A compass needle is not always balanced parallel to the7oduq1;t ltxs ktt/-bhvt:)po,x;. h Earth’s surface, but one end may dip downward. Elhq- u)/: tth bxoto;kt7;td1x.s,vp xplain.

Draw the magnetic field lines a ) a*mz ;xufexrd9kd0wg;q:g:round a straight section of wire carrying a current horizont : wzgx )e q0xdrk*g:f9dm;au;ally to the left.

In what direction arbg ygk+ifgg0-*8j .o*z:blh z e the magnetic field lines surrounding a straight wire carrying a current that is moving directly away hbl80gijg kbz**:-f g+ gz.oyfrom you?

A horseshoe magnet is held vertically with the nort9e:*rh:lu-ibd d5 . lj ee5czwh 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 wh:he5wd :j-.c5l bz9ui el er*dat direction is the force on the wire?

Will a magnet attrac9w(fb(-btf3u dol hy+ t any metallic object, or only those made of iron? (Try it and see.) Why is th+f lh -b(d9wyfo3tu( bis so?

Two iron bars attract each other no matter whictw y97srf3l ,nxxyd0 2h ends are placed close together. Are wxf 7l 90, t2x3srnydyboth magnets? Explain.

The magnetic field due to current in wires in your home can affe(l vz sowg7y37ct a compass. Discuss the effect in terms of currents, including if they are acvy s7o(w3 7lzg or dc.

If a negatively charged particle enters a region of uniform magnojfqok)g + h4sf+,mj2bu s/)getic field which is perpendicular to the particle’s velocity, will the kinetic energy+sb)o )/4gjf2+ ohkgjs, mfu q 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 particles829 u bn7sfa dyek2 m 0c5o*wp/slwa3x move in 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 the charge. For each of the particles, indicate the direction of the magnetic force due to the ms8/c m5 lk*adx2o9 s0b3y2pn 7eufwawagnetic field produced by the wire.

Three particles, a, b, and c, enter a ma1rg y vte03i+ kwx,p7ngnetic field as shown in Fig. 20–46. What can you say about the charge on eacvi+xg3kpy wnr 17,t0 eh particle?

A positively charged particle in a nonuniform magnetic fiel7grx z 43,bbned follows the trajectory shown in rg,n7 4e bx3bz
(Fig. Below). Indicate the direction of the magnetic field everywhere in space, assuming the path is always in the plane of the page, and indicate the relative magnitudes of the field in each region.

Can an iron rod attract a magnet? Can a magnet attract an iron rod? What mugyyvos(a: yd)2/kj sdqr1:5p st you con/)s: p5:1 rsv jyydk2g(dy qoasider to answer these questions?

Explain why a strong magnet held near a go +eka)p0g*x CRT 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 damage to ye + )g*gk0oxapour 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 magnetv bz640 e1oqdaized but the third is not. How would you determine 60vza1 4dqbeo which two are the magnets without using any additional objects?

Can you set a resting electron into motion with a magwm /m /pyg)es4s13cvlnetic field? With an electric field? Expl slpgvme)341/msc /ywain.

A charged particle ihmz/j qh+t.runvs22 1s moving in a circle under the influence of a uniform magnetic field. If an electric field that points in the same direction as the magnetic field is turned on, describe the path the charged particle will takhm/hqvtnrj uzs21 +.2e.

The force on a particle in f7.ygtfp2fc + e a/wclg0bs y)7gz- k9a magnetic field is the idea behind electromagnetic pumping. It is used to pump metallic fluids (such as sodium) and to pump blood in artificial heart machines. The basic design is shown in(Fig. Below). An electric field is applied perpendicular to a blood vessel and to a magnetic field. Explain how ions are causf.7y lf/p+ )g e920c7sgbw zy- tgkfaced to move. Do positive and negative ions feel a force in the same direction?

