A compass needle is not always balancecu:;* *timhw ed parallel to the Earth’s surface, but one end may diitu;h:*e* cwmp downward. Explain.

Draw the magnetic field lines around a straight sectio9hq im9*bw lf+nf:3ig n of wire carrying a current horizontally to 9 :3lifm+ni *9wgqbhf the left.

In what direction are the magnetic field lineva3u2oe2 bhu,i) ipw7s surrounding a straight wire carrying a current that is movinauw,puvi2o i eb2h37) g directly away from you?

A horseshoe magnet is held vertically with the north pole on the bwz9ip. 4pp 56-gi kgoleft and south pole on the right. A wire passing between the .giibw56- po9zpkp 4gpoles, equidistant from them, carries a current directly away from you. In what direction is the force on the wire?

Will a magnet attract any metallic object, or only those made of iron? (Try +sr 8jbm5(no*gbx7 gc 2pgv0qit and see.) 0g58*rp7n(m c+bs xg2qojg b vWhy is this so?

Two iron bars attract each other no matter whicom42kax7w (9ux2p tkmh ends are placed close together. Are both 2t2(7xx9kmp ma okw 4umagnets? Explain.

The magnetic field due to dls-ou,.:u9f xcvim*e0 gdk82g (zikcurrent in wires in your home can affect a compass. Discuss the effect in terms of currents, idv :z,(ls2xe8cg.9kiigk* u-do mu0f ncluding if they are ac or dc.

If a negatively char7/8zb p*nhj3 pw(ev nqbj2y8jged particle enters a region of uniform magnetic field which is perpendicular to the particle’s velocity, will the kinetic energy of the particle increase, decrease, or stay the same? Explain your answer. (Neglect gravity and assu jej2wjp b38zy np/8 qbv7(hn*me there is no electric field.)

In(Fig. Below), charged particles move in the vicinity of a current-carrying wir9j-v7 hw 3kjrve. For 7j3-9 rkh jvwveach 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 magnetic field produced by the wire.

Three particles, a, b, and c, enter a magnetic field as shown in Fig. 20–4z7 fw;drzn-m06. What can you say about the charge on ezfnwr ;z0m7-d ach particle?

A positively charged p7ta ;-apkdv25 gnt y e(lj1.vcarticle in a nonuniform magnetic field follows the trajectory shown in v 1c27;ntjtypdv(e5 ka ga-l.
(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 rjkq2zbbh+f o g-sq )pi /h-x(1od? What must you consider to answer these queb-1ob- /+ kiq( j xz2h)sghpqfstions?

Explain why a strong magnet4oe- +p mzau4,nue3 je held near a 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 your TV by trying this.][/But don’t risk damage to y-oae4jzen +u34um ep, our TV by trying this.]

Suppose you have three iron rods, two of which are mjn;( 1tyyu 7 kh,vixur m4-+.rbpv)c zagnetized but the third is not. How would you determine which two are the magnets without usinckr) ;- v+uz, i.rp1bvyhn74mj(yux t g any additional objects?

Can you set a resting electron into motion with a magnetic field? With an lcyvhm9 s7e4fl5 8 4fckf1pwrv+ ;d)pelectric fiell 5wrdv4l9fpe4c+)sk1 8yfmchfp7 v ; d? Explain.

A charged particle is moyn5po+ .;pkt5uiy wd 3ving in a circle under the influence of a uniform magnetic field. If an elecpwt n;+k53 .y5ioypdutric field that points in the same direction as the magnetic field is turned on, describe the path the charged particle will take.

The force on a particle in a magnetic field is the idea behind elm 01g +2+*oi fnwfsywlectromagnetic pumping. It is used to pump metallio +fi0n2lyg*1w w+fmsc fluids (such as sodium) and to pump blood in artificial heart machines. The basic design is shown in(Fig. Below). An electric field is applied perpendicular to a blood vessel and to a magnetic field. Explain how ions are caused to move. Do positive and negative ions feel a force in the same direction?

A beam of electrons is directed toward a horizontal wii4r 7oksgln4 w 6wl ufvae9-z41i +7krre carrying a current from left to l nzi+ 446kugvl97 i71krreo -4fswwaright
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields that surround a moving ,suahy kixm++ .th3m, electric charge.mah+u,3 xtk+.is hy m,

A charged particle moves in a s.wac 9ta (lf9ta71m tftraight line through a particular region of space. Could there be a nonzero magnetic field in this reg(f9al.act af 71 tmt9wion? If so, give two possible situations.

