A compass needle is not always balanced parallel to the Earth’s surn6mq*jn/3u iu2s1h brbqa3o)face, but one end may dip downward. Ex as2o j*)q h31/nuqbni ur3mb6plain.

Draw the magnetic field lintm4 37ztjnm ;tes around a straight section of wire carrying a current horizontally to the leftjm ;n47 tz3tmt.

In what direction are the magnetic/v dk9ch/t n r.,vdi fdj, t73(x-rtzc field lines surrounding a straight wire carrying a current that is moving d3/ ddf7rrk(nvt-td.i ,t,cjxc9/hvz irectly away from you?

A horseshoe magnet is held awzk 73y;/bm nvertically with the north pole on the left and south pole on the right. A wire ba/3 kywz;nm7passing between the poles, equidistant from them, carries a current directly away from you. In what direction is the force on the wire?

Will a magnet attract any metallic object, or only those mad9 1j9w wq6*hcbkpmr34 une7y ie of iron? (Try it and see.) Wh b pu9h41kj97n3* cwrwqie6myy is this so?

Two iron bars attract each other no ma/h,v ( qmivr+y*s;v1teh.pxm tter which ends are placed close together. Are both magnetstqs ; v*i1hh rmx.mv,(e+vpy/ ? Explain.

The magnetic field due to current in wires in yourq ddn p+m -);vs dcty)bcyax..f ey,(: home can affect a compass. Discuss the e v,bf:d t.cycn;) eqy(mp.s ddyx-+)affect in terms of currents, including if they are ac or dc.

If a negatively charged particle enters a region of uniform magne fl o8)fch3y)nze;mjezw* 0zu(f5m1 jtic field which is perpendicular to the particle’s velocitey)won*jff3(uf jh1 e5z )mz;mc zl80y, 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 in the vicinity of a cua0 20x,olvyp mrrent-carrying wire. For each charged particle, the arrow indicates the direction of motion of the particle, and the + or - indicates0, o lapv20ymx 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.2e jni1;dvop:4vrk gj lg7g)) 20–46. What can you say abou)g v1jgvp) e4knlodr7j gi: ;2t the charge on each particle?

A positively charged partkdmtoud*b 3,fbo 7. n*icle in a nonuniform magnetic field follows the trajecto* fkmobd.t3n 7 ubd*o,ry shown 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 magnew9jy d lwtw+pm33kw;0t? Can a magnet attract an iron rod? What must you consider to an+d93 j plkmy3t;0w wwwswer these questions?

Explain why a strong magnwqir7*ny:6.m4 s9p /ugsblnlet held near a CRT television screen (Section 17–10) causes the picture to become distorted. Also, explain why the picture sometimes goes completelyisgqn *ls l6 p9./m:4 nwuyb7r 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 magnetizedup nui;:3 rr lq0-rv3ug4aw t6 but the third is not. How would y4 :lrni0 tpv3;3wqr a6-uu gurou determine which two are the magnets without using any additional objects?

Can you set a resting electron into motion with a magnetic field?t))habe.- l w tncg*xm//mf,t With an electric field? Explain./n/l. m)tw)*a- mge ct,thf bx

A charged particle is moving in a circle under the influence ofn pi5 +coi),tl a uniform magnetic field. If an electric field that points in the same direction as thep olt) i,c+i5n magnetic field is turned on, describe the path the charged particle will take.

The force on a particle in a magneticl0aj un-em3t * 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. Th jntule3*a 0m-e 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 current vb l0z;hl 5hch+mc7 3ifrom left tohm7hc3+c z v l;h5i0lb right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields that surround a moving electric chargf4t)h:8pi4jds1 2 chntj pae1e.tjn: 4cjd81sa e24i pphh f1t)

A charged particle moves in a straight line through a parsr2c,0v z l,anticular region of space. Could there be a nonzero magnetic field in this region? If so, give two possi z,2c la0srn,vble situations.

If a moving charged particle 73z wuqe7:9 ju(fderx is deflected sideways in some region of space, can we conclude, for certain, tha dfr jeq u7w3uz9e7x:(t $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space theql(7 7 4 g.zf5pnfovvjre is a 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 mnhr9i-hb*6 r:lf)l;sw dpew 5 3,ga umoving electrons in a certain region of space are being dr,- uw;slp:)6imer fn9*g whbd ah35leflected by an electric field or by a magnetic field (or by both)?

