A compass needle is not always balanced parallel to the Earth’s s7m.n fy ws0jl7(jjut 8x/mi, 9ujjnl5urface, but one end may dip downwunw/n jf97 l,jmy7.im5l0 (jj8ujst xard. Explain.

Draw the magnetic field lines around a straigh7um5kb3a: z itmyy (3mt section of wire carrying a current horizb mk( a3 yumyzm3t75:iontally to the left.

In what direction are the magnetic field lines surr8(:dk -04wjzctshf hqrn0 adm +* 8fwlounding a straight wire carrying 8s: t*n4 z+0 mqwdakf( 8j0dl rh-cfwha current that is moving directly away from you?

A horseshoe magnet is held vertical8y)5 0wjej)hdl 7s giily with the north pole on the left and south pole on the right. A wire passing between the poles, equidistant from them, carries a current directly away from you. In what direction is the force o h ljid))5ejigw80sy 7n the wire?

Will a magnet attract any metallic oln 9w 9t5gyzq;*;wkywbject, or only those made of iron? (Try it and see. n5q ktyz*lw ;gw99w;y) Why is this so?

Two iron bars attract each other no matter which ends are placed close toek4y cqj8w g+cz1 *y(wgether. Are both magnets? Explai(*ce z8wkj4 gwycqy1 +n.

The magnetic field due to current in wi n0)9xs joug8az0b1v ryen(jk8gj/ 1w res in your home can affect a compass. Discuss the effect in terms of currents, including if thv891u08x1reg a/bnjz0jsjyon)gk w ( ey are ac or dc.

If a negatively charged partic1ee350a/se 4.ukh,pontaoe4bm; fr w le enters a region of uniform magnetic field which is perpendicular to the particle’s velocity, will the kinetic energy of the particle f31on4,4saa tp;/o.ehb er0we5u km e 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 current-carryingnj3o2ybr;i aqp;q pb-vkkvlqn7 :93* wire. For each charged particle, the arrow indicates the direction of motion of the particle, and the + or - indicates the anyqb7o*:k3ip; ;vv3 - k q2qnrl j9bpsign 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 cqr tyeop.tg4k, -ggxp56 ;t5w , enter a magnetic field as shown in Fig. 20–46. What can you say aboyqtg5r5to. 6e , ;4-gptxgkpwut the charge on each particle?

A positively charged particle in a nonuniform magnet;xzffc +8h5iz ic field follows the trajectory shown in f zcz8f5ih +;x
(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 uoro4s* (hw0mattract an iron rod? What must you consider to answer these questiow rm0us(4oho* ns?

Explain why a strong magnet held near a CRT tel1qf g:ircp am7/)ac4r3yf kf ,evision screen (Section 17–10) causes the picture to become distorted. rqf1)4cm r/, pakya7cfifg 3: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.][/But don’t risk damage to your TV by trying this.]

Suppose you have three iron .otvm( (5m-h arim i:wrods, two of which are magnetized but the third is not. How would you determine which two are the magnets without using any additiona -i.5v(:m( mmrhto iwal objects?

Can you set a resting electron into motion with a magnetic field? With an elewuh9s /i(r+p,x8 eqbot: 0t wuctric field? Explain.w+t/espb :0qh,w ru8 t 9xoui(

A charged particle is moving in a circle uzo lfi7 19l*gq,wwzj+ nder the influence of a uniform magnetic field. If an electric field that points in the same direction as the magnetic fii+zl*qw, z w7jo1gf9leld is turned on, describe the path the charged particle will take.

The force on a particle in a magnetic field is 2alv;81bhd xo vv q:s3gqug v3ip20t(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 a magob(glx8a2vidvv: u ;1qpt 3 ghq02sv3netic 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 wiret) tjex*ha p((2v12zala9;vf:(jllpge2ed b carrying a current from left to right agapb v)229z v2((txj jl;a1 eh et:f*dll pe(
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields that surround a movim6y rfz0yy xvak,** g167kn jeng electric charge.an, k yfyxm 0yzgjvr76k 1*6*e

A charged particle moves 5wzv3in/gj cdt0m17d in a straight line through a particular region of space. Could there be a nonzero magnetic field in this region? If3v j wi0cdnmzg1 5td/7 so, give two possible situations.

