A compass needle is not always balanced parallel to the Earth’s surfc5e1f(4h x m u47nehesace, but one end may 4e(4ex muc e51hfs7h ndip downward. Explain.

Draw the magnetic field lines/:t6/2 e jadt qp-uony around a straight section of wire carrying a current horizonta 6q/2 odet-na/tpyj:u lly to the left.

In what direction are thezf3br. noghhl4k f.yn*i416n magnetic field lines surrounding a straight wire carrying a current that is moving directly away from yohnfz 3y16fhbgn4 k.oni.r4 l* u?

A horseshoe magnet is helpm77x wmrl:/9yobs4ml2z m3 nd vertically 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 on thlrym : zlnmbmos79x /w2 734mpe wire?

Will a magnet attract any metallic object, or only was*av 6vo4x; qckt-vt hhw0 2u43)xathose made of iron? (Try it and see.) Why is this sox 2*wt0os46cx)a;aah v v w-4vtu 3qkh?

Two iron bars attract each other no matter which ends are placed close togeth 6aj9n/aw 8x ber9ddkypc/9f va46 )dger. Are both magnets? Expla9 6x/4wnc dy dd rab6g8va9efp/aj)9 kin.

The magnetic field due tjy qg o+qfk++;a8rz3lo current in wires in your home can affect a compass. Discuss the effo8l3k a;jr+zqgqy+ + fect in terms of currents, including if they are ac or dc.

If a negatively charged partit8 9o fhqegshx*pk)/0cle enters a region of uniform magnetic field which is perpendicular to the particle’s velocity, will the kinetie9)*g8ptqx ks o0hh/fc 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 vicinl51/ yzu5v2rn +yjof uz6*xn-alo*zj ity of a current-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 dif2* zj yl a1zlnoo5yrvnzu/5+ jx*-6urection of the magnetic force due to the magnetic field produced by the wire.

Three particles, a, b, and c,6hzb so7,pl6m enter a magnetic field as shown in Fig. 20–46. What can yous6o7m,bl zp6h say about the charge on each particle?

A positively charged pawgc2nw uiqp+,n:5 :byrticle in a nonuniform magnetic field follows the trajectory shn5 :yipnu b,w:gqw 2c+own in
(Fig. Below). Indicate the direction of the magnetic field everywhere in space, assuming the path is always in the plane of the page, and indicate the relative magnitudes of the field in each region.

Can an iron rod attract a magnet? Can a magnet attract an iron rod? What must y b1 1p*kia6 zcjs7f3amou consider to ansbm 3psa6 1z iajk*cf17wer these questions?

Explain why a strong magnet held near a CRT television screen (Sec,d esqq: jw 7 1+i yc zuk7912yij(aa:l.thxoftion 17–10) causes the picture to become distorted. Also, explain why the picture sometimz1ija d,:7(ih:y qu.k f2c l qt7e9xsya wj+o1es goes completely black where the field is the strongest. [But don’t risk damage to your TV by trying this.][/But don’t risk damage to your TV by trying this.]

Suppose you have three iron rods, two of which are mq 25y: 15sz.4zt z oghibvbl:zagnetized but the third is not. How would you determine which tw ts b:ioh 2:g5v 51.yzzqlbzz4o are the magnets without using any additional objects?

Can you set a resting electron into motion with a magnetic field? With an e 8 v8ohvdzfq)t*tbl*qtp*j ,hw96 -dxlectric vvz6to9hd qb, d p-j8l*tf)8htwx**qfield? Explain.

A charged particle is moving in a circle under the influence of a unis p,1a/z:ktf6bwi.w8dib yn21 rga.r form magnetic field. If an electric field that points in the same direction as the magnetic field is turned on, describe the path the charged parbkzb2ay. sir wgri8p1 : 1/f.d6w,natticle will take.

The force on a partih9t cffzm3 6+/l ,*yx6hozlswcle in a magnetic 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. Belocs66hhyz9 fz */twllfm x+,3 ow). 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 wire carrying a current knxn8 d9,wo7ifrom left to 8n,idox7wn 9k right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnewjf 4 1/ykanu)tic fields that surround a moving electric charge.w 4 f1k/jyuna)

A charged particle moves in a straight line through a particcm3;ya .xzg qq cy7;0h(3 qvtm,v8ssfular region of space. Could there be a nonzero magnetic field in this region? If so, give tw (qf;3 tv8s,hycma3gc7zqq.;v yx 0 smo possible situations.