A beam of electrons is directed toward a horizontal wire c qm8yn q0wsdymh 6;6)pghk 3m)arrying a current from left to righh) dh8mpsmq6 0kny3g y6)w;mqt
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fieldatxkm gokr*jj*kx o;p(-39y,s that surround a moving electric charge.-y 9o,(pr 3agxxjjkkmo*; kt*

A charged particle moves in a straight line through a particular region of spaceysqmdb 6 i7)*ctr.3 ( vy9ftypqw91 zs. Could theresqf9 b(6y31cwivr9 tmy7)pd s* zy. tq be a nonzero magnetic field in this region? If so, give two possible situations.

If a moving charged particle is dtcbf1w(x2 mpgg5 c/p5eflected sideways in some region of space, can we conclutbg c5x1mfc52 w/g p(pde, for certain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is aqfsril: v832a uniform magnetic field $\vec{B}$. Outside this region, B = 0 Can you inject an electron from outside into the field perpendicularly so that it will move in a closed circular path in the field? What if the electron is injected near the center?

How could you tell whether moving electrons in aqy) 4*dtsok 4g certain region of space are being deflected by an electric4tqo)*4skdyg field or by a magnetic field (or by both)?

How can you make a compass without uws4/ytfmt 9(y sing iron or other ferromagnetic material?

Two long wires carrying equal currents I 81*4qt6rkye.wklq43 bbb ttvare at right angles to each other, but d.rbve wq4 bt8b y61k*t3lkt q4on’t quite touch. Describe the magnetic force one exerts on the other.

A horizontal current-carrying wire, free to move in Earth’s gravitational fiekzrn h:)e fk1 8 zede0z3j(fq5p5k5qeld, is suspended directly a0 )(qre:z3zeej nd1k kq85h5pz e f5fkbove a second, parallel, current-carrying wire.
(a) In what direction is the current in the lower wire?
(b) Can the upper wire be held in stable equilibrium due to the magnetic force of the lower wire? Explain.

Why will either pole of a magnet attract an unmagnetized pzq;hyy7 v/ ws 6 q*;xuk/aype4t(0zd xiece of iron?

An unmagnetized nail will not attract an unmagnetized paper clip. H n:nm;lav9 g6zd7uuqob(sf 93 b;tw5gowever, if one end of the nail is in contact with ns n9 z qu95b; 3uawtv;mdlg76 f(go:ba magnet, the other end will attract a paper clip. Explain.

Two ions have the same mass, but onw63-c m ekms:g7 t/btle is singly ionized and the other is doubly ionized. How will their positions on the film of a b c/ml67st:emtg -wk3mass spectrometer (Fig. Below) differ?

What would be the effect on B insideu e,2rsdzd )l(*nwoj dxh-*7x, 3qgudcw e6 8h 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 soltm6s (v kfoiqnqu.w(4s(7-a t enoid 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 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 .6sqkw( umio(4v-qt(t naf7s starter doesn’t pass to the dashboard switch.

  (a) What is the magnitude of the force per meter of length on a straight wire c * .)llweak/lq:,u urf g9ek:lh5z9qa arrying an 8.40-A k.q q*:r / lullf,wuekg9 zhl:5ae a9)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 x+l0whw:c 3lcon a 160-m length of straight wire stretched between two towers carrying a 150-A current. The Earth’s magnetic fielhx+l0 cwc 3w:ld of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  Calculate the magnitude of the magnetic foo)f 0v,ozf6w dc;a 5rfrce on a 160-m length of straight wire stretched betwee;wro f6)5v,z d f0acofn 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 iq zzo/; jhy8e,6axb q.f the maximum force on it is 0.750 N when placed in a uni,jbhq y6a /.;xqo8ez zform 0.0800-T field?    A

  A 1.5-m length of wire carrying 4.5 A of current is oriented horizontallyveyb :qr6+ zcx5 a0ur7. At that point on the Earth’s surface, th 5a:uxbvr +e06zrcqy7e dip angle of the Earth’s magnetic field makes an angle of 38 $^{\circ}\,$ to the wire. Estimate the magnitude of the magnetic force on the wire due to the Earth’s magnetic field of $ 5.5\times10^{ -5}\;T$ at this point.    $ \times10^{-4 }\;N$

