A compass needle is not always balauoyb rlocn ysthbw( *60j,sg57o xu3a .(.fl)nced parallel to the Earth’s surface, but one end may dip dooc,()bhlj g nuw.y6a3 ufo 057sxsob*t. ylr(wnward. Explain.

Draw the magnetic field lines around a straight section of cr07x8cmlrpkhw.6 6uwire carrying a current horizontx6lc8w r7kch6 pr.um0 ally to the left.

In what direction are m w y5y.1(y.z46paxgyvc+jvfthe magnetic field lines surrounding a straight wire carrying a current that is movin+av j(yvymyw.z6xy54 pf .1gcg directly away from you?

A horseshoe magnet is held vertically with the north pole on ,t +m;lka n9tqthe left and south pole on the right. A wire passing between the poles, equidistant from them, carries a current directly away from you. ,qmt;t+k nla9 In what direction is the force on the wire?

Will a magnet attract any metallic object, or onl 6wb c2yi9eph4gcf;r4goz - a4 z4.ytpy those made of iron? (Try it and see469rw g i2ccy; gt.zb 44-h yzpfao4pe.) Why is this so?

Two iron bars attract each other no matter which ends are placed close together. rgp/b;(,c j*b emi,utr.kn9 u Are both magnets? Explaikj t,rg / m* b9c;i(,bu.epurnn.

The magnetic field due to current in wires in your home candphs.t9z /s- nu-mo - nb(6wrj affect a compass. Discuss the effect in terms of n -hb(us9noz.w-6dj /m-t rs pcurrents, including if they are ac or dc.

If a negatively charged particle enters a region of uniform magnetic ;a+7.mlncp i5hl fk976qwyzb y m d;e3field 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 assume th77 eznwm 9;dklpm35 yayhlbq i. f6c;+ere is no electric field.)

In(Fig. Below), charged particles move in the vicinity of a cus3) e)3mhuumtri e* :qrrent-carrying wire. For each charged particle, the arrow indicatesui3qeumht3)mer * ) :s the direction of motion of the particle, and the + or - indicates the sign of the charge. For each of the particles, indicate the direction of the magnetic force due to the magnetic field produced by the wire.

Three particles, a, b, and c, enter a magnetic field as shown in Fig. tb1+(d-kse,nwwzndh)v4k5 x 20–46. What can you say about the charge on each particle?k wz nnv 4s5h)bxe+, wk(d1t-d

A positively charged particle in a nonunif3;fnqszc jk.; zcxv y 9wlf*,0orm magnetic field follows the trajectory .wz nl*c9f c x;jqsz3,v;ykf0shown 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 .kqk54d2 zjyj0szu x;a magnet attract an iron rod? What must you consider to answer 2q4 5 zdjsux ;zy0kkj.these questions?

Explain why a strong magnet held near a CRejt.ntm9aen4 5 c gt ,d:5s:iuT television screen (Section 17–10) causes the picture to become distorted. Also, explain why the picture sometimes goes completely black where the field is the strongest. [But don’t risk dam 5j:meiu5 te:9ct.4atn, dngs age 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 magnetized but- ds1zv9,qd fi the third is not. How wouldv 9fqiz,ds- d1 you determine which two are the magnets without using any additional objects?

Can you set a resting electron into motion with a ma rk1a.l /+cexu bie2aqe qp6 n6tn-0(sgnetic field? With an electric field? Ekqec.x(p /21ast6q r6u+b0 inaele-n xplain.

A charged particle is moving in a circle under th( w ed/(pmhm(ve influence of a uniform magnetic field. If an electric field that points in the same direction as the magnetic field is turned on, desc( p/d v((mwhemribe the path the charged particle will take.

The force on a particnx9;q1n dz)v ple 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 de19d)p nq;nvx zsign is shown in(Fig. Below). An electric field is applied perpendicular to a blood vessel and to a magnetic field. Explain how ions are caused to move. Do positive and negative ions feel a force in the same direction?

A beam of electrons is directed toward a horizontazkb/ hkwkg, ;8l wire carrying a current from lefkw/;zkk,8 g bht to right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields that surround 6j-zywq8qdw ; a moving electric charge.zwdyq;6- 8qwj

A charged particle moves in a straigrare 3u jw s-v25s*8oy*x1pmyht line through a particular region of space. Could there be a nonzero magnetic field in this ruev y2 5 x*rspwra3j*syo8 m-1egion? If so, give two possible situations.