If a moving charged particle is deflected sidewaygp9(jr ,m 2y ts tn,kuc+p4+cks in some region of space, can we conclude, for ces+ 9tnp2u,pt ycg(,4r c+kjmkrtain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region ow/jiyo vk)e3(a n;5wuf space there is 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 w; 8w,.mecuxwa certain region of space are being defl;cuw ,w. xw8meected by an electric field or by a magnetic field (or by both)?

How can you make a com70p t qhhsfwih -zo;1zj.su* :pass without using iron or other ferromagnetic material?

Two long wires carrying equa d:qj wu 3 rqna6.zdue*q,)qt0l currents I are at right angles to each other, but don’t quite touz)qad6 qu,j dw0nrq. 3t*: equch. Describe the magnetic force one exerts on the other.

A horizontal current-carrying wire, freia:8omwmd/w *e to move in Earth’s gravitational field, is suspended directly above a second, parallel, current-carrying wiro*8d: mwa wmi/e.
(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 unmagnetized piece ofz3;,0(xbf skbmh ,qhx w0u,dqytf .2 k iron?

An unmagnetized nail will e8 def8 wvkj j:r)39wnnot attract an unmagnetized paper clip. However, if one end of the nail 89r ed kw3)w:jen8vfj is in contact with a magnet, the other end will attract a paper clip. Explain.

Two ions have the same mass, but one is singly ionized and the other is doubl6+s*zm z 5;lgk (.qwjkj*pv ;ixvho,cy ionized. How will their positions on ;i6 *;z vp cv+h,kx smgqjo*wj (k5zl.the film of a mass spectrometer (Fig. Below) differ?

What would be the effect on B inside a lonyn(r*,mxmx8epd0p fu t bv.1 pn0 xi*)g 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 solenoii i8z4(yy opjh,xgnb974nho7d 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 p,(7bh7zxoohn 8n4p jiyg94i yivot. 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 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 magn5 cbio3ez d;fjwd1r6(itude of the force per meter of length on a straight wire carrying an 8.40-A current when perpendicular to a 0.90-T uniform mdrczbw 1i(;e3f5 6o jdagnetic 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 160-75q,oku0f8y emxf.dr m length of straight wire stretched between two towers carrying a 150-A current. Thd, yufm0q75re ofx. 8ke 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 lesm8x,as6acuhr/ r3 c 4ngth of straight wire stretchedahc3c /,4 rx8smua6 rs between 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

  How much current is flowing in a wire 4.80 m long if th 26ge.kw(bi r(fb ypy.e maximum force on it is 0.750 N whg fyw6( 2y .b(pkeri.ben placed in a uniform 0.0800-T field?    A

  A 1.5-m length of wire carrying 4.5 A of current is orienta ,-+kult rqc 0rb *otfy3fg+1ed horizontally. At that point on the Earth’s surface-t 3 1aqkr+y tf0l f,bc*gour+, the dip angle 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 8.75 A is a 3tp qu 9zfq9cj72 zow1cp1:rv maximum of 1.28 N when placed between the pole faces of a magnet. If the pole faces are 55.5 cm in diameter, what is the approximate stren13qq u 2z9tccpprj z vw17f:9ogth of the magnetic field?    T

  The magnetic force per meter on a wire is measured to be only 35% of il 5ae(4l um6ryk2(z iits maximum possible value. Sketch the relationship of the wire and the field if the force had been a maximum, and sketch the relationship as it actually is, calculati (y5al4 reu6izlimk 2(ng the angle between the wire and the magnetic field.    $^{\circ}\,$

  The force on a wire is a maxim: nh/vyzfj9yk-wz6 dfd.z,k+ um 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-diamkr* b+6b9nprs eter copper wire could just “float” horizontally in air because of the forcpsbr9*b+k 6nr e 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 ch1 ci* s4i56yn,p;knkghn4x cfarge $q\,=\,+2e$ 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 electpbo pqxu z0n4:ehicxn /xlw) 2)d93t*ron 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 diagr go+y5xrh1vq kem+3d9am shown in (Fig. Below1k+ex +3v o5 hdymgq9r), 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 direction of )w1 -v ble7jen$\vec{B}$ 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 upward with a speed oqa0v4 ,h-9 3xxl0hc-+iwtz d3h udrwaf $1.7 \times10^{6 }\;m/s$ 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 f; mwk) 3idzjz;7b)xi50jlh g(j rtpd;yzn1,0.20-T field, in a plane perpendicular to the field. What is the radiusjy7x 0jz 5jbip kh1w)ld(nz;f; z3mdr t;,ig) of its path?    m

