsi)jp.wy ) pcao6 t vjpt827/vl e8bs flat on the ground. The Earth’s magnetic fi+ 867)bi8ycfa/spvw)j tol2. ev pptj eld 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 magnetic field. What vam2ap77 9 htcdzlue of electric field could make their paths straight? In what direction must it p p29dmaczt 77hoint?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atomso (wzmrpd 0stie)*3*f/vjp8e 5zn )qs have radii of curvature equal to 21.0, 21.6, 21.9, 22.2, and 22.8 cm. 5*dss0*qm(z jtz3f 8v w)eoe iprp)/n 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 the electric plates in the mass spectrometer -jt rh/(db5x r y;xpk:of (Fig. Belxj( ;xhp:- rrkbd/y5tow) 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 4 z adb)v*v(vhused to monitor air pollutants. It is difficult, howz4h*( )vavvbd ever, to separate molecules with nearly equal 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 accelerates ions by a voltage V befor +fs8qwlbr k4f2 /dqecm,(qq2 e they enter a magnetic field B. The ions 8w2cqf 2d,4 bks(meq frql/+ qare 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-A2 m7wrv+yb, h8v-6ufq-nwphvj b6l 0o ;eku7l current flows through the wiru yb76l0 b, w;vlm+w8r2 -khhovuf6 qp7-evn je. 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 g6:/8dndvy m lg00o nvxbjn2) 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 8jgyng0dnv o2xv /n6l) dm0: bwire. What is the permeability $\mu$ at this high field strength?    $\times10^{-5}\mathrm{T}\bullet\mathrm{m/A}$

  Protons with momentum axf/o lk*0 d a9(ft*5kbui r+h$4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 reeifo65fg20qi+)zcx r gion of constant magnetic field. What is the ratio of the radii of their circegfficxq50)+roz i 26ular paths?   

  The power cable for an electric trolley ( h* qknyj,35rj-j2b nrFig. Below) carries a horizontal current of 330 A toward the east. The Earth’s magnetic field haj,y -njknj3*r 5 2rbhqs 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 net charge +6 w:tj(iwgr vof $1550\mu C$ 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 Earthq-5-4rdgn n ky’s magnetic field points almost horizontally to the north and--nqr4gd yn k5 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 ma, aa;dy1 ol p(t,eez2cz)- aujss 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 launcher” is sq9gwki 8w1v v+ntetm74i6e y w(n2u;hhown 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 rest to 28m/s in a distance of 1.0 m? In what div 48 ni+nu7 t(q6wge2y1tvwh 9;iw mekrection 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 co5jlyn*ost:sz wags6g2 -7c 9bpper wire and is suspended in air due to the two magnetic forces from the bottom two wires. The current flow through the2caol zs:-s*97bwt n yg5sg6j 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 in a cwlf 1bvq o+48am(zj7horizontal plane act as rails to support a light metal rod of mass mczf(8q +7jmo4bwl va1 (perpendicular to each rail), (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 electron beam near the centermf:hq 6hho1 +b of a TV screen due to the :fmo6h qh+1b hEarth’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 dwuq 9(5; +jvu d oy,dn;t9dgbjevice used 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 electrid , doj9qt;w ;du yj9bu5gn(+vc 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 corner3prz*e +ml3l4,zgce w. wcg r1hgs1q +s of a square of side l, calqz 4 eer cpz1+3.gg*wslc3, whmr1+grry 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 particle accelerators -mwj-z )oub5lfor “beam steering”; that is, the magnetic fields can be used to change the beam’s direction without altering its speed (Fig. Be m)w-obzluj- 5low). 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 center je7.a5qt v: guof a circular coil of wire carrying a current gt 7 :ae5j.quvI (as in 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 the magnetic field is ab;31l mwyx 1vubout 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 ide -5r7q2f; wofob1c lpnvfs 82na of the magnitude of 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 tv;o pofc8-rlnb 15722sfq nwf o 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 6oft.x gq+,jud would make a beam of electrons, traveling to the right atout6 ,j+ x.gqf a speed 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 spiral path through a gas in a magnl+z zlq p /elk+zg4 3vg6szr44etic 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 Q, the radii are 10.0 mm and zzgevzp6443s+ qg z/+l lk4lr8.5 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:yfobc0 .mxsj794 tt i 0.30-T magnetic field at its center. If the maximum current is 5.7 A, how mm07c9st .btxoi 4j: fyany turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, each of diameter 0.50 mmjvm3yrzcn0 7(h4 -5sk +g/r i1g1lpf zg9sjld, carry the same current but in opposite directions. They are suspended by 0.50-m-long strings as shown in (Fig. Below). If the suspension strings make f kcig3/pn0 7slrygr h1dmj(-+z5z1lv94 gsjan angle of 3.0$^{\circ}\,$ with the vertical, what is the current in the wires?    A

  An electron enters a+o0bmqb8e.jrr 6*zqp uniform magnetic field B = 0.23 T at a 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$