A compass needle is not always balanced parallel to th nsrx0q-p2d4scd: pg ;e Earth’s surface, but one endd g2ps pn;c0xds4-:r q may dip downward. Explain.

Draw the magnetic field linesa5p/)hq4 zkdxa*ra xkh.qm ) . around a straight section of wire carrying a current horizontally to the lef* aq)dh).k.x x5 hz/4 qpmarkat.

In what direction are the magnetic field lines surrounding a straight wire( 53pme0ppwtylqah0 t/a m9 :a carry:wh0 a 5lp(at3mpp0yeq 9at /ming a current that is moving directly away from you?

A horseshoe magnet is held vertically with ty l w99bff5+nxhe 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 forcf x +lnbyfw959e on the wire?

Will a magnet attract any metallic f6u. vf:0e w-(ihbrdk -1tz97jibg, a2ljqewobject, or only those made of iron? (Try it aqwbl6e( d7hbfr e:u9j gwjaii21- z- 0.vk, tfnd see.) Why is this so?

Two iron bars attract each other no matter which ends are placed close2;x e hrex zb r1kq0s gpiy5*y11v4g4i together. Are both magnets? Exeqeb 0y 2441kz1*hi sr xr51givpgyx;plain.

The magnetic field due to current in wires in your home can affey)+dsn2sdp y-ct a compass. Discuss the ey)+- snys2p ddffect in terms of currents, including if they are ac or dc.

If a negatively charged partic;;0 1-qi ulk*:sau ygih+fql ole enters a region of uniform magnetic field which is perpendicular to the particle’s v+:oasl -i1hg; u*ikyf ;qlq0 uelocity, will the kinetic 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 imi-x/5j7c de n,mfwi-1dxc2en the vicinity 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 tnx ei1m 2,f diwc -cdex-7jm5/he 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. 20–4 lketyq jw(5n+z q*78u6. What ca5 *+yn qt (uz7jewl8kqn you say about the charge on each particle?

A positively charged pa+; 2b2+sipkp uebt+fi rticle in a nonuniform magnetic field follows the trajectory su b2ei +p+; tk2ipf+bshown 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? Cani+0a z ygpt55h a magnet attract an iron rod? What must you consider to answer these queia5 t 50+pgzhystions?

Explain why a strong magnet held near a CRT television screen (Sectiou *g ,q x9ke,wb,mla( ngba15npgy b*+n 17–10) causes the pie1b9 * abg5,xgl gk,p+u*nban,(yqm w cture 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 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 z*l ca 2t7i6by39pmhv/zm; pgthe third is not. How would you determine which two are the magnets without y7i *zpvlag2;/b3m6tz p9mhc using any additional objects?

Can you set a resting electron into motion with a magnetic field? With an electrqx--d v.7j pihic field? Expla.x -jip- hqdv7in.

A charged particle is moving in a circle under the influence of a unifor0j psvaq6k/b 9cx 0o/mlkg3;hm magnetic field. If an electric field that points in the same direction as the magnetic field is turned on, g9/xp bl/k0ovc 6jksmaqh ;03 describe the path the charged particle will take.

The force on a particle in a magnetic field is the8jf;djcze1,) ij*pb/ ts7jcv idea behind electromagnetic pumping. It is used to pump metallic fluids (such as sodium) and to pump blood ijc;7j /v j*szpt)i8cej ,d1 bfn artificial heart machines. The basic design is shown in(Fig. Below). An electric field is applied perpendicular to a blood vessel and to a magnetic field. Explain how ions are caused to move. Do positive and negative ions feel a force in the same direction?

A beam of electrons is directed toward a horizontal wire carrying a curr -(ufqvc 0,mneent from lee 0-nqu,fvm (cft to right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields t8 h3wi,*bwqr 8cmclvs5);( hlq og8vkhat surround a moving electric charge.8b ,( gvvcl8q 3r hswhi mqcwk;)8ol5*

A charged particle moves in a straight line through a particul )a p/.cetjfafc ;q,h2ar region of space. Co,c/2j c .eaaffqt)h;puld there be a nonzero magnetic field in this region? If so, give two possible situations.

