A compass needle is not always balanced paok,ro.0 p k(zlrallel to the Earth’s surface, but one end marpz( .o0kl ,koy dip downward. Explain.

Draw the magnetic field lines around a straight section of wire car8 l h/ .5p,v du;r-tp:gslwijuzc*+d/dsj n,wrying a current horizontally to the ls cu/l*;+/,puzjn8 5tgdv wplrds i:,-h .dwjeft.

In what direction are the magmlx:k 4:,s.ufm* ; yke: gotgknetic field lines surrounding a straight wire carrying a.kky; ust 4:*, f: emk:logmgx current that is moving directly away from you?

A horseshoe magnet is held vertically with the northuy tsfp 1fmdd x0n/j (v5()h4p pole on the left and south pole onsy5( n 1ptfm 4dhj/ u0f()xdvp 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 the wire?

Will a magnet attract aoyted l7; x;9s0w+ aopny metallic object, or only those made of iron? (Try it and see.) Why is this sosy de70t9; ;wx p+oalo?

Two iron bars attract each other no matter which ends are placed close together+2pe5 zbb1w ot. Are both magnet pt2e1ozw+bb 5s? Explain.

The magnetic field due to current in wires in your home can affect a compass. Diw88zmv6;mxk 6vtmk+)3hf qjvscush86vv v m)fx8k kz;qt+6mm3jw s the effect in terms of currents, including if they are ac or dc.

If a negatively charged pr(a0o7 hze nh7article enters a region of uniform magnetic field which is perpendicular to the particle’s velocity, will the kinetic energy of the particle increase, decrease, or stay the same? Explain your answer. (Neglect gravity and ass7(hzerh7ao n 0ume there is no electric field.)

In(Fig. Below), chargjas *64gj *yc(zlg 1maed particles move in the vicinity of a current-carrying wire. For each charged particle, the arrow indicates the direction of motion of the particle, and 4cg6* a*1jz(sg yaljm the + or - indicates the sign of the charge. For each of the particles, indicate the direction of the magnetic force due to the magnetic field produced by the wire.

Three particles, a, b, and c, enter a magnetic field as sh52/mk0bqm owh own in Fig. 20–46. What can you say abouk2bm/ moq wh50t the charge on each particle?

A positively charged particle in a nonuniform magnetic field follows the t ;qbg/dqb 4t7j2,cllwyvo8t 1 rajectory shown w/lq;v t,18ycb2g dlo4b jq7tin
(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 5of,kci)r.yxz h6y y4t-0wb y a magnet attract an iron rod? What must you consideyh6 ,bcr tki4)5 wy-x0o yzfy.r to answer these questions?

Explain why a strong magnet held near a CRT television screen (Section 17–10) caus5+ :g 56hx5zrz4gfi cmdi2suses the picture to become distorted. Also, explain why the picture sometimes goes completely black where the field is the strongest. [But don’t risk damage to your TV by tryi:r i5+c5ux gs 52gzsid4z6hmf ng this.][/But don’t risk damage to your TV by trying this.]

Suppose you have three iron rods, two of which are magnetized but the th:gl f2 zsn:5(+cgxl dqird is not. How would you determine which two a: :zsfg dllg cnx25q+(re the magnets without using any additional objects?

Can you set a resting electron into motion withlxoth4 ozb.djf8jkps/j u777i9q9n- a magnetic field? With an electric fi7hdjolq.unk i7t oj /4sz9 p7f8bx9 -jeld? Explain.

A charged particle is moving in a circle under the fr,px- 6 iplasp;q6 jp9 *+dakinfluence of a uniform magnetic field. If an electric field that points in the same direction +sp;pd 9p6axpa-qfikr, * 6lj as the magnetic field is turned on, describe the path the charged particle will take.

The force on a particle in a maitu7d9be 9 - -hexkb 2ny-tni/gnetic field is the idea behind electromagnetic pumping. It is used to pump metallic fluids (such as sodium) and to pump blood in artificial heart machines. The basic design is shown in(Fig. Below). An electric field is applied perpendicular to a blood vessel and to a magnetic field. Explain how ions are caused tou/iytnx9en2kt- h9-bdb ei 7- 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 fh x+.w8f j6vakrom ljkx.fvw +86 haeft to right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fieyf( zwad:; uu7cuql*2lds that surround a moving electric charge.:*uzf uwu;ac2 ( ld7yq

A charged particle moves in a straight line through a particular region of spachd mmdp )9k)y8 /zs.ffa ,u7zge. Could there be a nonzero mag h8. szmdu )/gf z)kfdm9,7pyanetic field in this region? If so, give two possible situations.