If a moving charged particle is deflected sideways in some region of spa frt8cvjvoo9(dbl9+ 6ce, can we covfd699b o8ol jc(vt+rnclude, for certain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there iq90zc m- z5j n-xdn nvh8-lu1rs 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 of space ar*z6nkx hq)rcootk x2g *4+ .2lcbng m+e being deflected by an electric field or by a magnetic field (orxx b +t2goo2nq ng4+mzc)crhlk k6.** by both)?

How can you make a compass without using iron ufd.ljvk8gc j+3zt h ) ):qow4or other ferromagnetic material?

Two long wires carrying equal currents )my(vytg*zu 9I are at right angles to each other, but don’t quite tzu t9g(y*v)myouch. Describe the magnetic force one exerts on the other.

A horizontal current-carrying wire, freee24dsu 6(fspqx5( ctacx, e/jvg 9 nnn nnv+(- to move in Earth’s gravitational field, is suspended directly aboveex2cc xnqf ( gn5ajnvt-n(6s9nepv+u4,s d/( 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 unmagnetized)5a:ge fb0o xo piece of iron?

An unmagnetized nail will not attract an unmagnetized paper clipmc,e0d cf;q tl;gq(q-. However, if one end of the nail is in contact witcgc(f;, qtl 0qe-d;mqh a magnet, the other end will attract a paper clip. Explain.

Two ions have the same mass, but onet9*u /ghbleyb+9a i+a6r 2nj m is singly ionized and the other is doubly ionized. How will their positions on the film of a mass spectrometer (Fig.h+am9ar bt b+ e/2jygiul9n* 6 Below) differ?

What would be the effect on B ig vo2/: r*ossv.kpo.d nside a long solenoid if
(a) the diameter of all the loops was doubled,
(b) the spacing between loops was doubled,
(c) the solenoid’s length was doubled along with a doubling in the total number of loops?

A type of magnetic switch similar t11a +sh-) ;gmna)xv8 vgics a8v*yweco a solenoid is a relay . A relay is an electromagnet (the iron rod inside the coil does not mo-esha8x8vv;1y a)cig)vsc gmw n+*a1 ve) which, when activated, attracts a piece of iron on a pivot. Design a relay to close an electrical switch. A relay is used when you need to switch on a circuit carrying a very large current but you 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 force per meter of length on a straight wire ca; yyag7tskw:0t(9el+znxd 7 e fc.77p-zcqx s rrying an 8.40-A current when perpeqzd7t c :t9wle c07exk n s(ygfysxaz-p+;7 .7ndicular 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 ofsj.o )p5 - munda-;1hniyxmq8 8jrdo8 the magnetic force on a 160-m length of straight wire stretched between two towers carrying a 150-A current. The Earth’s magnetic jo ns amhq1pijd8 dr885.x;)nym -- uofield of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  Calculate the magnitude of the magnets3k33-(bvo j vwvs vudfqhr 23g;v1l(ic force on a 160-m length of straight wire stretched between two towers carrying a 150-A curr-d; 3g k(shvv3o3v1 lbw sfv3uv(qj2rent. 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 maximum forsrhvr0p 8l4or lez 9+.b+/rn( yv4cqebtf) 6lce on it is 0.750 N when placed in a uniform 0.08o+rr r8lv4.+4tnhe(lq bl zc f6ry/)pse0 b 9v00-T field?    A

  A 1.5-m length of wire carrying 4.5 A of current is orientzp i+-lt)* (hs1q.+ezar m 8w k+tstnged horizontally. At that point on the Earth’s surface, the dip angle of the Earth’s magnetic e anhr)s +-*(wt1+t8q+ l.pi tz kgzsmfield 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 maximum of 1.28 N when placed betwvrm8m1yhrn )78 k*gz been the pole faces of a magnet. If the pole faces are 5gy b8vz rmhn7*rk m)185.5 cm in diameter, what is the approximate strength of the magnetic field?    T