If a moving charged particle is deflecl,kac6 0m-z dgs;k+m. dy.pqnted sideways in some region of space, can we conclude,kya; kqmdmp.s0+,6.n l gcz- d for certain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is a o-74s;/p8dqglsijj k 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 whe/i v5ou;7*mlad ;gqe pther moving electrons in a certain region of space are beiu ;ao7/ ie*lv5pgmqd;ng deflected by an electric field or by a magnetic field (or by both)?

How can you make a compass without using iron or other ferromagnetic matzauqj:,whk7lo 6z9 7i. -l rvuc*eee)erial?

Two long wires carrying equal tile e+;sb2zj:h4 q)u,mn) hfcurrents I are at right angles to each other, but don’t quite touch. Describe the magnetic force one exertsu etm)zfsnq+hbe ,24h): i;jl on the other.

A horizontal current-carrying wire, free to move in Earth’s gravitatio6kg0 se tvbo1l)79uz gnal field, is suspended directly above a second, parallel, current-carrying wz9lev 70ogsgtub ) 61kire.
(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 unmagnet;u t/x,mw6 )c4avke pkized piece of iron?

An unmagnetized nail will not attract an unmagnetized paper clip. However, if .zajc2x8 atzbiuj0hi6 8 pg69one end of the nail is in contact with a magnet, the other end will atta.x 8ug0 ijpih86j29zzba 6ctract a paper clip. Explain.

Two ions have the same mass, but one is singly ionized and thclj ;vsy+2uv0 e other is doubly ionized. How will their positions on the film of a mass spectrometer (Fig. Below) differ+ lcv0uy j;2sv?

What would be the effect on B inside a long solenoid if8i6gxc puz;ki 6 )k8az
(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 renm4 *+/tm( 2nbo3g8 ibmbh ozylay . 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 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 t2 h+ing/(43 z bm*myomn8obbto a relay so that the large current needed for the starter doesn’t pass to the dashboard switch.

  (a) What is the magnitude of theg; v*f e(t2w(j7cussv force per meter of length on a straight wire carrying an 8.40-A current when perpeswc g; s7jev *vt(f2u(ndicular 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 length of straight wir. ow ( lm*h.l9) 8kvtg/qepssoe stretched between two towers carrying a 150-A current. The Eh os*l./w9o e.g(t8 km)qpv lsarth’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 os.rd 5y nuiqg8 o1s4d/n a 160-m length of straight wire stretched betwds.n8yurs4g /id1oq 5 een two towers carrying a 150-A current. The Earth’s magnetic field of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  How much current is flowing in a wire 4.80 m long if the maximum force ow: uo*tpvv n4( 8gqr(an it is 0.750 N when placed in a uniform 0.0o*npu:v 4(8q vt(wrg a800-T field?    A

  A 1.5-m length of wire carryix: eqkl67-f* wd: w:pqtkze)bng 4.5 A of current is oriented horizontally. At that point on the Earth’s surface, the dip angle of the Earth’s magnetic fie kq6t- pkf7:wl:d*e):qexzwb ld 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 8.7-rq5gml: 5 ntm5 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, what is the 5- :ngtmm5lqrapproximate strength of the magnetic field?    T

  The magnetic force per meter on a wire is measured to 3a;a;/8 pzlp p8zzblebe 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 the angle between the wire and the magnetic field. p;p z azb8e/38la;zl p   $^{\circ}\,$

  The force on a wire is a maximopqiz /e8,e jhhs6b(( 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 co3/7fzbm exci-t zeumrw 1 (s/ )rrcs2;pper wire could just “float” horizontally in air because ofmc1mf2s erw-r()r/zt7zsu b c/3e;xi the force due to the Earth’s magnetic field $\vec{B}$, which is horizontal, perpendicular to the wire, and of magnitude $5.0 \times10^{ -5}\;T$. What current would the wire carry?    A Does the answer seem feasible? Explain briefly.