If a moving charged particle is deflected sideways in someg:gx5 spk6 fk) region of space, can we conclude, for certain, th:g5 6) kxsfgpkat $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is a un.h 46vndfm f8,y4jwyliform 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 are omct5c ;dtx9 h3,won(xpu as7./ ec/h being deflected by an electric field or by a magnetic fieunco t,pt3 .dxcmexa s/hwoh (/7c5 ;9ld (or by both)?

How can you make a com0.gqzo;dn, bm pass without using iron or other ferromagnetic material?

Two long wires carrying equal currents I are at right angles to each other,v9tv0 t)9kat j but don’t quite touch. Describe the magnetic fo9ta 0jt kvv)t9rce one exerts on the other.

A horizontal current-carrying wire, free to move in Earth’s gravitational f 39gglxis49ua ield, is suspended directly above a second, parallel, curreni9ug l9ga3s 4xt-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 a;qhjgwodl) :fu-o0:hxm q86os 9 7uacttract an unmagnetized piece of iron?

An unmagnetized nail will not attract an unmagnetized paper clip. However4(p (fedtf+nu , if one end of the nail is in contact with a magnet, the othu(fed(t fp n+4er end will attract a paper clip. Explain.

Two ions have the same masscsa .:8z/ekl ) ubkc, :jkrgy*, but one is singly ionized and the other is doubly ioni,:ae kcku)ykzsb:/j rc*.8glzed. How will their positions on the film of a mass spectrometer (Fig. Below) differ?

What would be the effect on 7ionv3*t g *fd2tbe+lB 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 similar to a solenoid is a relay . A re bn b3 9 jf,0js/kxxq* xuvagnvvj(72+lay is an electromagnet (the iron rod inside the coil gsvvx + 9xb ank2v, f(n0*jj7/jx3uqbdoes 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 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 cau 9k rtddq1*)jrrying an 8.40 kt rqd9)*d1uj-A current when perpendicular to a 0.90-T uniform magnetic field?    N/m
(b) What if the angle between the wire and field is 45.0$^{\circ}\,$?    N/m

  Calculate the magnitude of the magnetic force on a 160-m lc clh38-l5+rztyp4 fl+4* . xnhhyso dength of straight wire stretched between two towers carrying a 150-A cyy3 -x84cl+.l h pzl+hnsd4 och*rt5f urrent. The Earth’s magnetic field of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  Calculate the magnitude of the magnetic force on a mo/ 02+yh/cyjwoq+ bu160-m length of straight wire stretched between two towers carroom +u/ w+0/ 2jqyhbcyying 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 the maxb7np */(varewzg as/+ imum force on it is 0.750 N when placepranab + vg(/se*w/z7d in a uniform 0.0800-T field?    A

  A 1.5-m length of wi kqgvassb8bha s)q3)l)6hy;3re carrying 4.5 A of current is oriented horizontally. At that point on the Earth’s surface, the dip angle of the Earth’s magnetic field makes an angle o8hah3s;lyk)a q 6gbsvbs3 q))f 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 +0-r u-g;ualc9 hsyvvz8lzy 5 auy*z11.28 N when placed between the poley;gzs-5 uu1z uv*+8 y-acvyhlz 90arl faces of a magnet. If the pole faces are 55.5 cm in diameter, what is the approximate strength of the magnetic field?    T

  The magnetic force per)1bxf9( r+ot ,yrsu-ect2m.t 5cxnib meter on a wire is measured to be only 35% of its maximum possible value. Sketch the relationship of the wire and the field if the force had been a maximum, and sfs-2bxt1+,ceo.bu m i9y rt)t (xn rc5ketch the relationship as it actually is, calculating the angle between the wire and the magnetic field.    $^{\circ}\,$

  The force on a wire is a maximnkxa8 aeo81r :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-diameter copper wire could just “float” hopz6a/t ;l8artc7ch+ sm1tn 2rrizontally in air because of the forc ; tz+hcl2rtc/mntsr7 6p1a8ae due to the Earth’s magnetic field $\vec{B}$, which is horizontal, perpendicular to the wire, and of magnitude $5.0 \times10^{ -5}\;T$. What current would the wire carry?    A Does the answer seem feasible? Explain briefly.