  The magnetic force per meter on a wire is m lo35s v b0.tap9dav.teasured 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 sketch the relationship as it actually is, calculating theplaot.0dav5. 9s3v bt angle between the wire and the magnetic field.    $^{\circ}\,$

  The force on a wire is a9 1mz ya+uin5m 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 “flof6(w01dsi d,5;rf n2ezgq htqat” horizontally in air 6q(;szitd q521,f h d grnef0wbecause 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 cha83dm3irh1s f,4vhz6,f(so5,j ob cm szuuj 0xrge $q\,=\,+2e$ 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)q fzv35 3ui-dk3kgntp6x 0yd 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 charge for eav8k fw)cfe2x7u iy.g)ch diagram shown in (Fig. vu2 f)xfe7 yig.cw8) kBelow), 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 e6n i (aopq39c,6p2ooggmqsr(xx -1rud7ac / 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 upward with a speed o bjlejob7b5 1vf*. qf)f $1.7 \times10^{6 }\;m/s$ 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.:r8at3c s- qyec6;.o o pzto,i20-T field, in a plane perpendicular to the fiel;.po eiqors 86 tz-aco:ty c,3d. What is the radius of its path?    m

  An electron experiences the greatest s4:jshw.go dvjpy76jt i34q7 force as it travels $2.9 \times10^{6 }\;m/s$ in a magnetic field when it is moving northward. The force is upward and of magnitude $7.2 \times10^{-13 }\;N$. What are the magnitude and direction of the magnetic field?    T ----待选择----EastWest 

  What is the velocity of a beam of electrons that go undefle0ks /yg8+ ttbitw29 res .-xkdcted when passing throikd+r .8/t9 k xget tw-y2s0sbugh perpendicular electric and magnetic fields of magnitude $8.8 \times10^{3 }\;V/m$ and $3.5 \times10^{-3 }\;T$, respectively? What is the radius of the electron orbit if the electric field is turned off? $F_E$    $ \times10^{6 }\;m/s$ $F_{max}$   $ \times10^{ -3}\;m$

  A doubly charged helium atom whovwy ro hb9b,:yij-w9+g2h ( hsse 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 cl;0aw;rw,)h0djx h nska )-lsharge q moving with constant speed v to make one circular revolution in a uniform magn nhwxa)lsw0)ks0;;alj,d- h retic field $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge q moves in a circuluq *ohc4lq5k4 sn m7t0ar path of radius r in a uniform magnetic fieuq5 s7km tln ch40*q4old B. Show that its momentum is p = qBr .

A particle of mass m and charge q moves in a circular path in a magnefe *v p+4 tb:d wpnmqqu:v-89btic field B. Show that its kinetic e:p +bdw98tf bq*v4:m- u qevpnnergy is proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momentum of the particle in P/8xf *hfxyo2u roblem 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 th +7pg*f fgusc4e Earth’s magnetic fieldf *7u fc+4ggps 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 hr9q83lpuwu, 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 speed w07sqvz5 q1gum pjy- ($\nu=2.0\times10^5\mathrm{~m/s}$ 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 6p5hsz*x e9 (wq5-A current. How strong is the magnetic field 6ph* (esw9x qz5.0 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 field no larger than that+gqd4m)hk-w* kq )ivt ofiwqh-k )*)km4dt v+g q 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 dh px 2ven9yyk0tagm/832/jsstraight wire carries current I out of the page toward you. Indicate, with appropriate arrg x0/sh92njy28yapk md/v3etows, 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 exerts an attractive fopzh 3d8; 0k v9khhe:uyv 7jmf3rce per unit length pye3hzmu kfj:h7hvd;k9v 083of $8.8\times10^{-4}\mathrm{~N/m}$ 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 directio 3p069a fgqpokn of the force between two parallel wires 35 m long and 6.0 cm ap30p 9k6qopaf gart, 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 1.052l7 pyb4k.u4czf csjl6 r3v t0 m from an electric cable. What is the maximum allowable curr lt slfjz44pcr7ckb36.v25 yuent 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. What0nc -o8e5nbji +f6tbd is the magnitude of the magnetic field produced by this wire at the grounj56ne-b n+8t o0dci fbd? 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-A currents in the zhps bl2*.-arsame direction. Determine the magnetic field at point P, 12.0 cm from one wire and 5.0 cm from the other(Fig. Belo*l.s- p2 hzabrw).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18 ct;t26h m(e,t rodjt6mm due 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 component of the Earth’s, 2ej(6t;d tmhmtort6 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 :cyz qm7qts* ,jp2uu0net magnetic field 20.0 cm due west of the wire if the Earth’s fiel zcqp0sm:yj 2tu7u,* qd there points north but downward, 37$^{\circ}\,$ below the horizontal, and has magnitude $5.0\times10^{-5}\mathrm{~Т}?$
   $ \times10^{-5 }\;T$
$\theta$ =    $^{\circ}\,$ below the horizontal