  Alpha particles of charge 6* vqjxrsp:vi st391(zs pb6q$q\,=\,+2e$ 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 fuo 6,ud1lxw 8korce 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 nega*.cp 4;aeogunne 0 j-i/z:t.yhzv8 citive charge for each diagram shown in (Fig. Below), wiun j/ytnigzz:v -8e..4;* 0p eoc ahchere $\vec{v}$ (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 uzmg7f ;sjacqa +l)6ri;ms e: d c*)g6of $\vec{B}$ 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 vertinjni,, f(- vxycally 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 en+(oa aix ,sj3 ti;4btmters a 0.20-T field, in a plane perpendicular to the field. What is o(mx+a3; ti,b4tjsi athe radius of its path?    m

  An electron experiences the greav6zd j1(i;6u xf 1 yjca;ogv(rtest 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 undeflected when passini v:5x7ywc* ne4w vhn+i6m/ssg through perpendicular electric and magnetic fiew5mxe/7hvinw*yc s4 n is+6v :lds 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 whose m3kb2wn-o- pxe qks,u6 ass 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 requ9 ef j9dvjt 10k80fwft +f4guuired for a particle of charge q moving with constant speed v to make one circularg f4w9e 8duf00jffujkt v1+9t revolution in a uniform magnetic field $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge q moves in a circular path of radius r in a unifof, aewyt(6 63 0g zvdw(;8,ia nbdvibrrm magnetic field B,df0(w rb wtydv66i3evbang 8;a(i, z . Show that its momentum is p = qBr .

A particle of mass m and charge q moves in a circular pat e/5ap, 0xboixh in a magnetic field B. Show xi/pa5,xoeb 0 that its kinetic energy is proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momentum of the particle in Probl4 kjaxi /-2uk2 wdyvj/em 21 is $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves with a qn5,y2aez.tw- hh0pwd. +k psspeed of 160 m/s perpendicular to the Earth’s magnetic field of seppn+.hd w ayt z-k2.w ,5hq0$5.00\times10^{-5}\mathrm{~T}$, 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 magewlc ni j 2mz.u1h:10 ddl)9srnetic 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 speam daol2 yaj//;u m,l0 jwl,o;ed $\nu=2.0\times10^5\mathrm{~m/s}$ 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 ve 81fnx 6vey p884gc3yvr;6txg,xwst phicle carries a 65-A current. How strong is the magne1 3ep6sfgv8c 8rwxnxp,yx6g8 t4vty ;tic field 6.0 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 fiel p tw.tk22jwf.tv(6r 16xkceud no larger than that ofkc 1wx2kpwuj2t r6(fve6t.t. 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 wj9:4k1z(- swxq /ys.ogadzq)m(xob straight wire carries current I out of the page toward you. Indicate, with app z)oqzqj 4 mkgx d9boxa(s ws/:(1.wy-ropriate 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 exerts an fazv 3v 9+*yzbattractive force per ufzv+ *zy39ba vnit 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 g0kz 091b.h g9eslsiidirection of the force between two parallel wires 35 m long and 6.010keggizh9i lsb 0.9s cm apart, each carrying 25 A in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic field is beingwdit;n b f-2:x t;r ef258yb4*take ( talc4kn carried out 1.00 m from an electric cable. Whatftr e8:c4*by ;4btd nkiw a-252t nlke(;xfat is the maximum allowable current in the cable if the experiment is to be accurate to $\pm1.0\%?$    A

  A power line carries a current ofo h:* qen/i0ew 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’sw 0i/n:h*oeeq 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 1ht*g4sttbh 5 u +(i9mt3.0 cm apart carry 25-A currents in the same direction. Determine the magnetic field at point P, 12.0 cm from one wire and 5.0 cm from the othtt+ t uis*hg4bmh9( t5er(Fig. Below).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18 cm due south from a straight vertical wire cayk pu* +pn4,.u;0 vygwjj8tbarrying 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 +kwnb.j p0aguu4yvt*y 8;j p,point is $0.45\times10^{-4}\mathrm{~T}$ and the magnetic declination is 0$^{\circ}\,$.    $^{\circ}\,$ N of W