  The force on a wire carrying 8.75 A is a mk p,ypwhz9dg8kkv (l ,5 rr,k9aximum of 1.28 N when placed between the pohgkvk k5lr p r8pyzk, 9,d9w,(le 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 meter on a wire is measured to b *cb50ghtzh;re only 35% of its maximum possible v;trz*g5bch h0 alue. 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.    $^{\circ}\,$

  The force on a wire is a max6gn(y. xr rte4imum 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-diamep24 ,wkzpoz (a s-y;6kol+ guyter copper wire could just “float” horizontally in air because of the force due to the Earthp;pk yglzw-( zoo6sya2,u k4+’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, ss/.,3pi rwloznib1 $q\,=\,+2e$ 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 f 43xr 2lpn7y24ts m361wtig 2dmaqzpdorce 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 tht uu2gzd) d5-j5 etz7ke force on a negative charge for each diagram shown in (Fig. Below), whz zd-tj2ue g)dt k75u5ere $\vec{v}$ (green) is the velocity of the charge and $\vec{B}$ (blue) is the direction of the magnetic field. ($\otimes $ means the vector points inward. $\ odot $ means it points outward, toward you.)

Determine the direction of+p x.d/m v+ fjk)0xjyo $\vec{B}$ 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 upwardj1wb+ik ;* wslm3kdb1 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) prw41 h.sl7mr,j kkk8awz-o k y2oton enters a 0.20-T field, in a plane perpendicular to the field. What is t l2k17wk -rj kaos,mh4.zyw8khe radius of its path?    m

  An electron experiences the greatest force as it travelcevcaut 017f6 s $2.9 \times10^{6 }\;m/s$ 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 ulo*ug6o t;u ri k05)ta beam of electrons that go undeflected when passing through perpendicular ele girul6 to) ;5o0t*uukctric and magnetic fields of magnitude $8.8 \times10^{3 }\;V/m$ and $3.5 \times10^{-3 }\;T$, respectively? What is the radius of the electron orbit if the electric field is turned off? $F_E$    $ \times10^{6 }\;m/s$ $F_{max}$   $ \times10^{ -3}\;m$

  A doubly charged helium atom whose mass is p c33r2ktdl(g$6.6 \times10^{-27 }\;kg$ is accelerated by a voltage of 2100 V.
(a) What will be its radius of curvature if it moves in a plane perpendicular to a uniform 0.340-T field?    m
(b) What is its period of revolution?    $ \times10^{ -7}\;s$

  A proton (mass $m_p$), a deuteron $(m=2m_p,Q=e)$, and an alpha particle $(m=4m_p,Q=2e)$ are accelerated by the same potential difference V and then enter a uniform magnetic field $\vec{B}$, where they move in circular paths perpendicular to $\vec{B}$. Determine the radius of the paths for the deuteron and alpha particle in terms of that for the proton. $r_d$ =    $r_p$ $r_{\alpha}$ =    $r_p$

Show that the time T required for a particle of charge q moving with 8x64z 17c iikunu) oenkvk,4h constant speed 7k8n)x niv6uhe k1,44izcoku v to make one circular revolution in a uniform magnetic field $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge q mng 21rw3 9aaqf1p xjr(oves in a circular path of radius r in a uniform magnetic field B. Show tha2anq1( rj9 w3pf 1rgaxt its momentum is p = qBr .