If a moving charged particle is deflected scn/m s-f8hv8b ideways in some region of space, can we conclude, for certain, v8n-cfh m8 /sbthat $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is a unif.mdov;pl hq8;y b g 9.v0vkuw8orm 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 whya* ,m mh w.df58q+vtnether moving electrons in a certain region of space are being deflected by an electric field or by a magnetic fielt m dq*,.mh+ yf5n8avwd (or by both)?

How can you make a compass without using iron or other ferromagnetic material q b)b0nk vcrrs4pbmu9cohw/-i9x 8 0:?

Two long wires carrying equal currents I are at right angles id)uxr z6 q58hto each other, but don’t quite touczdx6u8r5i) qhh. Describe the magnetic force one exerts on the other.

A horizontal current-carrying wire, free to move in Earth’s gravitational :ggo woks.-h,6mo mw6( kxy7j field, is suspended directly above a second, parallel, current-co:6ogg hym owj .7 m(,-6kswkxarrying 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 y ) 1cwtf* zppg sf4,qje;) h,4w0zulbmagnet attract an unmagnetized piece of iron?

An unmagnetized nail will not attract an unmagne(ibx)3/er5 ks n nvi9q *pwk6stized paper clip. However, if one end of the nail is in contact with a magnet, the other en(pq/ vrx39*n)iikne k b ss5w6d will attract a paper clip. Explain.

Two ions have the same mass, but one is singly ionized and the other is dou7q pgcz kqwu6l d02d+i5(x5mdbly ion 6d0p uqk gcmxq5+( dwdi7z2l5ized. How will their positions on the film of a mass spectrometer (Fig. Below) differ?

What would be the effect on B inside a long r w jv,-)tpnen q2a7j4solenoid 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 si+;9 ilwf4 u 33jiobqfamilar to a solenoid is a relay . A relay is an electromagnet (the iron rod inside the coil does not move) which, when activated, attracts a piece oo3 i49q3u+ bajfl wfi;f 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 mete1kjadxvumgc pr us;)g:/f)t32:ql 0r r of length on a straight wire carrying an 8.40-A current when perpendiculm1v pl sk)2a j3;:gtugr q0:curd xf/)ar 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 length2dlrsm n hnzb .50vd1, of straight wire stretched between two towers carrying a 150-A current. The Eartn.sn,2ml h01 zrbdv5dh’s magnetic field of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  Calculate the magnitude of the magnetic force on a 160-m length of stss6b8( q,dr/przix 4 nraight wire stretched between twq xpsir,znds4 /b86 r(o 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;nx662gp gtyp long if the maximum force on it is 0.750 N when placed in a unifg yt;npg62p x6orm 0.0800-T field?    A

  A 1.5-m length of wire carrying 4.5 A of cl xlvo n:758j b6(zqfnurrent is oriented horizontally. At that point on the Earth’s surface, the dip angle of the Earth’s magnetic field makl nfjbq(oz l5n87x: v6es 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 aq1l uk/kvzfrl o,i66kkl5z 54 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 approximate strength of tz165 ki4orul k6 f,/qk vkll5zhe magnetic field?    T

  The magnetic force per meter on a wd /g*iilcbcvu /kmh;l*. 7o/tire is measured to be only 35% of its maximum possible value. Sketch/;igu*il. mk /7clt cb*hod/v 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 maximumy+ih8bpgnnvs1; 3h; a 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-di3ue, ca lw l+bi;4t9vwameter copper wire could just “float” horizontally in air because of the force due to the Earth’s magnetic fiellwlet3v+ 4b,aw9;i cud $\vec{B}$, 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 charg lzix72t* )u7tbtyj u(e $q\,=\,+2e$ and mass m = $ 6.6\times10^{ -27}\;kg$ are emitted from a radioactive source at a speed of $1.6 \times10^{ 7}\;m/s$. What magnetic field strength would be required to bend them into a circular path of radius r = 0.25 m?    T