  Alpha particles of charge fx j it/( dur::8tvoe9 nzvc64$q\,=\,+2e$ 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 ( dj7h),b ngtvdirection 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 c 6o ran0nd6+;cjwe0ppharge for each diagram shown in (Fig.apwnn orcedj 0 p+0;66 Below), 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 o ymqie gbw80fd6d8nn v a2*3wq0wp9 b.f $\vec{B}$ 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 upwah xp(*j- kcym(rd with a speed of $1.7 \times10^{6 }\;m/s$ into a uniform magnetic field of 0.350 T that is directed horizontally away from the observer. Describe the electron’s path in this field.    $ \times10^{-5 }\;m$

  A 5.0-MeV (kinetic energy) proton enters h4xj2t afz.8kznn1h 8xnx ( /ya 0.20-T field, in a plane perpendicular to the field. What is jn .4f2 (1hx8x n zyk8h/naztxthe radius of its path?    m

  An electron experiences the greatest hajva v+hm-: /w dj5(vforce 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 when passing thre*wjqsjkd2)i3d+0wwldx1 wov) t,7r 5 fb v3sough perpendicular electric and magneti53 *jeit ovbs3r1xdv0qw, 7ks 2jdd)wf+ lw)wc 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 7ewrko.:gv c(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 particle of charge q moving w o k*b 559xbb j0xc5(p3mgyyytith constant speed v to make one circular revolution in a unjbgb5 cxp905 5my(yko*x bt3yiform magnetic field $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge q moves in gv+bbo n6ku:8 yv70wta circular path of radius r in a uniform magnetic field B. Show that its momentum is p = qv06gnu+ b: 8otwk 7vybBr .

A particle of mass m and chargeaj/i.:yi:manxe/0h sb7j7c h q moves in a circular path in a magnetic field B. Show that its kinetic energ7:jibn ihhc/m/a:s.ye7 ajx0 y is proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momentum of the particle in Problem 21 ih)k ocsv4oz9w4m +: +iov je9bs $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves with a speed of 160 m/s perpendb m5ze++otsz1icular to the Earth’s magnetic fie15ot bmz+e +zsld 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 ms7g4me)oka k5nic ;, tagnetic 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 with spcce 0f-67k oql +zzqr0eed $\nu=2.0\times10^5\mathrm{~m/s}$ 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 carri v6jssf2o -1 .eqkl;4xmmh)xges a 65-A current. How strong is the magnetic field 6.0 cm away from it? Compare to the Earth’smgk jo.4l6sx;1xq 2-sm) evfh magnetic field. $B_{cable}$   $ \times10^{-4 }\;T$ the field of the cable is about    times that of the Earth.

  If an electric wire is allo,( -4bhk v rlmwrrcmoxu2o034wed to produce a magnetic field no larger than that of x or4 24rk,cml(3bhwuvm0r-othe Earth $(0.55\times10^{-4}\mathrm{~Т})$ at a distance of 25 cm, what is the maximum current the wire can carry?    A

In (Fig. Below), a long straight wire carries current I out of the page towar jal1ze :f * 3uc4k5b2tqixo/wd you. Indicate, with appropr5i:efuo/3lxjkz cbqwt*21 a4iate arrows, the direction of $\vec{\mathbf{B}}$ at each of the points C, D, and E in the plane of the page.

  A vertical straight wire carrying an upward 24-A current exertsr -yya46eku4 v yjq98r an attractive force per unit le 9 44vaqreykujy 86ry-ngth 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 magnitpyz;qq 6qaava3 0xp1: bs2k6)pjnq v,ude and direction of the force between two parallel wires 35 m long and 6.0 cm apart aqq36zx62pyka1v0:q sq a)pjb,vn;p, each carrying 25 A in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s m93p:, q 1eg)a.p f1abyticj vtagnetic field is being carried out 1.00 m from an electric cable. What is the maxima 9btp1:g cpe)av. jy q1fi,t3um allowable current in the cable if the experiment is to be accurate to $\pm1.0\%?$    A

  A power line carries a current of 95 A along the tops of 8.5-m-high pot:tsia9 hx*2fles. What is the magnitude of the magnetic fielxisf *th:t a92d produced by this wire at the ground? How does this compare with the Earth’s field of about $\frac{1}{2}G$?    $ \times10^{-6 }\;T$ The field of the cable is about    % that of the Earth.(retain two decimal places)