If a moving charged particle ik13 dnvbb6-hhs deflected sideways in some region of space, can we conclu3h n1b6v- hkbdde, for certain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is a unif nq5wo8gckdx/o ) z.d us;,vd8orm 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 m95sq ja5w4x yooving electrons in a certain region of space are being deflected by an electric field 5jy95q4saxwo or by a magnetic field (or by both)?

How can you make a compass withou9n8cq+sa k;f l(cew v,t using iron or other ferromagnetic material?

Two long wires carrying equal currents -p yn-rb-*mc qI are at right angles to each other, but don’t quite touch. Describe the magnetic for-*q- -cn ypmbrce one exerts on the other.

A horizontal current-cara. d a,ye);z;hxa-bks. pdbi. rying wire, free to move in Earth’s gravitational field, is suspended directly above a second, parallep. bydhsead b;ki.z; aa.x),-l, 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 piece of.hk:o 1(q2oawzq 4 ubb iron?

An unmagnetized nail will not attract an unmagnetized paper clip. Hpt e.3h5h0yauv(: vn-+wlllb owever, if one end of the nail is in contact withw0vlpl th:vbnyl e. (+hua5-3 a magnet, the other end will attract a paper clip. Explain.

Two ions have the same mass, but one is singly ionized aqd1e3 .c1js iund the other is doubly ionized. How will their positions on the filmi3q1jcsue1d . of a mass spectrometer (Fig. Below) differ?

What would be the effv +tll:orwe*9 ect on B inside 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 hkh fs ,7q7m*l+ bi,khig, i0xsimilar to a solenoid is a relay . A relay is an electromagnet (the iron rod inside the coil does not move) which, when activated, attracts a piece of iron on a pivot. Design a relay to close an electrical switch. A relay is used when you need to switch on a circuit car mhq bfh7ilkix7 g,,+i s0,*hkrying 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 s vyzhing5a(e/wf2u8 6x00 so ltraight wire carrying an h28 w06e5o/xyusv lagi( fz0n8.40-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 forceyb u4wxg/e me3i9ti90 on a 160-m length of straight wire stretched between two towers carrying a 150-A current. The Eart tx0uebi4ge 9 iy/9w3mh’s magnetic field of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  Calculate the magnitude of the magnetic force on a 160-m length of stgj)x fx6hg; rr*d p(fp7s7lost)w, /traight wire stretched between two towers crx/ ;o))fg*r,pt(fxhgst 67djp sw 7larrying 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 longmy*bf 6t:a:lbnwkf rw t38u -. if the maximum force on it is 0.750 N when placed in a uniform 0.0800-T fi- f:tny* l 6 wuw:8t.fa3mrkbbeld?    A

  A 1.5-m length of wire carrying 4.5 A of current is o nkew0e *q*lsy 3mt9m)ob9i/zriented horizontally. At that point on the Earth’s surface, the dip an* sq/izoblywe3n)90 e*9t m mkgle 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 ak,ttd o0tm k,aohe 7wy12o)fo*1zq /carrying 8.75 A is a maximum of 1.28 N when placed between the pole faces of a magnet. If the pole faces are 55.5 cm in diameter, whafyok, d/,*zoaaq2tohow)e1 10t t mk7t is the approximate strength of the magnetic field?    T

  The magnetic force per meter on a wirsqj)fp1fxs 1 l k*d;3ke 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 sketch the relationship as i3d)sl;1fpxsjkk q*1f t actually is, calculating the angle between the wire and the magnetic field.    $^{\circ}\,$

  The force on a wire is a maximua)06 *bmxjs ;+ga:5sg.l +ws mzx kzqym 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 scb-g(c3,jya qv-f+lok 85xa “float” horizontally in air because of the force due to the Earth’s magne3cco + --xqgsy,l5 vbkafj (a8tic 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 chargernbycr 1-w51s *p ugm5 $q\,=\,+2e$ 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 elecu(qcp 8 e6;muptron 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 diagram shown -ri a ;)kqvp :glm4k3iin (Fig. Below4kqmkr l:;-g iv 3p)ia), 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 ofs0 gzl)/ lqja;p9e5jj $\vec{B}$ 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 ygro;xn z4t 1q/t6o/h vertically upward 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 fi*txf2s1v5 ,qgz4 z ,/ml lwvgleld, in a plane perpendicular to the field. Whvtfg/ zls4q1lzgm ,vlx*,25w at is the radius of its path?    m