  A straight stream of protons passes a given point in space at -p8k /jou5s,l cr,lg lr8szs1a 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 long se xn5xv rbd/.0traight wires 2.0 cm apart in terms of the current rbd. /0vx xe5nI 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 conducts 25.0 A of dc current to, an .ffq63 l)r5tq9s tlhfd from, an instrument. If the insulated wires are of negligible diameter 3.9) ffltrq56lt hf qsbut 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 plane of xdv33 /embt*z iqf w0x;*7axmthe two wires shown in (Fig. Below), parallel and just to the right. If it carries 25.0 A upward, what force per meter of length does*zbqmx*v fxt;/d w733e0mx ai 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 pointsh/jlk b3,icml z2h(, j bj1rnv:v 0:fz 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 pl:8vfd +yvj.duane as a straight wire, as shown in (Fig. Below). There is a current of 2.5 A in both wires. Determine the magnitude and direction of the net forj . v:fvdud8y+ce on the loop.    $ \times10^{ -6}\;N$  ----待选择----away from wiretowards wire 

  A long horizontal wire carries a current of 48lg) /a(pk0zrq8 .i msob 0pw 8;cik-hr A. A second wire, made of 2.5-mm-diamete8(kiz0lpcgr/) qs.iwk r 0-ah;bop8 mr 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 ork fu/3x syavjb4w-6n s().jov iented so 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 po.wv 6uks )34xf(/jaov- bjsnyint 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 par5j1q5 * xctnzoallel wires are 15 cm apart. Wire A carries 2.0 A current. Wire B’s current iq1j5con5ztx *s 4.0 A in the same direction.
(a) Determine the magnetic field magnitude due to wire A at the position of wire B. $\approx$    $ \times10^{-6 }\;T$(retain one decimal places)
(b) Determine the magnetic field due to wire B at the position of wire A. $\approx$    $ \times10^{-6 }\;T$(retain one decimal places)
(c) Are these two magnetic fields equal and opposite? Why or why not?
(d) Determine the force on wire A due to wire B, and the force on wire B due to wire A. Are these two forces equal and opposite? Why or why not? $\approx$    $ \times10^{-5 }\;N/m$(retain one decimal places)

  Three long parallel wires are 3.8 cm from one ano7weik6di.c g,) 9jrjb ther. (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 opposite to kcd,j)b6gierw ij.97that 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 th :yb37 7t9hwiqnwm4kbe magnitude and direction of the magnetic field at the midpoint of the side of thb bqw : nytkwi7473mh9e triangle between wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a distance d apart, carryzvrhj cq7 f (,-b-(li7vmey)bsk5 gw; equal currents I in the same direction. One wire is at x = 0, the othee75g- 7bsrwbv z ;vmj)y (il-c,fqkh(r 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 tursgwxzmn 46c 90ns of wire and carries a current of 2.0 A. Calcula ng6x90c4smzw te the field inside near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameter is t4 e a+-jgxmry3o produce a field of 0.385 T at its center. How much current should the solenoid carry if it has 975 turns of the wir- agme+r 34jyxe?    A

  A 550-turn solenoid is 15 cm long. The current in it i++fo9qb z0sac :es,z fz4q :oks 33 A. A 3.0-cm-long straight wire cuts through the center of the solenoid, along a diameter. This wire carries a 22-A current downward (and is connected by other wires that don’t concern us). What is the force on this wire fks b:o f,zc+q ozq+40:s9 ezaassuming the solenoid’s field points due east?    N