A particle of mass m andnx yoy1r,1(7ubyq9e5r rh t p0w0 edz. charge q moves in a circular path in a magnetic field B. ty1uzwy h9(x.n,5rr0 e1eqd7 ro0pbyShow 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 r8*x8ng u/ zdbProblem 21 is $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves with a spk2xn63ur3+ z gmhcjz*eed of 160 m/s perpendicular to the Earth’s magnetic fuj63hxz2 3 k *nrgcm+zield of $5.00\times10^{-5}\mathrm{~T}$, If the bullet possesses a net charge of $13.5\times10^{-9}\mathrm{~C},$ by what distance will it be deflected from its path due to the Earth’s magnetic field after it has traveled 1.00 km?    $ \times10^{-7 }\;m$

  Suppose the Earth’s magnetic field at ty)fdps.t6jx. g -th3t he 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 sj ybb:7v:c:ns peed $\nu=2.0\times10^5\mathrm{~m/s}$ in a field-free region abruptly enters an essentially uniform magnetic field $B=0.850\mathrm{~T~}(\vec{\mathbf{B}}\perp\vec{\mathbf{v}}).$ If the proton enters the magnetic field region at a $45^{\circ}$ angle as shown in (Fig. Below),
(a) at what angle does it leave, $\theta$    $^{\circ}\,$
(b) at what distance x does it exit the field? x    $ \times10^{-3 }\;m$

  A jumper cable used to start a stalled vehicle carries a 65-A / xjc2qe8 f0tjcurrent. How strong is the magnetic field 6.0 cm x e82jqj0c/tfaway 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 allowedat /mcpgr4xvnns yy -hh) a4fk8n53 -8 to produce a magnetic field no larger than that of thy8xm8fnn) r3 nva44-/-g a5htc hpskye 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 yiq9t)jpb nn0:; ibd* v2hbc+wire carries current I out of the page toward you. Indicate, with appropriate arrows, the dirb b2y+*)nji hd;qb:nipct90 vection of $\vec{\mathbf{B}}$ at each of the points C, D, and E in the plane of the page.

  A vertical straight ojq tt)-c-+k tl ju69mb2k+5z iz+siewire carrying an upward 24-A current exerts an attractive force petzo 962u lk jjt+ibq)ti-+ e-zsk c+m5r unit length of $8.8\times10^{-4}\mathrm{~N/m}$ on a second parallel wire 7.0 cm away. What current (magnitude and direction) flows in the second wire?    A  ----待选择----upwarddownward 

  Determine the magnitude and direction ofwlp4l *aid;9hpr9q),tu o+:csj 9 qwv the force between two parallel wires 35 m long andw *jaiv,4o);q9tcph :dsl9qr9p l+wu 6.0 cm apart, each carrying 25 A in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic field is being carrieds0.(p4v lshfy out 1.00 m from an electric cable. What is the maximum allowablel.y4ps sv0(hf current in the cable if the experiment is to be accurate to $\pm1.0\%?$    A

  A power line carries a current of 95,rhc2a*jyz,hw; l ds0 A along the tops of 8.5-m-high poles. What is the m j,hls yzhca;,2rwd0 *agnitude of the magnetic field 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 tuf6ajph .+6;:2t8lnusjwg gz he same direction. Determine the magnetic field at point P, 12.0 cm from one wire and 5.0 cm from the z2fs8: 6tuh jwg;6+angl ujp.other(Fig. Below).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18 cm due south from a straight vertical wiq)sh:- xch:r)d,v. kx z/hmbk re carrying a 35-A current downward. In what direction does the compass needle p ,x/)xkm.s rkvdq bc:): zhh-hoint 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 current due north. What is the net magcctr z+t 7:+p68 ueys bo,:xa andt/t2netic field 20.0 cm due west of the wire if the Earth’s field there points north butos t8+cbz de: p:2a +ur6 tnt/y,xtca7 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 pxv rw ;y9hfl8(rotons passes a given point in space at a rate of $1.5\times10^9\mathrm{~protons/s~}.$ What magnetic field do they produce 2.0 m from the beam?    $ \times10^{ -17}\;T$

Determine the magnetic field midway between two long ib ,ju*1htgc3 1 3(lb q64exe+jdgzgc straight wires 2.0 cm apart in terms of the current I in one when the other carries 15 A. Assume these cuucc3( 6jg 1gbelhqix jz,* +4b1ge 3tdrrents are
(a) in the same direction,
(b) in opposite directions.