  An electron experiences the greatest force as it traj ./drwmi a.3 .lqag -wmsi.:cvels $2.9 \times10^{6 }\;m/s$ 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 when paox7a. d47-w4vp zfpdbssing through pb -axp47 vwp4od. z7fderpendicular 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 heliumzs/ysb am/p4*fc :o +p atom 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 parthhn 3r(zb vk87icle of charge q moving with constant speed v to make one circular revolution in a uniformk hh8v(7rnb z3 magnetic field $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge q moves df3j.: scuaxt :;4y3 ikl1npg in a circular path of radius r in a uniform magnetic field B. Show that its momentum igdi1l4af t nsk y;:cj.33pu :xs p = qBr .

A particle of mass m and charge q moves in a crc .7/xuw 2p k w o-tc;qd.zj23pclyt1ircular path in a magnetic field B. Show that itskd .-/ql 7opy x.;22jpwuwtczc3 tr1 c kinetic energy is proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular moment,hm)8j v7 l q.ss2uboyum of the particle in Problem 21 is $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves with a speed of 160 m/s perpendicular to the Earth’s magdkj jhwh 4 df;r29x+o1netic field dx wr+d;ohj1k9 jhf4 2of $5.00\times10^{-5}\mathrm{~T}$, 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) :f-pj asaqv5 field 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 withkt3iq .dqa.(,7x sp e::srd- jii* lr:,cemzt speed $\nu=2.0\times10^5\mathrm{~m/s}$ 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 tb cfz6y ,9vcs2x-1rkto start a stalled vehicle carries a 65-A current. How strong is the magnetic field 6.0 cm away from it? Comp rvxc,c zs-y tb6f291kare 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 figts7va xz8-5;n/y m8qv xf1uueld no larger than that of th /x guyxqs8;vma-v7u1 n5ftz8e 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 stra b) yxc-e /fsyh ll+5 0lzr/x:kwz77yright wire carries current I out of the page toward you. Indicate, with appropriate a7rlhx:fsy-yl0/cl+x)z75e b wr yzk/ rrows, 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 exermj ls7kxw:x85 mp47r3pjrie)ts an attractive force per un 7kr 85wj7 persp xmlx)m:34jiit 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 two p6wh0 ;p+p fbvgl(tw: karallel wires 35 m long andb+ pk0pv6wt:f gh l(;w 6.0 cm apart, each carrying 25 A in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magng z(r v.g0g1iiv-xs o6etic field is being carried out 1.00 m from an electric cable. What is the maximum allowable cu0r1vgg6 i-v os (gx.izrrent in the cable if the experiment is to be accurate to $\pm1.0\%?$    A

  A power line carries a currenb,43njzbpe8* ay.vzq 2 o ,f5m8uaev zt of 95 A along the tops of 8.5-m-high poles. What is the magnitude of the magnetic field produced by this wire at the ground? How does this compare with the Earth’s fizz,4auzbv b,f8o3y m 2qe.jvape85 * neld 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 cpt0ta rl-h ub;s+e4g mj pz;+:arry 25-A currents in the same direction. Determine the magnetic field at point P, 12.0 rlh + t -jbs0g+ ptp:a;;zemu4cm from one wire and 5.0 cm from the other(Fig. Below).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18 cm due south from a straig3 m* yy2r).pey,q,emabg rl/rht vertical wire carrying a.g)3r m/la, ,emp2* bye qyrry 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 wire carries 22.0 A of ca:c ;5m.urjfe urrent due north. What is the net magnetic field 20.0 cm due west of the wire if the Earth’s field there points north but down5m af:;e .rcjuward, 37$^{\circ}\,$ below the horizontal, and has magnitude $5.0\times10^{-5}\mathrm{~Т}?$
   $ \times10^{-5 }\;T$
$\theta$ =    $^{\circ}\,$ below the horizontal