You have 1.0 kg of copper and want to make a practical solenoid tf/eim .w ;nw/jhat produces the greatest possible magnetic field for a given voltage. Should you make your copper wire long anew;nf /.m w/jid 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 a9wtp k: 0de;q+x5yrzf circle (Fig. Below). Use Ampère’s law along the circular path, shown dashed in (Fig. Below a), to deterf5 et0pywx 9dq:kzr+;mine 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 vjh8t,*newbe er 4il8u:2hh 6 the conductors of a coaxial cable (Fehhi 42te hu6jl:wve,b * 8r8nig. 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 o3 n(p:qr l zfs,rbh1zyj3e62b f wire 22.0 cm on a side is placed 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 torqu 23jfshn1(3 bpb 6,:zerzlyqr e on it is $0.325\cdot N$. What is the magnetic field strength?    T

  A galvanometer needle deflects full scale f*m*pa506 u3aznzxuwn hzm:1u or 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 weakens by 25% over themnw3 ah,wb0:0a e+fud years, what current wi ,:wdwfuha 0be n+3m0all give full-scale deflection if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by what factor does the hv 749pt1,vq d:y3*k pskcyuqoutput torque chanc vd9q hvy3ps1y:tkq u7,4p k*ge?

Show that the magnetictr,v9k9bj * qh8c khx/xu;+et dipole moment M of an electron orbiting the proton nucleus of a hydrogen atom is x98 ux* +k e;/9,jtrkhbhc vqtrelated to the orbital angular momentum L of the electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in dir/nk4lo( -e,xi6pxlzb,ct 1 nameter and containing nine loops lies flat on the ground. The Earth’s magnetic field at this location harx c znl- p/o(b,e ,lkn46tx1is 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 circ03- l jyvev(svle of radius 5.10 cm in a 0.566-T magnetic field. What value of electric field could make their paths straight? In what dirlsvj 3v-0yev(ection must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atoms have radii of curv0a1nqohm ; kb olc6ue6s-7 zii*1:bayature equal 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 the atomic masses of thezk0nqambu7:i 6aio1 -o;c b6yls h*1 e other isotopes?

  Suppose the electric field bet4q6teea-e ov: m +b,qdween the electric plates in the mass spectrometer of (Fig. Below) is ,qoed: q4-tv6e mbae+$2.48\times10^4\mathrm{~V/m}$ 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 ,r d*4ni zswwg:c4*egdifficult, however, to separate mo cr z *d*4seiw4g,g:wnlecules 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 before they entlsfsbg j1; .m7er a magnetgslb f 7m.js1;ic field B. The ions are assumed to start from rest. Show that the mass of an ion is $m=qB^2R^2/2V,$ where R is the radius of the ions’ path in the magnetic field and q is their charge.

  A long thin solenoid has 430 loops of wire per meter, and a 25-A c.o-dn4zkt21 cz309iu.k uogr mt 4z9t.rni pturrent flows through the wire. If the permeability of thec z.tut iu9k n-z1g4i43zm0ktn.rd2ro 9.otp iron is $3000\mu_0$ what is the total field B inside the solenoid?    T

  An iron-core solenoid is 38 ;o, dm h3yrd, 6 gg(svzgv/fw)cm long and 1.8 cm in diameter, and has 640 turns of wvdggs,fd3zm;rwhoy/ 6, v)g (ire. The magnetic field inside the solenoid is 2.2 T when 48 A flows in the wire. What is the permeability $\mu$ at this high field strength?    $\times10^{-5}\mathrm{T}\bullet\mathrm{m/A}$

  Protons with momentu b+1ia+n b+lfc99cgbjm $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 regitc+,cl9pd6cbi3fdd27 ccxw; on of constant magnetic field. What is cxb79dc;tdi63w p dc+2 ccl f,the ratio of the radii of their circular paths?   