How can you make a compass without using iron or nhxu synt dloj,b59f2:7p3 y(other ferromagnetic material?

Two long wires carrying eqratf ,3 c*c4nnv4x iu:ual currents I are at right angles to each other, but don’t quite touch. Describe the magnetic force one exerts on the i c: r3a*nc4nfxtuv4,other.

A horizontal current-carrying wire, free tompp*lx ax esr47nm4 w.v u(d556gj3b t move in Earth’s gravitational field, is suspended directly above a second, parallel, curren5 ag*xlbsd45 7vmp6exutm( 3.jr4pwnt-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 attrov96g:ozhf.* u y upk9act an unmagnetized piece of iron?

An unmagnetized nail will not attract an unmagnetized paper clip. Hoa oci5d9 dv+r4wever, if one end of the nail is5ic ar+4v ddo9 in contact with a magnet, the other end will attract a paper clip. Explain.

Two ions have the same mass, but one i gkx1s/kg4 mt3s singly ionized and the other is doubly ionized. How will their positions on the film of a mass spectrometer (Fig. Below) differ? /g 3mkk 1stx4g

What would be the efpg0x ::4sohc:-d mvyffect on B inside a long solenoid if
(a) the diameter of all the loops was doubled,
(b) the spacing between loops was doubled,
(c) the solenoid’s length was doubled along with a doubling in the total number of loops?

A type of magnetic switch similar to a solenoid qi2f3 +lkud)n 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 starter doesn’t pass to the dashboard swudqfi+3 l nk2)itch.

  (a) What is the magnitude of yogo tn x(xdq*)31;mlthe force per meter of length on a straight wire carrying an 8.40-A current when perpendicular to a 0.90-T unifolo td*oxm(y 1 x3q;gn)rm 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 16le(* o 5k4hp.kkt vlp30-m length of straight wire stretc vp5tle ko*(lkp3k 4.hhed between 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

  Calculate the magnitude of the magnetic force on a 160-m length of straig,t*c 6koeanj+sriktc)v 18spzmul()og 0 g3-ht wire strs lk c)ena1cs *z-gt3(08)t j imoprvuk ,6+goetched between 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 fxsj89o:vmn e3)am,d uorce on it is 0.750 N wh,m3 xdaj8m:uev 9)nsoen placed in a uniform 0.0800-T field?    A

  A 1.5-m length of wire carrying 4.5 A of current is oriented horizuwe4s3l 6cnt+ontally. At that point on the Earth’s surface, the dip angle of the Earth’s magnetic field makes an angle6lncuest 3w+ 4 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 maximum of 1.28 N when placed between tbm154bar (xzspj / qc,he pole faces of a magnet. If the pole faces are 55.5 cm in diameter, what is the approximate strength of theb pazjxs/ ,54r b1cq(m magnetic field?    T

  The magnetic force per meter on a wire is measured to be only 35% of i,aui6kxhs 8 nxnf ve y0,qk7e0m,+0 rvts 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 is6xn,0yvahneksmvk ,q+u0r i 0f,xe87 , calculating the angle between the wire and the magnetic field.    $^{\circ}\,$

  The force on a wire is a ma,b6wuo7 hk; npyb5u+ tximum of $ 6.50\times10^{-2 }\;N$ when placed between the pole faces of a magnet. The current flows horizontally to the right and the magnetic field is vertical. The wire is observed to “jump” toward the observer when the current is turned on.
(a) What type of magnetic pole is the top pole face?  ----待选择----North PoleSouth pole 
(b) If the pole faces have a diameter of 10.0 cm, estimate the current in the wire if the field is 0.16 T. $\approx$   A(retain one decimal places)
(c) If the wire is tipped so that it makes an angle of 10.0° with the horizontal, what force will it now feel?    N

  Suppose a straight 1.00-mm-diameter copper wire could just r vw3-tpsh9k7“float” horizontally in air because of the force due to thesh-7tpk3w vr9 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 char+p: wdlwjpg55 ge $q\,=\,+2e$ 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 direbrs+3x (+uih iction of the force on an electron traveling $ 8.75\times10^{5 }\;m/s$ horizontally to the east in a vertically upward magnetic field of strength 0.75 T.    $ \times10^{-13 }\;N$  ----待选择----NorthSouth 