  A long horizontal wire carries 2rc45 9nz(si id* o xsbzchs.bz7(c;i32.0 A of current due north. What is the net magnetic field 20.0 cm due west of the wire if the Earth’s n34s5 7z;x(c(bsdoi 9 bscz.richi* zfield 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 a rate/ .u1 qr8ven fjcch(.s 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 fi1 kgu+ wx:c:b,hgh k.zeld midway between two long straight wires 2.0 cm apart in k1,kh.xgzh u::+cb wgterms of the current 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 25.0 A of dc:90qaw9i v+dfjls s(-bjesm( current to, and from, an instrument. If the insulated wires are of negligible diameter but are 2.8 mm apart, what is the magnetic sl 9qjves -a+d:9msw0( b fji(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 plackk;ta2 m1x07 a w8qv(bl4padxed in the plane of the two wires shown in (Fig. Below), parallel and jaatx 80lakbvm4;7 d p k(xw12qust to the right. If it carries 25.0 A upward, what force per meter of length does it exert on each of the other two wires? Assume it is 2.8 mm from the nearest wire, center to center.
$F_{near}$ =    $ \times10^{ -2}\;N/m$  ----待选择----attractrepel 
$F_{far}$ =    $ \times10^{ -2}\;N/m$  ----待选择----attractrepel 

  A compass needle point7h ,)f xkr 3fpe4dkg+j55 xchd:q0r jms 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 of2fr +a5 jm.z*5w s:b cghkhg(oo2nn( i wire lies in the same plane as a straight wire, as shown in (Fig. Below). There is a cuiskg(5nb2a (g *oocf+jwr. 5 hhnz 2:mrrent 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 a current of 48 +)-;3mlule-3 wvpebucaf +r fA. A second wire, made of 2.5-mm-diameter copper wire and parallel to the first, is kept in suspension magnetically 15 cm beloeua3v+uff+m3 lp ;-c- b)l reww (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 perpendiculan7.:yk r f )dezhwrh58r to each other. At their closest, they are 20.0 cm apart (Fig. Below). What is the magnitude of the magnetic field at a point midway between them if the top one carries a current of 20.0 A and the bottom one dwyz r5f)r7:n. hh8kecarries 5.0 A?    $ \times10^{-5 }\;T$

  Two long straight parallel wires are 15 cm apart. Wire A carries 2.t+0l 7nz -aef)g6 apjr+zdm k84)kjas0 A current. Wire B’s current is 4.0 A in the same direction-fnzkma t+6js)+7p jdg 4l kazra )0e8.
(a) Determine the magnetic field magnitude due to wire A at the position of wire B. $\approx$    $ \times10^{-6 }\;T$(retain one decimal places)
(b) Determine the magnetic field due to wire B at the position of wire A. $\approx$    $ \times10^{-6 }\;T$(retain one decimal places)
(c) Are these two magnetic fields equal and opposite? Why or why not?
(d) Determine the force on wire A due to wire B, and the force on wire B due to wire A. Are these two forces equal and opposite? Why or why not? $\approx$    $ \times10^{-5 }\;N/m$(retain one decimal places)

  Three long parallel wires are 3.8 cm from one another. (Loo ,pr5 :me5bnduking 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). Determin rp m5,en5bdu:e the magnetic force per unit length on each wire due to the other two.
$\frac{F_\text{M net y}}{l_\mathrm{M}}$ =    $ \times10^{ -4}\;N/m$ =    $^{\circ}\,$
$F_{N\,net}$ =    $ \times10^{-4 }\;N/m$ $\theta$ =    $^{\circ}\,$
$F_{P\,net}$ =    $ \times10^{ -4}\;N/m$ $\theta$ =    $^{\circ}\,$

  In (Fig. Below), determine the magnitude and dir.)q0v ed*t5 ho nn- lasd)j;c 0q(hcvtection of the magnetic field at the midpoint of the side of t)t;qhdv (j.o-0cdces) n5alq n0* hv 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 equh75 earm..xx8ia-dy g al currents I in the same direction. One wire is at x = 0, the other is at x = d, (g ra.- x 87axhye5mi.dFig. 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 ofy mu8/ ,dfdathhtx,00 420 turns of wire and carries a current of 2.0 A. Calculate the field insidd8tm ,d,xu0t / ayhh0fe near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameter is to produce a field of 0.38k7l lxle.y5zsgk(2zh t+/p+zcxpv*;5 T at its center. How much current should the solz (*kt. v+5z ep/ lxzlpg7x2hk c+y;slenoid carry if it has 975 turns of the wire?    A

  A 550-turn solenoid is 15 cm long. The ,avs n 2w1skb7lr;m y-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 assuming the solenoid’s field points due ea 7,;vwrnsb2y1ka msl- st?    N

You have 1.0 kg of copper and want to make a prs z27l4lyy tf*actical solenoid that 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? Considef y*7lz2ty4slr other variables, such as solenoid diameter, length, and so on.