  A straight stream of protons passes a given point in space at a rate ofb:bry5 n0m-vt $1.5\times10^9\mathrm{~protons/s~}.$ What magnetic field do they produce 2.0 m from the beam?    $ \times10^{ -17}\;T$

Determine the magnetic field midway between j,6nj5gtgqq 7two long straight wires 2.0 cm apart in terms of the currej7qng6qg, j5 tnt 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 conducts 25.6n ta.6w5sb6g- xeo(b 5uxl-yjhn z (f0 A of dc current to, and from, an instrument. If the insulated wires are of negligible diame-st n5xube(6 (lhog6a6.5x zbyjf-w nter but are 2.8 mm apart, what is the magnetic field 10.00 cm from their midpoint, in their plane (Fig. Below)? Compare to the magnetic field of the Earth.
   $ \times10^{-6 }\;T$ The field of the wires is about    % that of the Earth.(retain two decimal places)

  A third wire is placed in the plane ojs*jx;i7 (ztdk: mehj+ 7eh9df the two wires shown in (Fig. Below), parallel and just to the right. If it carries 25.0 A upward, what force per meter of length does it exert on each of the other two wires? Assume 9hx j;tkd7i(eh+se md j* :7jzit 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 poito6+ 8 so)wztdnts 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 pod-(cbl:i3bb n l p0r8lane as a straight wire, as shown in l-l c:bb3i( dr0onb 8p(Fig. Below). There is a current of 2.5 A in both wires. Determine the magnitude and direction of the net force on the loop.    $ \times10^{ -6}\;N$  ----待选择----away from wiretowards wire 

  A long horizontal wire carries aj sja70.e6b ruhdy0avv 6z)(h current of 48 A. A second wire, made of 2.5-mm-diameter copper h(s d0vr.z0ea6ujvy jhb)a67wire 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 eao57+leh yj c, (8o9dz khul2apch 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 of 20.0 A and the bottom one caj( eo5z8,uhy9+c7pl ko dl2ahrries 5.0 A?    $ \times10^{-5 }\;T$

  Two long straight parallel wires are 15 cm apart. Wire A carries 2.0 A cur(y,i09g xle 58qgr3yqhms vz(d4y z(orent. Wire B’s current is 4.0 A in the same d(5 d,qzl q0ygg4x(o shvy i8m(ez93 yrirection.
(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 ano3au37s 7.jfppql t8 h)vz0ubuther. (Looking along them, they are at three 3)7aj8phb7fzqu3ul vp.sut0 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 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 magnitw*,cf5eu:2l j 5ru) ebkp8a o2cc zr+qude and direction of the magnetic field at the midpoint of the side of the triangle between wire M acc efj )uwk+2,5c pa8*qeb:zlru25rond wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a distance d apart, ca e1 m+0w6hptwum bpo5w 4yy8a7rry equal currents I in the same direction. One wire is at x5 bmyt1 y0mw wa+4 huopw86ep7 = 0, the other is at x = d, (Fig. Below). Determine $\vec{B}$ along the x axis between the wires as a function of x.

  A thin 12-cm-long solenoid has a 7ogwk d gd*c;4total of 420 turns of wire and carries a current of 2.0 A. Calculate the field inside near th*k4go7; cgddw e center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenosgusxs8zm )p, n22 *cfid 1.25 cm in diameter is to produce a field of 0.385 T at its center. How much)sm8ngs xpz 2,cu2sf * current should the solenoid carry if it has 975 turns of the wire?    A

  A 550-turn solenoid is 15 cm long. The current in it is 33 A. A 3.0-cm-ls-v75)b kg 5ud0ycw5epng s u;ong straight wire cuts through the center of the solenoid, along a diameter. This wire carries a 22-A current downward (and is connected by otherpsn-gs c5 5ve750 dk)ywbu;gu wires that don’t concern us). What is the force on this wire assuming the solenoid’s field points due east?    N

You have 1.0 kg of copper and want to make a practical solenoid that produkcee y* y8:jxtr9de59yg yb9.ces the greatest possible magnetic field for a given voltage. Should you make your copper wire long and y 8c9e:g9.xk9eytryyd5e j*b 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 /6xj03 vz3awtjv+tb n a circle (Fig. Below). Use Ampère’s law along the circular path, shown dashed in (Fig. Below a), to determ /+njtwbv0j a3 ztv36xine 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 ma;36+p7y-vwsn e wmy xku47czfgnetic field between the conductors of a coaxial cable (Fv+uwy7 3;z snfykc4 wxm6 7-peig. Below) is $B=\mu_0I/2\pi r$ if r is greater than the radius of the inner wire and less than the radius of the outer cylindrical braid.
(b) Show that B = 0 outside the coaxial cable.