  An electron experiences the greatest forc. /v5(e ftqbsae 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 of electrons that go undeflected j*n ww2u (4upmwhen passing through perpendicular electric and magnetic fiejn( mw u4*w2pulds 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 atomcc(uq ns- 313cu0zhw5utygf 2 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 of charge q moving with con7.xdx/oowt )ii e2 pzy*ej4d.stant speed v to make one circular revolution in a uniform magnetic fzejix p yxi )w2*o4 /.7ed.todield $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge q moves in a circular path of g6s hg*y492p7b7advyge5 j,7 brbuzd radius r in a uniform magnetic fij7r5g7y2ub*e 6bdbg,azyh7 ps4g9 dveld B. Show that its momentum is p = qBr .

A particle of mass m and chm tkypx fcwe64;r9*) targe q moves in a circular path in a magnetic field B. Show that4fe6ymk9wr; t*)xc pt its kinetic energy is proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momph) ukzq (/mx/p(vr +fentum 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 of7sg2 awbow98d 160 m/s perpendicular to the Earth’s magnet 8bg w79so2dwaic 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 equator has x f*l:o+fsyur96d 7lbmagnitude $0.40\times10^{-4}\mathrm{~Т}$ 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 speed g+8jlx:h1kl y$\nu=2.0\times10^5\mathrm{~m/s}$ 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 dw22f;chkt;2 dwnd 7 jcarries a 65-A current. How strong is the magnetic field 6cdw j; hwn;22dftd 72k.0 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 fieldcnii:g6jbq+n)yq5 5m no larger than that of the Ear +gn)5i jq6n:qbiyc5mth $(0.55\times10^{-4}\mathrm{~Т})$ 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 toii3mo:2/z c kra3la k4v e61ezward you. Indicate, with appropriate arrows4czvim ea31 kz:3aoe62l/ ikr, 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 upward 24-A current exev zd/kl1o/-ok 9/tlf hrts an attractive force1hzk/vt/l9d/ oo-f k l 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 magnitud g0vq+k rgqo a*2,kvj5e and direction of the force between two parallel wires 35gj+0 vqvk52o,a*g q rk m long and 6.0 cm apart, each carrying 25 A in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic field is being carried out 1.00 m from anojxer3muw so2o29v7ph *1 ul) electric cable. What is the maximum allowable current in the cable if the experiment is to be accurate t oujm7ls9x 223o1rwh*opuve)o $\pm1.0\%?$    A

  A power line carries a current of 95 A along the tops of 8.5-m-high poles. Whar7.r 5syn -jnc ayk( *hiiq6j;t is the magnitude of the magnetic field prod r; (k 567*rqy .njyh-ijsiacnuced 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 c*g7z9knzf z 9zarry 25-A currents in the same direction. Determz9 97znfzz*g kine 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 soutk qw,t2 6v:m(ns0jgq gh from a straight vertical wire carrying aw ,(qnsgqmj6g02kt v: 35-A current downward. In 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 wireiyso wgswe ze:bh 2kp,uj +api*6(8-8rcr8o- carries 22.0 A of current due north. What is the net magnetic field 20.0 cm due west 8ujw si(-gczrp+ h 6o8ebk2o:i, p8e-way *srof the wire 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 prodyl)+ fvm/)m zk*ns; ibkea ;5tons 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 between two *d0-hzk xv bq3xynqmhma)94cqpi ;49 long straight wires 2.0 cm apart in terms of the cz n9 di4-qy*q49q)xch;mh0 pkabvm3x urrent I in 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 07n(wfhdy3ja conducts 25.0 A of dc current 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 theirw3ahf0j d ny7( 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 shownk36nok i -xdbns6dy)1glm/ t( 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 wln)3g-1tnbdkxiy m(6/ dk6os ires? 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 pointsf )0sip 0mudvgc-1ta/ 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 afay6eu awto /fe/l5., straight wire, as shown in (Fig. Below). There is a current of 2.5 A in both wires. Determine the magnitu/y/6w,5al e.f tfe uaode 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 4 z+/2dhk0b -ftpmo e 0p.ql-dt8 A. A second wire, made of 2.5-mm-diameter copper wire and parallel to the first, is kept in suspension magnetically 15 cm below +pdpb0mzdk-q . lt/2hto0ef- (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 soh6wl 6svi,mp1rm.; my that they are perpendicular to each 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 t vyp1h,immw.m;6 6 srlop one carries a current of 20.0 A and the bottom one carries 5.0 A?    $ \times10^{-5 }\;T$