  Two long thin parallel wires 13.0 cm apart carry 25-A currents in the same ds+4 1pgkd*ah* nsk1w kirectios* 1h1awk spdk+kgn*4 n. Determine 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 south from a straickas(tb0r/ppb /-gno81 zx3s ght 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 field at this poi s 8xog/k-/acrn (pt130ps bbznt 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 ir -js6hoz *m;a j 4knquq5g(f)s the net magnetic field 20.0 cm due west of the wire if the Earth’r5u fqqo(j6hn jk*s4 ag);z -ms field there points north but downward, 37$^{\circ}\,$ below the horizontal, and has magnitude $5.0\times10^{-5}\mathrm{~Т}?$
   $ \times10^{-5 }\;T$
$\theta$ =    $^{\circ}\,$ below the horizontal

  A straight stream of protons passes a given point in s/ m7*lc mn:(xlxmwv 3gpace 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 long straight wires 2.0 cm ap8;n rw6x;fxedart in terms of the current I in one when the other carries 15 A. Assume these currents a6;fxnx 8;rdwe re
(a) in the same direction,
(b) in opposite directions.

  A long pair of wires conduct g xgb;z: l1vr ft+flf:*.t+ xo8wf:bds 25.0 A of dc current to, and from, an instrument. If the insulated wires are of negligible diameter but bt + : x1;frzdlbff+. wf8txl:vgo:g*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 piv)62:aeh - xvjiqvj:,+ lumjf*o 9qplane of the two wires shown in (Fig. Below), parallel and just to the right. If it carries 25.0 A upward, what force per meter of length does it exert on each of the+ux: q:pj mh)*v,vie2vj9fj6 ioq la- 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 poin9m(u .q7y0e ikjlf-mtts 23$^{\circ}\,$ E of N outdoors. However, when it is placed 12.0 cm to the east of a vertical wire inside a building, it points 55$^{\circ}\,$ E of N. What are the magnitude and direction of the current in the wire? The Earth’s field there is $0.50\times10^{-4}\mathrm{~T}$ and is horizontal.    A  ----待选择----updown 

  A rectangular loop of wire lies in the same plane as a straight wire, as show( +-(6j e/xisad)3lswrxxg q1wbyw d)n in (Fig. Below). There is a current of 2.5 A in both wires. Deter s ww/ 1+i6a)(d-(ys)3bgdlx xrejxq wmine the magnitude and direction of the net force on the loop.    $ \times10^{ -6}\;N$  ----待选择----away from wiretowards wire 

  A long horizontal wire carries a currenj;o s, 1wc4rout of 48 A. A second wire, made of 2.5-mm-diameter copper wire and parallel to the first, is kept in sus so,14cor;j uwpension 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 each oth -xzrddl24 kb.er. At their closest, they are 20.0 cm apart (Fig. B4xzkd. br -dl2elow). 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 carries 5.0 A?    $ \times10^{-5 }\;T$

  Two long straight parallel wi0 04l2;rgq;pyhkme ucm f4+uares are 15 cm apart. Wire A carries 2.0 A current. Wire B’s current is 4.0 A in k+;2a 4;eufm0u0qpm glhry4cthe 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 anot( o sf3y s0f6awxedg)0her. (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 that in wires N and P (Fig. Below). Determine the a6s0gy ffe3 0(sd)xowmagnetic 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 magnw6gur0jf jy.f0zj g q7xq+)a:itude and direction of the magnetic field at the midpoint of theg.qjfzj)7u f+6yaj g rq 0xw:0 side of the triangle between wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a distance d apart, carry equal curktrp0um);gu 0 rents I in the same direction. One wire is at x = 0mutg0u;0r pk) , 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 solen6/xmhe *bxsllo p( ld9h0 cb;:oid has a total of 420 turns of wire and carries a current of 2.0 A. Calculate the ficl;6 bld : sb*/xxmop0e lh(9held inside near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameter is to produce a field of j /ejrtru13k u,a7dfj hj);6z0.385 T at its center. How much current should the solenoid carry if iu,3ju1 rejktr )67/dhfz ajj; t has 975 turns of the wire?    A

  A 550-turn solenoid is 1do:, 7i3 ws+ tru(syhiv7 +ese5 cm long. The current in it is 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 assuy3 +uo+7srhd :e(wvi e7tsi,sming the solenoid’s field points due east?    N

You have 1.0 kg of copper and want to make a practical solenoid th kyuegu c.q:ps) 3n3e5at produces the greatest possible magnetic field for a given voltage. Should you make your copper wire long and thin, short and fat, or something else? Consider other variables, such as solenoid diameter,3g3s p)5cekq.y eu :un length, and so on.