Find the direction of the force on a negative charge for eaczqf0uiv h;4 h3h diagram shown in (Fig. zfi40;uvqh3hBelow), 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 directionvmg y, +7dkkehk qbh35v7. cb5 of $\vec{B}$ 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 upward wioowe*mj3py (vvv9 (1bth 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 av4g-.mowycx(kk)d)o evj)e+ne 1vn5 0.20-T field, in a plane perpendicular to the field. What is the radius of go-we )5jn4(x1n vy) evmcke+vo)k .d its path?    m

  An electron experiences the greatestg3.i5 nq1xtez 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 th+)hd;*t yisu fkoaain 9z8 (s4at go undeflected when passing through perpendicular electric and magnetic fields of magnitos d)9+ tf ( 4nzisikuhyaa;8*ude $8.8 \times10^{3 }\;V/m$ 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 massfiqf vq; 9o(,l 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 m2ehrd i rf-zyqc2uhd*.)zi0-j c fe*-j1 ob;noving with constant speed v to make one circular revolution in a uniform magne.2 zc-*1d)qjf0rrei-ic ;b 2yhd-fz*noe ujhtic field $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge q1appn+8f;q0fx q 1gre*j x(qp2+r k0w g(gctz moves in a circular path of radius r in a uniform magnetic fier0(pj0raz +pg1(px k*g+ 8gw;tfxefqnq 2cq1ld B. Show that its momentum is p = qBr .

A particle of mass m and charge q moves in a circular path in a magnn-j f)r:c *jaeetic field B. Show that its kinetj rf *j-anec):ic energy is proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular4u4 wzrq9 q;ee37; jqh6e+e7wmrb zpr momentum of the particle in Problem 21 is $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves with a speed of 160 m/s perpendicular;vwz m v6+jpe +k2wrz)4lz :wr to the Earth’s magne6zmr+2 4zvw l;:ev jpkrw+ zw)tic field 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 th: s8lmi07d* q5oh19phuxftjbe 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 spenbgmexngke7 :f86(/0sdtnf )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 s8h3a7d. xmlyfo k)uy, tart a stalled vehicle carries a 65-A current. How strong is the magnetic fielfx)k8hu3m.y 7o d,ylad 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 field no larger than thatsjeo-meh4jki 5 q),u 0 of thij0,h5-)mskjeuo4 qee 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 w o3lz:j lv;fgnsp(g. )ire carries current I out of the page toward you. Indicate, with appropriate arrows, the (:ls3lpf;vzg .jo)ng direction of $\vec{\mathbf{B}}$ at each of the points C, D, and E in the plane of the page.

  A vertical straight wire carryingfz0t r5 eug.0cq;yt, y an upward 24-A current exerts an attractive force per unizrcyfgy e.tuq,0;0 t5t 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 direct.wuh3ne ; 90bugnqm0uavu .,l ion of the force between two parallel wires 35 ,hu.u3au0;n .b0 v ueq gwln9mm long and 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 carried outgvz b5a4gfaf 2v0a)o 0q3y rd4 1.00 m from an electric cable. What is the maximum allowable current in the cable if the experiment is to be accurate tovyqf0fgbaav3r5 oz ga0) d 424 $\pm1.0\%?$    A

  A power line carries a current of 95 A alon5p nq 4 * )lrv0wxfisj,i57cfog 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 wit f5sji f,vqlwc n5i7*0 r4xp)oh 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 25-7b:+buahgo1i 2 - mv)t2fbuxmA currents in the same direction. Determine the magnetic field at point P, 12.0 cm from one wire and 5.0 cm from the other(Fig. Be) bu b:i1vob +-umth22gx7amf low).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18 cm due south from a straightr j2isuc io//. vertical wire carrying a 35-A current downward. In what direction does the compass needle point at this lo crs/2 iouji./cation? 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 njz:ki1 .iued7qeafb er7 o aa/u;;:(xet magnetic field 20.0 cm due west of the wire if the Earth’s field there points north but downi eeqx.d;7e u;rb/ z: 1:k auoaa7fij(ward, 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 itqj 6syez 0mg *;u/3da 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 midwaypmxo-fm vh, m3u ,vp2if/ei; pt;* s,:nner .t between two long straight wires 2.0 cm apart in terms of the current I in one when the other carries 15 A. Assume these 3xpm i .,ts;m n;*t,/pv:i mp u2nevf,h-orfecurrents 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 int7huk4, n /vehrk1hxtqv1i0 + bdp-u6strument. If the insulated wires are of negligible diameter but are 2.8 mm apart, what is the magne,7v eh1 6vhkrk/uihdxtq bp4n u0+t1-tic field 10.00 cm from their midpoint, in their plane (Fig. Below)? Compare to the magnetic field of the Earth.
   $ \times10^{-6 }\;T$ The field of the wires is about    % that of the Earth.(retain two decimal places)