  Determine the magnitude and direction of the force on an qdqu4fn9otf ;( o21uhelectron 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 charlqit,x)/ ou 2;s n(mdtge for each diagram shown in (2dosxuqt i m/t(,nl ;)Fig. 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 of ,ky8/ vg4p rw/ixym d*$\vec{B}$ 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 ver7jgp1l *( oylwaar6x +tically upward with a speed of $1.7 \times10^{6 }\;m/s$ into a uniform magnetic field of 0.350 T that is directed horizontally away from the observer. Describe the electron’s path in this field.    $ \times10^{-5 }\;m$

  A 5.0-MeV (kinetic energy) proton enters a 0.20-T k:qo4z(q.z0 ooyrk6f w3ks3oy h6gc; field, in a plane perpendicular to the field. What is the radius of it4k3 y .z: o6(yqqo fswzo c6ko0krg;3hs path?    m

  An electron experiences the greatest force as it t) 82s*qlf4omyd+hek rxqd 20i ink4c(ravels $2.9 \times10^{6 }\;m/s$ 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 undeflec izvap3 m s)ofor9vs4d(6c q-/ted when passing through perpendicular electric and magnetic fields of magnitfras4- c m3z osod9iv(/v6)p qude $8.8 \times10^{3 }\;V/m$ 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 d+c fp-8 za vjg)81awkmass 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 movixez,f71bmp r h8jo w+)ng with constant speed v to make one circular revolution j 7 )8hwfbz+orp,1xe min 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 uniform mi1p3t cw,oa rz0(p;tly+ ,nlsagnetic field B. Show that izcao+; p0w ,lrt si(tlp ny13,ts momentum is p = qBr .

A particle of mass m and charge q moves in a circular path in a magnetic field91pvx 8zam, qv B. Show that its kin1a8mxvpqz v,9etic 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 Problem 21 is*n,fh-jw,ozubu-on9 8s tp 4v $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves with a spez,th xpv3(fy,ed of 160 m/s perpendicular to the Earth’s magnetic field ofp3xh ,(,tzv fy $5.00\times10^{-5}\mathrm{~T}$, 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 mag8o j 09m;trzcmnetic 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 speedmege(j ktsk40bo d4. l8 0f3qy $\nu=2.0\times10^5\mathrm{~m/s}$ 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 cnxfpkk9trm6 qt ):gm04t 14up urrent. How strong is the magnetic field 6.0 cm away ftgkm4r:pu)mk91 txt 4n0pqf 6rom 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 magneo/raw0e.d6efaiv j v;/a 6u)xtic field no larger than that of t)o6/ a efe;ixu60vaj /awr. dvhe 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 pagd;dj*et-z :q vmkit+8e toward you. Indicate, with appropriate arrows, the j ev; *+8-z dmdkt:qitdirection 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 upwal5 l53fkyyc) s1/ueezrd 24-A current exerts an attractive force perfey 5cye1s5zllu k )/3 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 directs ibiq:bsy9 ;yc 7+u)vb c0k-aion of the force between two parallel wires 35 m long and 6.0 cm aqc ks;icv7-bs+aybi9 )uy0b :part, each carrying 25 A in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnet0cv 7h l ;h;jpc,y 0jhj,8xhopic field is being carried out 1.00 m from an electric cable. What is the maximum allowable current in the cable if the experiment is to be accurate to phhl ycv,7p;x ,o hc j8hj;0j0$\pm1.0\%?$    A

  A power line carries a current of 95 A along the tops of 8.5-m-hig9 4eiimrjhq *18*1/kmg0rma msm 6cuk9fh,j xh poles. What is the magnitude of the magnetic field produced by this wire8r mr mhmcmu h9ajk 0jgk,f*1ixseim 6q/4 91* 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 t,1dyqx-appgfci;4;y qh2v3n he same direction. Determine the mpp xfqn,-2 idgayq; c1y4v;h3agnetic 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 izm 9jlg/u to-b/.ja;lzh;,zrs placed 18 cm due south from a straight vertical wire carrying a 35-A current downward. In what direction does thez,atz- //b lhorj.j9l;g zu m; compass needle point at this location? Assume the horizontal component of the Earth’s field at this point is $0.45\times10^{-4}\mathrm{~T}$ and the magnetic declination is 0$^{\circ}\,$.    $^{\circ}\,$ N of W

  A long horizontal wire carries 22.0 A of cu pm8cle w,:7*iandx :trrent due north. What is the net magnetic field 20.0 cm due west of the wire if the Earth’s fa8, n cpe:md* 7lxw:tiield 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 4 cfk76f:uucfa 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 magnetvu w7o9j,ty w6z7 ahc1ic field midway between two long straight wires 2.0 cm apart in terms of the current I in one when the ot9oyw 6 c 1uzvwh7t7ja,her carries 15 A. Assume these currents are
(a) in the same direction,
(b) in opposite directions.