  The power cable for an ewsi 5n.x*bvg/xv jl(+lectric trolley (Fig. Below) carries a horizontal currentxn ibs(+wgj . l5x*v/v of 330 A toward the east. The Earth’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 h /9d cw6qtv *r:g-p h/yghsft)as 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, thex(fjc;jyd)9g pyp* t, Earth’s magnetic field points almost horizontally to the north and has myydtxj,(p 9 *jg;p c)fagnitude $B=0.50\times10^{-4}\mathrm{~T.}$ What should be the magnitude and direction for the velocity of an electron if its weight is to be exactly balanced by the magnetic force?    $ \times10^{-6 }\;m/s$  ----待选择----eastwest 

  A doubly charged helium atom, whose mass is e lg25ukh5j 9jj6ov3tgg v4:f$6.6\times10^{-27}\mathrm{~kg},$ 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 “projectily :ev8w.xb,23 +u81-d v fhuzm toa zy30ewdgue launcher” 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 t8bow da-u:3 ,.emvtyyzg1wuux38+ f2e hdv z0he bar has a length L = 22cm, a mass of 1.5 g, and is placed in a field of 1.7 T, what constant current flow is needed to accelerate the bar from rest to 28m/s in a distance of 1.0 m? In what direction must the magnetic field point?
   A
the magnetic field must be ----待选择----updown 

  In (Fig. Below) the top wire is 1.00-mm-wfn sb*9ye(4. iqe:um diameter copper wire and is suspended in air due to the two magnetic forces from the bottom two wires. The current flow through the*qmn b4:uefw.s9 (eiy 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 horizontal n0;/cr *acqapp) tv 0eplane act as rails to support a light metal rod of mass m (perpendicular to each rail), (Fig. Below). A magnetic fi ;rp0*0ectp vqc na)/aeld $\vec{B}$, 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 vae7+ (2m-c nbo7 zvw nyt5q5felectron beam near the center of a TV screen due to the Ea2wto-b7vn (ycmn+5q5f vz ae 7rth’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 au a3wc d;cs/jfc. lr82ccelerate elementary particles such as protons to high speeds. Particles starting at point A with some initial velocity travel in circular orbitsw .jc8l;c dcfr /2su3a 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 pa3 0,/jt7 oxj9 saiqhfbrallel wires, located at the corners of a square of side lb0atq xs7iho 9fj/3 ,j, 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 v/eaf9u*jxrn /ery useful in particle 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 i9uen /r xj*/afs 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 ce* *qd4wp x1hfmnter of a circular coil of wire carrying a current I (as in Fig. Bel4* *wxm qdfhp1ow) 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 polb 7p75 p81)wi ,pusyd5hsmd ewes the magnetic field is about 1G($ 1\times10^{ 4}\;T$) Imagine a simple model in which the Earth’s field is produced by a single current loop around the equator. Roughly estimate the current this loop would carry. [Hint: Use the formula given in Problem 80.]    $ \times10^{ 9}\;A$

  You want to get an idea oc4i b4*jb,xxunwbd+ 79m by 6if 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 th4yb4dbimx u cbjw+7,n*ix b69 e lines operate at 10 kV and provide a maximum of 40 MW to the local area. Estimate the maximum magnetic field you might experience walking under these power lines, and compare to the Earth’s field. [For an ac current, values are rms, and the magnetic field will be changing.] $B_{net}$ $\approx$    $ \times10^{ -5}\;T$(Round to the nearest integer)

  (a) What value of magnetic field would make a beam of electrons, travelv9(q4 b6pi2m0evclo ling to the right at a speelp( cv6 4eq vio9bm0l2d 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 q6 -abno7 lv-2)dfh7hh(h sghfield 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 8.5 mm, respectively. Calculate the change in the kinetic energy of the proton as it travels from P to a- hgn2hd b) olh6h(q-sf7 hv7Q.    $ \times10^{-20 }\;J$

  A 32-cm-long solenoid, 1.8 cm in diameter, is to produce a 0.30-T6ymqf;g 8 icz3 magnetic field at its cente 3cm;ygq8zif6r. If the maximum current is 5.7 A, how many turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wire0(eo emn*ehq tjg*p5c.kjgr 0 /i* e.js, each of diameter 0.50 mm, carry the same current but in opposite directions. They are suspended by 0.50-m-long strings as shown ( kejc pr5mj *hq etjgeo0*.eni/.*0gin (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 adq6o65d2t p wpon7,kz fv; b0zt 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$