A toroid is a solenoid in the shape of a cir x997drtxtgh8f)a;o m cle (Fig. Below). Use Ampère’s law along the circulafaox9ttx d8hmr9g) 7 ;r path, shown dashed in (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 ma(mgb z zoj*cs/xsli w9.)*s 3lkgw 0f7gnetic field between the conductors of a coaxial cable (Fig. Below) issw 7 0 s9ilc g3.ofk)( jbgzlw*sz*/mx $B=\mu_0I/2\pi r$ 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 sideszh,i02p2v pcwz9 t 5a)e+u ol is placed with its face parallel to9lc tiwzp+ 0,o 5ahe upzvs2)2 the 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 flvpecq i7 29v:ull scale for a $53.0 -\mu A$ current. What current will give full-scale deflection if the magnetic field weakens to 0.860 of its original value?    $\mu A$

  If the restoring spring of a galvanometer weakens by 25% over the yearlmg fd,e9+q. f43wrnys, what current will give full-scale deflection if ffg m ny 3.+d94erwl,qit originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by what factor does the outpu9 vg(3 gfl 7:h1d0qhbdzqgbf6vu /y)zt torque change? 36dbvul(/ dz1fh0qgqfg: v 9b)y7z gh

Show that the magnetic dipole moment M of an electron orbof0r;to2mwmicmk go +lj0 4u6z. f6/fiting the proton nucleus of a hydrogen atom is related to w0 ;mg4lmio u6/oft+ c2rjk f.o06mzf the orbital angular momentum L of the electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter and containing nine lvf(mw1ps1g0)ee+ fx4g d ca ;joops lies flat on the ground. The Earth’s magnetic field at this locatiod)m 0+ 4j a;xesgpvge1 f1c(wfn 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 cmzo ysxju )4.. 6lg1p8vgjd6 su in a 0.566-T magnetic field. What value of s 1x6 4sygj).uld86uvpozj.gelectric field 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 to v /o*m:lik)3:mts- ey m tl5co21.0, 21.6, 21.9, 22.2, and 22.8 cm. The largest radius corresponds to an atomic mass of tkt eimo mo/cy:v*l5)s :-l3m 76 u. What are the atomic masses of the other isotopes?

  Suppose the electric field between the electric platesj.wf 8q (ps8tz in the mass spectrometer of (Fig. Below) izfp88(stj q .ws $2.48\times10^4\mathrm{~V/m}$ 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 mc rtpz4 htcik;:lam; +s6cp )qpi;q6:onitor air pollutants. It is difficult, however, to separate molecules with nearly equalr66ci:pkt m lhitcq s ;a;qc zp+:;4)p 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 spel )7, crto1hle7fy5y,gz: oquctrometer accelerates ions by a voltage V before they enter a m7qo g5zl yr,ey7t1c uf),ho :lagnetic 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 current fl vavlq52 w03u7nmce0qows through the wire. If the permeabi3q7ve25 ancu0 0vqlmwlity 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 in diameq,u5 q1jfkpt( ter, 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 th (qp5j, fqtuk1e permeability $\mu$ at this high field strength?    $\times10^{-5}\mathrm{T}\bullet\mathrm{m/A}$

  Protons with momentu ys h.ps:i3auu9cj+lafo e ;.9m $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 enterxdc/j cp9 v :mo(4fpi)ing a region of constant magnetic field. Wha4)(pd :pcmjov9/ f icxt is the ratio of the radii of their circular paths?   