  A long pair of wires conducts 25.0 A of dc current to, and from, an i;hv *b/5 a7i ochhtok:nstrument. 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 viha7o5kbo: ht;/*h c(Fig. Below)? Compare to the magnetic field of the Earth.
   $ \times10^{-6 }\;T$ The field of the wires is about    % that of the Earth.(retain two decimal places)

  A third wire is placed in the plane of the two wires shownr v5ez(b )(mit in (Fig. Below), parallel and just to the right. If it carries 25.0 A upward, what force per meter of length does it exert on each of the other two wires? Assume it is 2.8 mm from the nearest wire, cv(rm t i)zb5(eenter 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 poina s*q:wnj9n +p,xq jmo9ln 0q5ts 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 lw(9q vz89g8k ipgr: o62 diojpies in the same plane as a straight wire, as shown in (Fig. Below). There is a current of 2.5 A in both wires. Determine the magnitude ang68 j8idpg9 vz i2o9wrko:q(pd direction of the net force on the loop.    $ \times10^{ -6}\;N$  ----待选择----away from wiretowards wire 

  A long horizontal wi 7dy2j cw:rw0hf gdo-16 jo77w5iwzhjre carries a current of 48 A. A second wire, made of 2.5-mm-diameter c dh 7jc1jg2 : wjif6hwo77rzw y0do5w-opper 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 so that they arezblnwu*t-,4q+ z ))b2 valtpk 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 kz*z -4)tnlt +ubab)l,2vq wptop one carries a current of 20.0 A and the bottom one carries 5.0 A?    $ \times10^{-5 }\;T$

  Two long straight parallel wires are 15 cm apart. Wire A carries 2.0 A9frrw( wysxhj4fq)3 6 current. Wire B’sx4 jq)wy9 6rfw sfh3r( current is 4.0 A in the same direction.
(a) Determine the magnetic field magnitude due to wire A at the position of wire B. $\approx$    $ \times10^{-6 }\;T$(retain one decimal places)
(b) Determine the magnetic field due to wire B at the position of wire A. $\approx$    $ \times10^{-6 }\;T$(retain one decimal places)
(c) Are these two magnetic fields equal and opposite? Why or why not?
(d) Determine the force on wire A due to wire B, and the force on wire B due to wire A. Are these two forces equal and opposite? Why or why not? $\approx$    $ \times10^{-5 }\;N/m$(retain one decimal places)

  Three long parallel wires adg6t aqqri*57,ooak0 ush9 (p re 3.8 cm from one another. (Looking along them, they are at three corn d(7au iaqp 5 ktr096ogs,qoh*ers of an equilateral triangle.) The current in each wire is 8.00 A, but its direction in wire M is opposite to that in wires N and P (Fig. Below). Determine the magnetic force per unit length on each wire due to the other two.
$\frac{F_\text{M net y}}{l_\mathrm{M}}$ =    $ \times10^{ -4}\;N/m$ =    $^{\circ}\,$
$F_{N\,net}$ =    $ \times10^{-4 }\;N/m$ $\theta$ =    $^{\circ}\,$
$F_{P\,net}$ =    $ \times10^{ -4}\;N/m$ $\theta$ =    $^{\circ}\,$

  In (Fig. Below), determine the magnitude and directiop mz6)ai8n ;hgn of the magnetic field at the midpoint of the side of the t6ig n8mp)h ;azriangle between wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a distaddzn8f62m o.v nce d apart, carry equal currents I in the same direction. One wire is at x = 0, the other is at x = d, (Fig. o fdmvz6.8nd2Below). Determine $\vec{B}$ along the x axis between the wires as a function of x.