  A single square loop of wire 22.0 cm on a side is placed with it o dx 3yx3regf.1*hfc9li:r7d s face parallel to t3xelf9 *xdrf: ig d3ry1c7o. hhe magnetic field between the 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 deflects full scale u( . zxl a. *pey4s/b+/fhjaysfor 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 bywyk+1h m/ it ;ieiohj/n((k ,q 25% over the years, what current wi k/inj;thimi( +ehq, /w1oky( ll 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 out;kligqbq jr-4) zozehlp 16/(put torque chang1zeg zqrihl(/q - 6k;boj4)pl e?

Show that the magnetic dipole moment M of an electron l9j i (aw6u+t4h kh+xforbiting the proton nucleus of a hydrogen atom is related to the orbital angular momentum L of the e6h9(hl+au4xw+ t kfj ilectron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter and containing b(ou mt(i //rj rhc7v5e9g zriuq(+*b nine loops lies flat on the groun cvbo7m rh9utue(i + z/riqbrj5/(g*( d. The Earth’s magnetic field at this location has magnitude $5.50\times10^{-5}\mathrm{~Т}$ and points into the Earth at an angle of 56.0$^{\circ}\,$ below a line pointing due north. If a 7.20-A clockwise current passes through the coil,
(a) determine the torque on the coil,   $\times10^{-5}\mathrm{m}•\mathrm{N}$
(b) which edge of the coil rises up: north, east, south, or west?

  Protons move in a circle of radius 5.10 cm in a 0.50xm.q/ t(+8xtj9 go c4htghgo66-T magnetic field. What value of electric field could make their paths strahoj8t 0qx(gxth+gc .otg4 9m /ight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atoms have radii of curvatuq6katt ;k6)o*u pdo :2jam rj:re equal to 21.0, 21.6, 21.9, 22.2, and 22.8 cm. The largest radius corresponds to aakp:a;qjjt or6*tou2dm k6 ):n atomic mass of 76 u. What are the atomic masses of the other isotopes?

  Suppose the electric field b e2k6vp yt6m) g8/4v,iwdx3 phpev7 uwetween the electric plates in the mass spectrometer of (Fig w6mkp2/xu,v vy4p3g 6 7wihp)ved8et. 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 po 8s tp8sqzjd.trlc7u02fz3 m/llutants. It is difficult, however, to 8l /.s7p03dz zcqf8ur ttmjs2separate 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 accelerate4i6lo p)e0:g2 ihs2b gv2fyiswmy *,xs ions by a voltage V before they enter a magnetic field B. The ions are assumed to start from rest. S gyp2*mw4h bss ii:0)2 iyv o,f26egxlhow 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 cux2p*q+je3h w: tdn(vh+h).x yu4td ivrrent flows through the wire. If the permeability of the : di2jv+hhx( dt uv3+t4yh )q*nx.pweiron is $3000\mu_0$ what is the total field B inside the solenoid?    T

  An iron-core solenoid is 38 cm long and 1.kvi185xt) gzz8 cm in diameter, and has 640 turns of wire. The magnetic field inside the solenoid is 2.2 T when 48 A flows in the wire. What is the permeabilityv5z 81gz)xtki $\mu$ at this high field strength?    $\times10^{-5}\mathrm{T}\bullet\mathrm{m/A}$

  Protons with momentu,*e3zvkc,ccas5e 8z 5 xf.hn zh/.varm $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 hawl)ku4fewv(3 df k)v 5p1f5 bpve the same kinetic energy upon entering a region of constant magnetic field. What is the ratio of the radii of their kvff 1w bpef()pk5)du5v4l 3 wcircular paths?   