  Two long straight parallel wires arek+qm 7uc):vl w 15 cm apart. Wire A carries 2.0 A current. Wire B’s current is 4.0 A in the sau v )km+cwql7:me 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 wiacdx..feo w1(. bbmm w6ajg--3fqvy )res are 3.8 cm from one another. (Looking 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 oppos.b3g-.6vwb(c d q.1 a-m e famfxoyj)wite 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 the magnetic )2-ebd tn cb6wfield at the midpoint of the side of the triangle between w dbn2c) b6-wetire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a distance d apart, carry equal curr d o5*f;d 9 euhelx*zydowh:3;ents I in the same direction. One wire is at x = 0, the other is at fy h**9ddx3l;ozd ouwe:;5eh x = d, (Fig. Below). Determine $\vec{B}$ along the x axis between the wires as a function of x.

  A thin 12-cm-long so -xkif8wh ,j:(,gme oc) d6lhklenoid has a total of 420 turns of wire and carries a current of 2.0 l,k:hkw-) gh,of8j 6m cdeix( A. Calculate the field inside near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in d mly5mg r: .dx-klmf7: :zbmk2iameter is to produce a field of 0.385 T at its center. How much current should the solenoid carry if it has 975 b2:kf mkrlm x7ly ::mm.z5-gdturns of the wire?    A

  A 550-turn solenoid is 15 cm long. The current in it is 33 A. A 3.lm(xx p r-.0zv0-cm-long straight wire cuts through 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 tlzr m-.p(0vxxhis wire assuming the solenoid’s field points due east?    N

You have 1.0 kg of copper and want to make a practical solenoid tha :pikfanz0om,4 a)b 7e,dha6ft produces the greatest pos6 ,a7f4nhi:)0daf ,omepkz b asible 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. if9emp;+u/kr Below). Use Ampère’s law along the circular path, shown dashed in (Fig. Below a), to determine that the magnetic field ike mup+9 r;f/
(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 cel*cwg h+a. r71 qfta;onductors of a coaxial cable (Fig. w1 leqac; *hfgr7at.+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 siv. on.o 30i xphf;ss0wde is placed with its face parallel to the magnetic field between the pole pieces of a large i ;0ov0.s.3hosfwnpxmagnet. 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 deflects full scale for ae7j1q/ a;mt ki $53.0 -\mu A$ 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 weakens by 25% over the years, what )h5hreqx (o8 ccurrent will give full-scale deflection if it oriroc8he)h 5 x(qginally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by wha8faz zd(+ czg6t factor does the output torque ch8 zza6d+fz (gcange?

Show that the magnetic dipole moment M of an electron orbiting the proto+4y* 4fm9rrsp8y-mdfv( oq y en nucleus of a hydrogen atom is relatedy+(rfpr moe *4 y9v8sdy4qm f- to the orbital angular momentum L of the electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diamete8w xcd3o 5yd+hr and containing nine loops lies flat on the ground. The Earth’s magnetic field at this locatio ydhxc5+d8o3 wn 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 fieldn f.(2d :na7vp/kjey u. What value of electric field could make their paths straight? In what direction must uyk7jn d:(f/p ean.2vit point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atoms have radii of curvature e+ben:wed 8o ba.egj:3 qual to 21.0, 21.6, 21.9, 22.2, and 22.8 cm. The largest radius corresponds to an atomic mass of 76 u. What are thwoe:a+j: .eb8egnbd 3e atomic masses of the other isotopes?