  A third wire is placed in the plane of the two wires shown in (Fi)j .czzys.ue7s k4p :6n6vnkh g. 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 i:uz ).e zs .k6kns674cjphy nvt 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 poindo5zqcrp l2vyr+/p l5m 6z(t6yw:n ; pts 23$^{\circ}\,$ E of N outdoors. However, when it is placed 12.0 cm to the east of a vertical wire inside a building, it points 55$^{\circ}\,$ E of N. What are the magnitude and direction of the current in the wire? The Earth’s field there is $0.50\times10^{-4}\mathrm{~T}$ and is horizontal.    A  ----待选择----updown 

  A rectangular loop of wire lies in the same plane as a straight 0/w eh +0j 3slue*6lpjrfb,hp- f h5dkwire, as shown in (Fig. Below). There is a current of 2.5 A in botwk/u, pfs -b3l r0+5jfelhpdh j6*eh0h 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 A. A second wire, mamgeiro70 y0w5de of 2.5-mm-diameter copper wire and parallel to the fiyi0e70 g5mw orrst, 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 somhh /7utnz9 y 4kv *yel3p;4ni that they are perpendicular to each other. At their hkuh*ly/venm i 7y 44;p3znt9closest, 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 carries 5.0 A?    $ \times10^{-5 }\;T$

  Two long straight parallel wires are 15 cm apart. Wire A carries 2.0 A cur,4t:q/qxu5cz g1 yexal8 mj5orent. Wire B’s t/axcu4 yz:xg58jqlq ,e1m 5ocurrent 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 are 3.8 cm from one another. (Looking alobn4 bp 1blw;mhp t/w4p1no( v3ng 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 (F( ;4t4 /1 hpnwbnl1pbvo b3pmwig. 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 directionx)rq0yp f:r7/ f 0mlb;bot (ystbsk+6 of the magnetic field at the midpoiyt ml7k;bf()pr6bt0r+ qsbosf0 /:xynt of the side of the triangle between wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a distance d apart, carry equal current:56u-j8hcs ntk pyol/ s I in the s o/j-cpnuy86h5:s tl kame direction. 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 solenpluwvr6) 8w *j*qc8m ioid has a total of 420 turns of wire and carries a current of 2.0 A. Calciww*v) 8*6lj8 qc urpmulate the field inside near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm **km(.p, ia k+fzjvq uin diameter is to produce a field of 0.385 T at its centqka+,*j z up* fk(im.ver. 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 cur(8 h/huco,ni: 08nr 4lb zl (zldltjxnei2e)*rent 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 :t e ih/e 8holdnc208z x4 ( *nlzjl(u)rbiln,force on this wire assuming the solenoid’s field points due east?    N

You have 1.0 kg of copper and want to make axd(/ waf.xgf ) lc(vq) 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, and s(w d fgx) ./cxqaf(v)lo on.

A toroid is a solenoid in the shape of a circle (Fig d,z2ps7+;o xuqpvd sv9vh,m3. Below). Use Ampère’s law along the circular path, shown dashed in (Fig. Belomdh ,2suv, v;zds37q p9+opv xw 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 tdi.fq*lb p1 1e4a -iaco show that the magnetic field between the conductors of a coaxial cable (Fig.ad4p1a-ebqii .l *1fc 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. m zw,8sawc57b0 cm on a side is placed with its face parallel to the magnetic field between the pole pieces of a bw5mcs,z 8a w7large 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 scalnl, e0 95x bmyv(ck)svo56yjbe 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 galvanometerg(*0yoj*bv 8t ox1f ap+dkec- weakens by 25% over the years, what current will give full-scale deflection if it or *fgey0txka+j8o b(dcp*1 - voiginally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%,skoztd m(p9d8c j(;k8 by what factor does the output torque change?kpdd(;(st8okjz9 m 8 c