  A thin 12-cm-long solenoid has a total of 420 turns of wire andg;)n:tmb6mbtq l9o a3 carries a current of 2.0 A. Calcu; tmnqbtl ab:9) o3m6glate the field inside near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameti teu k0a*:/)m5q3xzd w)jxbjer is to produce a field of 0.385 T at its center dqj t ):)xk3i m*jxw/uaz05be. How much current should the solenoid carry if it has 975 turns of the wire?    A

  A 550-turn solenoid is 15 cm long. The current in it is 33 A. A 3.0-cm-ueqkw *uzw9/wmg6a+-vd er 5 2long 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 -ewdu/+qwru 6 vg *makz952wewire assuming the solenoid’s field points due east?    N

You have 1.0 kg of copper and n y 0aisbcxnwnns 0yu wbqd8978;0r+5want to make a practical 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? Consider other variables, such as solenoid diameter, length, anwr 0 i7scbbn8ad q 08+xu nyyn;sn950wd so on.

A toroid is a solenoid in the shape of a circle (Fig. Below)avd9zq pql u7+/h v4(s. Use Ampère’s law along the circular path, shown dashed in (F l4(vvqu9 dzqaph/s 7+ig. 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 conductb94zbp amh8 p/ors of a coaxial cable8 bp/94hbzm ap (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 wi8 ;gzhgghxb )x d5*nf7klp0u shz0j43re 22.0 cm on a side is placed with its face parallel to the magnetic field between 70h5p 3g84u*0) zjgh xgndsl xb;zfhkthe pole pieces of a large magnet. When 6.30 A flows in the coil, the torque on it is $0.325\cdot N$. What is the magnetic field strength?    T

  A galvanometer needle deflects full scale u)0 -e-ijedjv 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% ovejmqw(km ev .zy hwuq5+* *88rpr the years, what current will give fu.h+mpjeqwqyzkuw8v8m** r (5ll-scale deflection if it originally required $36-\mu A$ ?    $\mu A$

If the current to a m) z9mv m4qazpzm0qy5, otor drops by 12%, by what factor does the output torque cha9z q)mz 05zmqpm ay,4vnge?

Show that the magnetic dipole moment M of an electron orbiting the 4w*vgl c)+6*fm mt leaproton nucleus of a hydrogen atml*eg cal4tw 6+mfv*)om is related to 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 loops lies flat qv dflux9h69-4ky qm.on the ground. The Earth’s magnetic field at thisd9 uh9kmq6q v -4ylfx. 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-T magnetic field.blmh2 gkf1w 1hdqd8wy;), 6uz What value of electric field coul;h, zh18w1)ldmqbu6yf wk2g d d 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 tey6vm c x1sl9;o 21.0, 21.6, 21.9, 22.2, and 22.8 cm. The largest radius corresponds to an atomic lm;s1 ce9 y6vxmass of 76 u. What are the atomic masses of the other isotopes?

  Suppose the electric field between the electric plates in the ma .xkzgdz0*ohk4 a;5d8wohoj 4ss spectrometer of (Fig.z.; *koo04w 4ahhdj8xdz5o kg Below) is $2.48\times10^4\mathrm{~V/m}$ and the magnetic fields $B=B^{\prime}=0.68\mathrm{~Т}.$ The source contains carbon isotopes of mass numbers 12, 13, and 14 from a long-dead piece of a tree. (To estimate atomic masses, multiply by $1.67\times10^{-27}\mathrm{~kg.}$)
How far apart are the lines formed by the singly charged ions of each type on the photographic film?
$2r_{13}$ - $2r_{12}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)
$2r_{14}$ - $2r_{13}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)
What if the ions were doubly charged?
$2r_{13}$ - $2r_{12}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)
$2r_{14}$ - $2r_{13}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)

A mass spectrometer is being used to monitor air polluta2+i 4;obaeixv. msb *t (bhp.wxh iv,;nts. It is difficult, however, to separate molecules with nearly *i , mv2xi4wh;(xh;+i pb as e.bbv.toequal mass such as CO (28.0106 u) and $N_2(28.0134u)$. How large a radius of curvature must a spectrometer have if these two molecules are to be separated on the film by 0.50 mm?