  Suppose the electric field between the electric plates in the mass 8 ex a;w.sbb.zz6qbw.spectrometer of b b 6wews;.zx.b .qaz8(Fig. Below) 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 difficul0 fa5mwsas.hr(d; b)bfw eo ,-t, however, to separate molecules ffbrmsbwd(a ,e- wsoh)a 50;.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 spem*; j.c+rzbad ctrometer accelerates ions by a voltage V before they enter a magnetic field B. The ions are assumed to start from rest. Show thzr*d.jcm; b a+at 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 o,f:byag:3id zzk oak vg;an*4 7g-0nsf wire per meter, and a 25-A current flows through the wire. If the permeability of th: 0;gk nzonizgv7*34afb d yakas -,g:e iron is $3000\mu_0$ what is the total field B inside the solenoid?    T

  An iron-core solenoid is 38 cm long and 1.8 cm in diameter, and has 9.rcww o )f1l2-xlznn640 turns of wire. The magnetic field inside the solenoid is 2.2 T when 48 A flows in the wirew1 -2 n o.9rlcf)zxwln. What is the permeability $\mu$ at this high field strength?    $\times10^{-5}\mathrm{T}\bullet\mathrm{m/A}$

  Protons with momentumjyfftr7c g:3n :z9 j5l $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 hc* s-sztq)dru :rjfkg )zl.s)3xu7)upon entering a region of constant magnetic field. What is thz j)h)ucssr) flg*r3k )s t -.z:7xqude ratio of the radii of their circular paths?   

  The power cable for an elecaf b9gn7e )ayzyk,ek0zt:) t *tric trolley (Fig. Below) carries a horizontal current of 330 A toward the east. The Eaenz g: k*0yyt)t)z7bk efa 9,arth’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 acquirx z/lnetjv5+at t(v )f+p4 e 27evmhi8ed 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’sjz1hm ec.td+/y ia 2h* magnetic field points almost horizontally to the north a+dy2a*/imzt.c h jh1e nd 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,30qon3srt 0w i whose mass 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 shown izk1ccobauuv5j1u9 , qw2d65 y n (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 ,9w1cuuvq 2c6zu5 1bdo5jayk 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 wire 78qwa0d55z d mvpx4q4qrg g 1ub :o1zgand 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. Calculaqx4ogd :r01 uwpz8bqzm4q 517 gv dg5ate the required current flow in the suspended wire.    A

Two stiff parallel wires a distance l apart in a dv :ybf8 0spt8)b2hnqhorizontal plane act as rails to support a light metal rod of mass m (perpendicular to each rail), (Fig ndb0yhvs8) q8t b2pf:. 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 deflectiyrk+ gim +vk11.emw3uon of the electron beam near the center of a TV screen du3ik.+g1 mkvrm+w y 1eue 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 accelerate el31ne2 h xjlr8bementary particles such as protons to high speeds. Particles starting at p ln1xj283 berhoint 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 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 square u:g 8kd7 +tunteig b0w4+hr6n of si0 +br:w+htktn4 87i6ug egudnde l, carry 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 for “be( qsiuo x,ds5p4qilc(;-br / r5pn5wx am 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 what anglscdr(p/ r l (wsi,u-;4iqx5 x5po5nqbe 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 wk.coq3t99 )gjqyx t ,eire carrying a current I (ct.qy gtj3k9)9e, xqo 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 iskk(0-e8quqh m 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 magnitude ofhcix7 ooq,d f /l1+lx9 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 theicxh o719xqfl/ + ,ldo 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 field would make a beam o7mbto8xm u0u6;.kyh gemxgc9hy.8 1qf electrons, traveling to the right at .8 hem67hyc80bt um.9;xg qguxmk1yoa 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 magnetic field 9hmsw/ a9o x3gof 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 8.5 mm, respectively. Calculate the change in the kinetic energy of the proton as it travels from 3 /oagm9h9wsxP to Q.    $ \times10^{-20 }\;J$

  A 32-cm-long solenoid, 1.8 cm in diameter, is to produce a 0.30-T magnetic kn 4k-t4jh 3l1zrwc c7field at its center. If the maximum current is 5.7hjc4rkz3 kt14w-7 l cn A, how many turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, ef0fa(5g4 e tfdach of diameter 0.50 mm, 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 efa4(d0f5f gtstrings 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 = 0.2jho* 7w:0n oh2sf5 2pab7qfne,ops7z3 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$