  The power cable for an electric troldqqo*o/9 de 5sley (Fig. Below) carries a horizontal current of 330 A toward the eastesq9 o o5qd/*d. 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 has acqyra) x5nqo 9/e*j+hfh uired a net charge of $1550\mu C$ and moves with a speed of 120 m/s perpendicular to the Earth’s magnetic field of $5.0\times10^{-5}\mathrm{~T}$.    $ \times10^{-6 }\;N$

  Near the equator, the Earth’s magnetic field pointstnwr1)6xdeec;g* k1e i w:s s. almost horizontally to the north and hasrgnx :de6 s1i 1);w s.tw*ceek 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 ; mkti. 4ccx;qmass 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 in (Fig. Below). A large curren *ffk kshn -:iu/dl9jkm:++ni t moves in a closed loop composed of fixed rails, a power supply, and a very light, almost frictionless bar touching the rak +j-i:h/d: nn*kuik 9fflms+ils. A magnetic field is perpendicular to the plane of the circuit. If the bar has a length L = 22cm, a mass of 1.5 g, and is placed in a field of 1.7 T, what constant current flow is needed to accelerate the bar from rest to 28m/s in a distance of 1.0 m? In what direction must the magnetic field point?
   A
the magnetic field must be ----待选择----updown 

  In (Fig. Below) the top wire is 1.00-mm-diameter coppzn e4n 7sy.,(g 9ghbjfps7qj 0er wire and is suspended in air due to the two magnetic forces from the bottom two wires. The h9gj7q4f.pn(s,ybe ns0jg z 7current flow through the two bottom wires is 95 A in each. Calculate the required current flow in the suspended wire.    A

Two stiff parallel wires a distance l apart in a horizontal plane :g/c9mg 2jt:g(v uepq)ji4vnm n 6ve:+;yyqaact as rails to support a light metal ron;:v4yp +q:gn 6vt/eu jvc(9 i2jme gqmgy:)ad of mass m (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 defl25fcp/6zh mrlection of the electron beam near the center of a TV screen due tmhcpl6/zrf2 5o 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 elementary ga9 sps p1zz5)sqm3af(*gml- particles such as protons to high speeds. Particles st sm3lg fzaz 15p)sag -q*psm(9arting at point A with some initial velocity travel in circular orbits in the magnetic field B. The particles are accelerated to higher speeds each time they pass through the gap between the metal “dees,” where there is an electric field E. (There is no 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 straigh9n,am 7qdr*lx t parallel wires, located at the corners of a square of side l, carry equal currendlm 7na,q9 *rxts $I_0$ 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 acj2q xlrkx. 7,rpxz+y- celerators 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 wi qk,rlz -r pj7+x2.xxyth 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 of a circular coil of wire carrying a curjjpw*+bkf4e4h 8onn 7 rent I (as in Fig. Below)jofe n bn*k+p87j w4h4 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 mad qw.j/b3dvns /:j)l mgnetic field is about 1G($ 1\times10^{ 4}\;T$) Imagine a simple model in which the Earth’s field is produced by a single current loop around the equator. Roughly estimate the current this loop would carry. [Hint: Use the formula given in Problem 80.]    $ \times10^{ 9}\;A$

  You want to get an idea of the magnitude of magnetic fields produced by over7v)f7;ajwy-84*a,v fz w:n e s gbxgcyhead 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 en48x :gvyf7c-a7*wwbjs g,v;yf)az 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 ofi vndmx)m h)dr+x v/w 5mcj29* electrons, traveling to the right at a speedrw d ) *vdcvj/mm9h2mx5)+ nxi 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 a4ndiqap z55 q. gas in a magnetic field of 0.010 T, perpendicular to the plane of the spiral, as shown in (Fig. Below). In two successive loops, at points P and Q, the radii are 10.0 mm and 8.5 mm, respectively. Calculate the change in the kinetic energy of the proton as itz5p5 d i.nq4aq travels from P to Q.    $ \times10^{-20 }\;J$

  A 32-cm-long solenoid, 1.8 cm in diameter, is to produce a 0kc5p yu2 -gdksvw 7iyn +aa y95fo*88e.30-T magnetic field at its center. If theef878psnw y2ac5 9*+aigou k v-ky5yd maximum current is 5.7 A, how many turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, each of diameter 0.50 mm, carry the se/z9a6x.vy lxb kpp7 hr+.g)szqcb86ame current but in opposite directions. They are suspended by 0.50-m-long sabrbekpszq h/87p)+l6cx. 6g 9vyxz. trings as shown in (Fig. Below). If the suspension strings make an angle of 3.0$^{\circ}\,$ with the vertical, what is the current in the wires?    A

  An electron enters a uniform kv d lm;2/mqcfbtd 9(3magnetic 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$