  A long pair of wires conducts 25.0 x0cq m *t,jrbz ( 0d( h6egps3w-(dfvlA of dc current to, and from, an instrument. If the insulated wires are of negligible diameter but are 2.8 mm apart, what is the magnetic field 10.00 cm from their midpoint, in their plane (Fig. Below)? Compatf(v(d-,sxd*el 0rc 0g q wmzp63j(hbre to the magnetic field of the Earth.
   $ \times10^{-6 }\;T$ The field of the wires is about    % that of the Earth.(retain two decimal places)

  A third wire is placed in the plane of the )etnan 0; xjtbgy943r 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 t4 b3e0yrx9ja); tgtnnwo 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 points 23ca3 s/q.qbn8 h( fb,sx$^{\circ}\,$ 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 -2 x1dql2xlj(evl it .shown in (Fig. Below). There is a current of 2.5 A in both wires. Determine the magnitude aj1e-q( d i. x2llvxtl2nd 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 A. A second wire, pph -q/;e nv86ze;vxc 5d9y qkmade of 2.5-mm-d6 k vhqv;p-/cnd8ze9;yxeqp 5iameter copper wire and parallel to the first, is kept in suspension magnetically 15 cm below (Fig. Below).
(a) Determine the magnitude and direction of the current in the lower wire.    A the current is to the  ----待选择----leftright 
(b) Is the lower wire in stable equilibrium?  ----待选择----not in stable equilibrium in stable equilibrium 
(c) Repeat parts (a) and (b) if the second wire is suspended 15 cm above the first due to the latter’s field.

  Two long wires are oriented sob0.)he 8lri+rstj pm:gzk o+6 that they are perpendicular to each other. At their closest, they are 20.0 cm apart (Fig. Below). What is the magnitude of the magnetic field at a point midway between them if the top one carries a current of 20.0 A and the bottom one lg pio+ :s.tzb+hm)6jre0 8krcarries 5.0 A?    $ \times10^{-5 }\;T$

  Two long straight parallel wires are 15 b7yiy )oft yx;9h4py2cm apart. Wire A carries 2.0 A current. Wire B’s current is 4.0 yp o2fb74yx ;yti9)hyA in the same direction.
(a) Determine the magnetic field magnitude due to wire A at the position of wire B. $\approx$    $ \times10^{-6 }\;T$(retain one decimal places)
(b) Determine the magnetic field due to wire B at the position of wire A. $\approx$    $ \times10^{-6 }\;T$(retain one decimal places)
(c) Are these two magnetic fields equal and opposite? Why or why not?
(d) Determine the force on wire A due to wire B, and the force on wire B due to wire A. Are these two forces equal and opposite? Why or why not? $\approx$    $ \times10^{-5 }\;N/m$(retain one decimal places)

  Three long parallel wires are 3.8 cm from one another. (Loousk5 61phk+woavt;b7;,9q he jkd.a u king along them, they are at three corners of an equilateral t.9b ke udha51k qja6;u7t,kp+v;soh w riangle.) 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 magnitude and direction of the magnetic fieldfjgbl b2 9z:q. at the midpoint of z lbf9.qjb:g2the side of the triangle between wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a -7jane+ x8ab2vxam 2jdistance d apart, carry equal currents I in the same direcjjxm+b -an28v a7 e2axtion. One wire is at x = 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 tot+u;q; zs/jpj 1vitrn9al of 420 turns of wire and carries a current of 2.0 A. Calculaut;;z1si9q/v nrjj+p te the field inside near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameter is to produce a fi438i8q h/q 3tbja) p qega0ajbeld of 0.385 T at its center. How much current shouldja q i8a3 q/38gat be4j)0bhqp 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-long vk6 ko;t **kiyb7 ,tbvstraight 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 doi v *7*vt6kkt ;,bkybon’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 prou t33m;ncn u4v, kdg0 7.rlu qklk:uq*duces 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 variablesv4 .k ugc 7 ;u0*uqutn rm,kdlln3q:3k, such as solenoid diameter, length, and so on.