A toroid is a solenoid in the shape of a circle (Fig. Below)..kk;xyd 9qfnhob c(vn8 9 g;ner0. -mu Use Ampère’s law along the circular path, shown dashed ix( dyg nk q.0bk;un9r.fh;m -8 o9ncven (Fig. Below a), to determine that the magnetic field
(a) inside the toroid is $B=\mu_0NI/2\pi r$ where N is the total number of turns, and
(b) outside the toroid is B = 0 .
(c) Is the field inside a toroid uniform like a solenoid’s? If not, how does it vary?

(a) Use Ampère’s law to show that the magnetic field between the co;ie62ml2pivk d (5j7knx5c s qnductors of a coaxc mj2ndp iq esxi756v;lk 2k5(ial cable (Fig. Below) is $B=\mu_0I/2\pi r$ if r is greater than the radius of the inner wire and less than the radius of the outer cylindrical braid.
(b) Show that B = 0 outside the coaxial cable.

  A single square loop of wire 22.0 cm on a side is placed x3.23hbsrpnu 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 torrpux s3h 23nb.que on it is $0.325\cdot N$. What is the magnetic field strength?    T

  A galvanometer needle deflects full scalql :/d z1e*2jk;dn 6z3ljx kqle for a $53.0 -\mu A$ current. What current will give full-scale deflection if the magnetic field weakens to 0.860 of its original value?    $\mu A$

  If the restoring spring of a galvanometer weakens by 25% over theeb8* ar udfy;7ron ,bq6br - )llh-2op years, what current will give full-scale deflbhbr -ly eo6plbra 28uon-f)*;qr 7,d ection if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by what factor8h 9px j8pz9wo does the output torque change hz8woxj9pp89?

Show that the magnetic dipole m+ tmj( ywzr,)5fv z a(ikx8*bqoment M of an electron orbiting the proton nucleus of a hydrogen atom is related to the orbital angular momentum L of the 5abtmz vjyw(rik +qfx,( *)8 zelectron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter and containing nine loops lies flat vy kv* jc4+hu8on the ground. The Earth’s magnetic field at this locatioh ju8y +*vkvc4n 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 ma homh-3m;xe,p gnetic field. What value of electric fiel xo,3pehm-;h md could make their paths straight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atoms have radii of curvature equal tm :g9kqbeyeuyz0b z,j5 6u6z*o 21.0, 21.6, 21.9, 22.2, and 22.8 cm. The largest radius corr9y6z*z mque0bj5y, 6eg: uzkbesponds to an atomic mass of 76 u. What are the atomic masses of the other isotopes?

  Suppose the electric field between tzh9(j6cb p 9s,gdhsqk uc t;5hsn+ n68/h f*uihe electric plates in the mass spectrometer of (Fig. Belowc5 s;ct hhhzhq 6 pujsud* (6n+9b9g8i,f/ snk) 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 use9te6 kzd r u( (2bg3okdw1/kckd to monitor air pollutants. It is difficult, however, to separate molecules with nearly 29uw rt (kc/d(3 6e gkokd1zbkequal 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 iou 0et:u sa+w+gns by a voltage V before they enter a magnetit+as+0u: eguwc 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 ofphk4; pvq a ur7w,)r(:n/ekz,1bk sbx wire per meter, and a 25-A current flows thror):p7k eabkx(/,v w, 4knbz 1rpsh;quugh the wire. If the permeability of the iron is $3000\mu_0$ what is the total field B inside the solenoid?    T

  An iron-core solenoid is 38 cm long and 1.8 cm ibpr 6jf 3l2 n5,cz)sps4 u.orln diameter, and has 640 turns of wire. The magnetic field inside the solenoid is 2.2 T when 48 A flows in t,rbl52 rzlp6 fnjp .s4)s co3uhe wire. What is the permeability $\mu$ at this high field strength?    $\times10^{-5}\mathrm{T}\bullet\mathrm{m/A}$

  Protons with momentuzqu1 k c0k27ctq:7bq-rfs-a pm $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 electronpa (1t,d/a0mgg rbo:w have the same kinetic energy upon entering a region of constant magnetic field. What is the ratio of the radii of their c 0wrgdbaomg( ,a1:t p/ircular paths?   