  The power cable for an ew ;/jszxizj*.d-8zadht t+: b4nx ;lllectric trolley (Fig. Below) carries a horizontal current of 330 A toward the east. The Earth’s magnetic field has a sdsln :-;*dl.i;t 4jz zxa+xhtj 8b /wztrength $5.0\times10^{-5}\mathrm{~T}$ 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 whichs rn(5vvtbtb8 :k 96cl has 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, the Earth’s magnetic field points almost hor6qg g,mb,.bcd45o5mqsle m0kizontally to the north and hasq,gmo0bk5 sgcm 5.e b 6q,dl4m 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 mass ff +p6mvfrs3 epu29;l9(sdstis $6.6\times10^{-27}\mathrm{~kg},$ 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. Belod /: xe 1ddd(*hxp-5r+oysx-owtlc *fw). 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 f*x(*xho+xed1to- c: /d dpd sywr-5lis 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 t:kn) o,tfs,b lzbk03 kop wire is 1.00-mm-diameter 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 A in ,3 b):kkklb0z t,onfs each. Calculate the required current flow in the suspended wire.    A

Two stiff parallel wires a dista r nbqr365o+wonce l apart in a horizontal plane act as rails to support a light meta 3wb6oq +r5norl rod 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 deflection of the electron beap(uvi nz: t)c7m near the center of up :(czn 7i)tva TV 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. Bz)jd6te h5: cyelow) is a device used to accelerate elementary particles such as protons to high speeds. Particles starting at point A with some initial velocity travel in circular orbits in the magnetic field B. The particles are accelerated to higher s)ed5tyz jh6:cpeeds 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 fk x0*vd sh8i*s-xio3parallel wires, located at the corners of a square of side l, carr k-*xi 30hissofx d*v8y equal currents $I_0$ perpendicular to the page as shown in (Fig. Below). Determine the magnitude and direction of $\vec{B}$ at the center C of the square.

  Magnetic fields are very useful in particle accelerators for “beam stee bj2 z;qvwwa ;l:moi,8ring”; that is, the magnetic f zbim;al;j,v: ow8w 2qields can be used to change the beam’s direction without altering its speed (Fig. Below). Show how this works with a beam of protons. What happens to protons that are not moving with the speed that the magnetic field is designed for? If the field extends over a region 5.0 cm wide and has a magnitude of 0.33 T, by approximately what 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 kc 0rkv j7;owi g b5,4.zjj5m ld40lckwire carrying a current I (as in Fig. Below5 c0rwoj 5 ;d.l v07ij zl4gkk4kjcbm,) 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 magnet q4*,l(co1l o 8iahbjgic 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 ofo2uzi * ticg4hw11kbb 11ov*a 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 cio2kcbg4* 11b 1tuh1a *oiz vwompare 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, travezo fvhy /.*i+yp3p7yg usv(v.x85yiz ling to the right at vsi .(v 3yp.+ y gx*oy5huzy8z/fp iv7a speed of $4.8 \times10^{ 6}\;m/s$ go undeflected through a region where there is a uniform electric field of 10,000V/m pointing vertically up?    $ \times10^{ -3}\;T$(retain one decimal places)
(b) What is the direction of the magnetic field if it is known to be perpendicular to the electric field?
(c) What is the frequency of the circular orbit of the electrons if the electric field is turned off?    $ \times10^{7 }\;Hz$

  A proton follows a spiral path through a gas in a magnetic field of l: lwl9m1/xp8gcy9wo+(p nn e1- sjsc0.010 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, l198 ompncyjw+ l-/(s c:w91 np eglxsrespectively. 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 magd w;vajk2 t/j(netic field at its center. If the maximum current is 5.7 A, how many2ak/(vjt; wj d turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, each of diameter 0.50 mm, carry the samedj1 sp(0c(3hzlj- y s,ygknx * current but in opposite directions. They are suspended by 0.50-m-long strings as shown in (Fig. Below). If the suspension st(s3 x-kc1*njh(, yg sdypjz0 lrings make an angle of 3.0$^{\circ}\,$ with the vertical, what is the current in the wires?    A

  An electron enters a unifo,+ahv 1ey3pjt rm magnetic field B = 0.23 T at a 45$^{\circ}\,$ angle to $\vec{B}$. Determine the radius r and pitch p (distance between loops) of the electron’s helical path assuming its speed is $3.0 \times10^{6 }\;m/s$. See (Fig. Below).
r $\approx$    $ \times10^{-5 }\;m$ (retain one decimal places)
p =    $ \times10^{-4 }\;m$