One form of mass spectrometer accelerates ions by a voltage V before they ente.9 z 43ingvouar a magnetic field B. The ions are assumed to start from rest. Show that the mass ofu4.vi3z n oga9 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 mezmv6xwp.pe 8 8 xjvu kvd5/,a8ter, and a 25-A current flows through the wire. xdx85wmvvu6jz, va p8pe/ k8. 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 in diameter, and h .k9oqnpheyrgd)0 uog 03723v.a bfvpas 640 turns of wire. The magnetic field inside the solenoid is 2.2 q37 2.oo n)p gkr09yed3 ba.hf0vpgvuT 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 momentum suk6usoqm 7bfjm 92 )1$4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 eleczi0qph,kc x0v+2ms jdv5r *5 wz *i*qltron have the same kinetic energy upon entering a region of constant magnetic field. What is the ratio of the radii of thei,d5cz+5*wmixv2* szrqjk lv 0 p*hq i0r circular paths?   

  The power cable for an electrich2sl,acqd x)3 ovq26 i trolley (Fig. Below) carries a horizontal current of 330 A toward the east. The Earth’s magnetic field has,)v6 o2q 3i2lacxds qh 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 a ne v2lna.7d, ej(yo oky9t 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 magnez erw6woqxcnm ,ajfu ;4c61 48tic field points almost horizontally to the north and has jr;1 ou cm4 fzxq e,w8nwc4a66magnitude $B=0.50\times10^{-4}\mathrm{~T.}$ 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 heliu*so5(bfop7v:nc4i g i m 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 launchmn7 .okz5upx) 5jlq3dz 2v*veer” is shown in (Fig. Below). A large current moves in a closed loop composed of fixed rails, a power supply, and a very light, almost frictionless bar touching the rails. A magnetic field is perpendicular to the plane of the circuit. If the bar has a lengtvd5kl.op) m 5jv2qnzz*xu7e3 h L = 22cm, a mass of 1.5 g, and is placed in a field of 1.7 T, what constant current flow is needed to accelerate the bar from rest to 28m/s in a distance of 1.0 m? In what direction must the magnetic field point?
   A
the magnetic field must be ----待选择----updown 

  In (Fig. Below) the top wire is 1.00-mm-diameter copper wire h vhpk iz1.uyw:, 7-phand is suspended in air due to vh:.-wzhk,ui1p p 7yhthe 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 in the suspended wire.    A

Two stiff parallel wires ar xrr7+ pkgy;-5lka:ms ks13r/ igyo2 distance l apart in a horizontal plane act as rails to support a light metal rod of mass m (perpendicular tokr 5p ;iar2+krgs71-omsk:y /x 3rgl y 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 mamz(m /v0oi; fmnsv b0*ximum deflection of the electron beam near the center so /v0m(zni*;mm fv0b of a 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. Below) is a device used to accelerate eleewx 7deo 23dr-mentary 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 thded -r73x2eowe 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 parallel wires, located at the corners of a squarf3p- jfs vp6e5e+oo.ue of side l, carry equal curo effpsju3 6+p5 .-oevrents $I_0$ 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 partinoqp 0xfrbt*fg xz9.)7w5: ftcle 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 prob0nzq f*)wtfx: 5fx9.og7p rttons 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 wireek(5s 5 ijbq3es,l m*a carrying a current I (as in Fi 5ska3*ibs(e,lm5q j eg. 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 mag44zn *bcf( q9 .kzoldgnetic 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 t50q6 ngdjdl),8ynw(kzc y sb8he magnitude of magnetic fields produced by overhead power lines. You estimate that the two wires are each about 30 m above the ground a50sq)ybzkl8n y ,jc d8wn( g6dnd 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 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, traveling to x owkrvi2gd)o4 5n4u/the right at 2dwrno gu)o/x vi54k4 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 0.0g r ,p f 3be50vmz5r0x.emw1pww l2c*s10 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, respectivelf gxzem wwp35*,cs e .0vp1rbm rw52l0y. 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 ootdxyb -/dzbg ;m4 hu01a b7tfd2n 6.cm in diameter, is to produce a 0.30-T magnetic field at its center. If the 12y/60d.gu tz4mhbo;f7b a xdt-ndbomaximum current is 5.7 A, how many turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, each of diameter 0.50 mm, carry the same cutfn,l5o0nw t7uy o e8zjvp-u24 2/go krrent but in opposite directions. They are sutzujn5t4fyvkn- o l 20oewg2op u 87,/spended 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 magnetic fie1 hrnar (/k(rd y0cum53xwn;zld 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$