  The power cable for an electric trolley (Fig. Below) carries a horizontal;k1du; t3nwf t current of 33 fk1wnu;3ttd;0 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 has acquired ;w )keg v;m oru:(av)ca 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 prq. u;iase5 0b;i9rrcoints almost horizontally to the north and9rqr;au i 50esr.cb;i 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 atomldkq k fr/ )acr: 4mup43rr4k2, 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 in (Fig. Below). A ll2w j*gaqlb)172c 1k 6 suhwetarge 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 il)1h2e qs6*w1ka7b2 ugwjctls 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-diametevq:w/z17jb e hr copper wire and is suspended in air due to the two magnetic forces from the bottom two wires. The current flow through the two bottom wires is 95 bzq :hv1/j7w eA in each. Calculate the required current flow in the suspended wire.    A

Two stiff parallel wires a distance l apart in a horizontal planeitz6nz)p: rpysk/0w hm1 (g*pdel( u+ act as rails to support a light metal rod of mass m (perpendicular to each rail), (Fig. Below). A magnetic fielu(:)dr0lpng p*e ps(z tiw/6mh+z1 kyd $\vec{B}$, directed vertically upward (outward in the diagram), acts throughout. At t = 0, wires connected to the rails are connected to a constant current source and a current I begins to flow through the system. Determine the speed of the rod, which starts from rest at t = 0, as a function of time
(a) assuming no friction between the rod and the rails,
(b) if the coefficient of friction is $\mu_k$.
(c) Does the rod move east or west if the current through it heads north?

  Estimate the approximate maximum deflection of the electron beam . *j oub+vztg.ir 7)zhnear the center of a Tgtz)ir7h.uo.b* j z v+V screen due 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 ele m 2*l/8d yp:dkspum;wmentary particles such as protons to high speeds. Particles starting at point A with some initial velocity travel in circular orbits in the magnetic field B. The particles are accelerated to higher speeds each time they pass through the gap between the metal “dees,” where there is an electric field E. (There is no electric fid2k:p8; mp d*y/m suwleld 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 cornxwtf 6,/ssukrn9xus qg3h )7; i7dgj1 ers of a square of side l,x;su r s3g kfn,)6 sj7gquxid1wth9/7 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 part.u c-a;jegp )p;sf1w * uj0z4q,btlvvicle 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 beagp;0*ab q sf.p4jvcw;ujz-l )v t1e, um of protons. What happens to protons that are not moving with the speed that the magnetic field is designed for? If the field extends over a region 5.0 cm wide and has a magnitude of 0.33 T, by approximately what angle will a beam of protons traveling at $ 1.0\times10^{7 }\,m/s;$ be bent?    $^{\circ}\,$

  The magnetic field B at the center o-gmj ftnb ;/6nf a circular coil of wire carrying a current I (as in Fig. Below njgtnf/-;6m b) 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 fielrrx;b5 u wfdwobr4s9y/94wd *d 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 magnitudei ; fhn) uz6fb--im+6x/lgeut of magnetic fields produced by overhead power lines. You estimate that the two wires are each about 30 m above the ground and are about 3 m apart. The local power company tells you that the lines operate at 10 kV and provide a maximum of 40 MW 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 c6f in+ eizb/f-) mgu xthlu-6;urrent, 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 fa ,v 04) ven3eplz):.f4r opp4gqtlkn ield would make a beam of electrons, traveling to the right at a speo3epe 4vtk p pa4fln.n ) z)0rv,l4qg:ed 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 of 0.010 T, p:l;1ms 5eb , sk,gciroerpendicular to the plane of the spiral, as shown in (Fig. Below). In two successive loops, at points P and Q, the radii are 10:,igl1es b, rmokc;5s.0 mm and 8.5 mm, respectively. Calculate the change in the kinetic energy of the proton as it travels from P to Q.    $ \times10^{-20 }\;J$

  A 32-cm-long solenoid, 1.8 cm in diameter, is to produce a 0.30-T maxv: ayoxn5ik kpz4+f,b2ib 7/gnetic field at its center. If the maximum current is 5.7 A, how many turns must thebyiv xizpa 4 xk ,5+bn:of7/k2 solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, each of v9a(i)w5zdx(s jx 97*s 0d np qk1lgnrdiameter 0.50 mm, carry the same current but in opposite directions. Theyaing9 9zd *(()lnq vp10d 5 xswrxj7ks are suspended by 0.50-m-long strings as shown in (Fig. Below). If the suspension strings make an angle of 3.0$^{\circ}\,$ with the vertical, what is the current in the wires?    A

  An electron enters a uniform magneti:qd (8 yqbb7xqc 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$