A toroid is a solenoid in the shape of a circle (Fig. Below). Use Ampèp o9eo tw93e9vre’s law along the ci9e o3w9top v9ercular 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 magnetiauy0qtkav8-l mhd7*ad* z:z6 c field between the conductors of a coaxia7vqz: 8*0l6da-*ay dhm zu takl 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 with its face par (a j e(m;d7lzaru1:lfallel to the magnetic field bea ;17zd ljrmeu fl(a(:tween 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 scal xmi6s /fs (-22fzxwmye 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 galn)re 2;fu/yz 7g*mun fr.i w.bvanometer weakens by 25% over the years, what cu ;urmi/f.we7 ng*y.fu 2z)r bnrrent will give full-scale deflection if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12m k+q5qlr k.yu,xrj64%, by what factor does the output torque chan jqx,y. rk54k+ rquml6ge?

Show that the magneti8d--pqhet.b uw ; ,rnic dipole moment M of an electron orbiting the proton nucleus of a hydrogen atom is related to the orbital angular momentum L of the electdb;npw-e8-ti hq u,r. ron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter and containing nine loops lies fo)mv;p b2qyam:u(5uf5lnuf; lat on the ground. The Earth’s magnetic field at tm 5 )aovnfbq uy;pflu;u2: m5(his 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 0.566-T6xja *a0,;bh) qek fhl magnetic field. What value of electrah0j ,blexf *a;)q 6hkic field could make their paths straight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium ato; 70/w:qnr e+jozyikrms have radii of curvature equal to 21.0, 21.6, 21.9, 22.2, aniy ;er w:qnoj70+z /rkd 22.8 cm. The largest radius corresponds to an atomic mass of 76 u. What are the atomic masses of the other isotopes?

  Suppose the electric field between the elel,fuipp w 81y+ctric plates in the mass spectrometer of (Fig. Below) is pwi+yl 1u ,8fp$2.48\times10^4\mathrm{~V/m}$ 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 m8otg/kf v0.ye8twn+ p onitor air pollutants. It is difficult, however, to separate molecules with nearly equal mass such ow p8g.kyv/et08+tn f 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 spectrometedpf gtri8 /nh/ )mje-/r accelerates ions by a voltage V before they enter a magnetic field B. The ions are assumed to start from rest. Show gijten /-/rpm8 d/ f)hthat 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 acc)2abymz,qz29: wkm 25-A current flows through the wire. If the permeability of the iron iszm,9m q:2 bcay)2kwzc $3000\mu_0$ what is the total field B inside the solenoid?    T

  An iron-core solenoid is 38 cm long and 1.8 r sddnk7jc/092m ybf4cm in diameter, and has 640 turns of wire. The magnetic field inside the solenoiyds k7 2brm0dc/j4fn9d is 2.2 T when 48 A flows in the wire. What is the permeability $\mu$ at this high field strength?    $\times10^{-5}\mathrm{T}\bullet\mathrm{m/A}$

  Protons with momentu v.otxic xd1kj91kr6 ;m $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 kiyqy: b:e 2m-,lrqqb r-netic energy upon entering a region of constant magnetic field. lqq :brb-2:e yr-y,mqWhat is the ratio of the radii of their circular paths?   

  The power cable for an electric trolley (Fig. Below) carries a horizon,1 oys/fp. yratal current of 330 A toward the east. The Earth’s magnetic field has a s ,1y.fy /srpoatrength $5.0\times10^{-5}\mathrm{~T}$ 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 uz udnh j-:le6afv- a1 (cy)vjj,*ck. 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 horizontally t4remt n rl;0sj3.y7b iuy;6u zo the ntzlr s7 0;4 m ibnyery;uu6j3.orth and 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 helium3 4vq6wps60dc+82pzhhjyb ay atom, 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 6 aq;u0 zgvthr;q;z.y). A large current moves in a closed loop composed of fixed rails, a power supply, and a very light, almost frictionless bar touching the rails. A magnetic field is perpendicular to the plane of the circuit. If the bar has a length L = 22cm, a mass of 1.5 g, and is placed iqztyg 6rvuah.;0z;;q n 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 copper wire and is suh 8xy (w*urwp)spended in air due to the two magnetic forces from the bottom two wires. The current flow through the two bottom wires is 95 A in each. Calculate the required current flow wry*wxp(u8)h in the suspended wire.    A

Two stiff parallel wires a distance l apart in a hor+tzlzb2hpgxo,0 rx( n(e8 u(hizontal plane act as rails to support a lig8lx eu+(hngzz potx(,hr 0(2b ht metal 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 f9cc r/,yh.sautd7, hwae p :9/x k8yppg.hp4 deflection of the electron beam near the center of a TV screen d apx rk/u ge ppsh h8phf79, /.ytc4y.a9wc,d:ue 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. Belogble0b p c-u8bih3w*. w) 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 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 halb gchpi*3el-bu.08bwf-cycle, owing to an ac voltage $V=V_0\sin2\pi ft,$ so that the particles are increased in speed at each passage through the gap.
(a) Show that the frequency f of the voltage must be $f\,=\,Bq/2/pi m,$ where q is the charge on the particles and m their mass.
(b) Show that the kinetic energy of the particles increases by $2qV_0$ each revolution, assuming that the gap is small.
(c) If the radius of the cyclotron is 2.0 m and the magnetic field strength is 0.50 T, what will be the maximum kinetic energy of accelerated protons in MeV?

Four very long straight parallel wires, located at the corners of a square ofr,/ve0 a6qibu5rw p1 k side l, car65wa u/rebi1pq0vk,r ry 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 qfwp t:k8s* 7 e9vy0 rc*y/piqin particle accelerators for “beam steering”; that is, the magnetic fields can be used to change the beam’s direction without altering its speed (Fig. Below). Show how this works with a beam of protons. What happens to protons that are not moving wi 8tk /ey *0yw7pipqqvs*r :cf9th 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 thee2g2wgo82ww3qve+rt gk s( b ) center of a circular coil of wire carrying a current I (+w g8gsg(2keb322we)o tq wrvas in Fig. Below) is
$B=\frac{\mu_{0} N I}{2 r},$
where N is the number of loops in the coil and r is its radius. Suppose that an electromagnet uses a coil 1.2 m in diameter made from square copper wire 1.6 mm on a side. The power supply produces 120 V at a maximum power output of 4.0 kW.
(a) How many turns are needed to run the power supply at maximum power?    turns
(b) What is the magnetic field strength at the center of the coil?    $ \times10^{-4 }\;T$
(c) If you use a greater number of turns and this same power supply (so the voltage remains at 120 V), will a greater magnetic field strength result? Explain

  Near the Earth’s poles the magnetic field is about 1)cpa6-p2sxt s G($ 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 prod1e ;uvuw.+3zovlsj;uuced 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 .;+3zv u jv1olw ueus;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 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 magneticezfdsr6 : n1:hn ;n0wy field would make a beam of electrons, traveling to the right at0 ns:1nd;y ef z:hwn6r a 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 0.010g x,oh4yeh c1vw+) j2x 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. Calculatehxh +,v1go4)ew2j xcy 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 7;.n3s0hbot78n uufco1uynd diameter, is to produce a 0.30-T magnetic field at its center. If the maximum current is 5.7 A, how many turns must the sole7;u 7udnf8h1y3bton.s u0nc o noid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, each of diameter 0.50 tb sv :; 5carzm74rhf/mm, carry the same current but in opposite directions. They are suspended by 0.50-m-long strings as shown in (Fig. Below). If the suspensionar5:z7s/ 4mfbtvc h r; strings make an angle of 3.0$^{\circ}\,$ with the vertical, what is the current in the wires?    A

  An electron enters a uniform magnetic field B = 0.23 T pfzam+tb4pv - - zmf n.vs*x,4at 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$