Show that the magnetic dipole moment M of ae:pr / 3 0g6y++uxpya elgs3ahn electron orbiting the proton nucleus of a hydrogen atom is related to the orbital angular momentum L of the e3p +3/h:gsxy6+ep ge rauyl 0alectron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter and containing n9(i4 bqfh *vv *gf*rqline loops lies flat on the ground. The Earth’s magnetic field at this location h qqf4*bvi(rvf h**9 glas 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. qn0hz rvlp6s+)98 zy69ne vdkx ;cqw;What value of electric fiehz8q ; v rwp+qx69cde60 ; lnynkvs9z)ld could make their paths straight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germexfps0o2a1 8gceefb;k a.a84 anium atoms have radii of curvature equal to 21.0, 21.6, 21.9, 22.2, and 22.8 cm. The largest radius corresponds to an atomic mass of 76 u. What are the atomic masses of the other isoto8a ea kgopbf82 0a1f;.xcse4epes?

  Suppose the electric field between the electric plates in the ml9dxmq9 fj: c;)5edg mass spectrometer c qm 9djed9;:xm)5gflof (Fig. 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 mfq cal96me:g,onitor air pollutants. It is difficult, however, to separate molecules with nearly equal mass such as CO (28.01:mag 96le,cq f06 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 qh wg//b,r 3z;e*kq z+a*abfxions by a voltage V before they enter a magnetic field B. The ions are assumed tw* x;/ q,fh3qbekbgr a*azz/+o 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/, a+/xjgo frgivd61ngqb y7lgu5 .: i has 430 loops of wire per meter, and a 25-A current flows through the wire. If the permeabial6 fib7 1//xrg j,gi.duon:5+ gyqvg lity 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;irrgw3kdv: )ppg c1 x19lgo /.8 cm in diameter, and has 640 turns of wire. The magnetic field inside the solenoid is 2.2 ;cwkgrg)o3rl 9pvg :1p /1dixT 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)-0uk(o5 mk )jfl tqk5mzz5z n $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 upo. 2zgo2:p aqu /,cnfjsn entering a region of consg:/.un 2 ,opcjf2zs qatant magnetic field. What is the ratio of the radii of their circular paths?   

  The power cable for an electric trolley (Fig. Below) carries a )+l 7hfds)n f.c0r sbchorizontal currenbdrh0lcfcf+ 7s . ns))t of 330 A toward the east. The Earth’s magnetic field has a strength $5.0\times10^{-5}\mathrm{~T}$ and makes an angle of dip of 22$^{\circ}\,$ at this location. Calculate the magnitude and direction of the magnetic force on a 15-m length of this cable.    N the force on the wire is  ----待选择----southerlynortherly  and   $^{\circ}\,$ above the horizontal .

  Calculate the force on an airplane which ha33p 8ayf gvdw;s 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 9s0,a:upyqf jl4v rs /field points almost horizontally to the north a,v0uly:s9/afsrp4 q j nd has magnitude $B=0.50\times10^{-4}\mathrm{~T.}$ What should be the magnitude and direction for the velocity of an electron if its weight is to be exactly balanced by the magnetic force?    $ \times10^{-6 }\;m/s$  ----待选择----eastwest 

  A doubly charged helium atom, whose 6yjti(2/hsd lmass is $6.6\times10^{-27}\mathrm{~kg},$ is accelerated by a voltage of 2400 V.
(a) What will be its radius of curvature in a uniform 0.240-T field? $\approx$    m (retain three decimal places)
(b) What is its period of revolution?    $ \times10^{-7 }\;s$

  A sort of “projectile launcher” is shown in (Fig. Below). A lar,v 9uqhw h4d)ucl 9:pzhr6 *r)grki.lge current moves in a closed loop composed of fixed rails, a power supply, and a very light, almost frictionless bar touching the rails. A magnetic field is perpendicular to the plane of the circuit. If the bar has a length L = 22cm, a mass of 1.5 g, and is placed in a field o zq*ruh)dh)v 9prcwhu.k : gil6rl,94f 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 su365u. z cbbik-eaq mf.spended in air dm kca zbe.q6f5 b3i.u-ue 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 in the suspended wire.    A

Two stiff parallel wires a distance l aparvh-tl;. 77,/r mhsgh9yuoha wt in a horizontal plane act as rails to support a light metal rod of mass m (perpendicular to each rail), (Fig. Below). A magnetml,h/u 7ta ovywsr;gh.79 h -hic 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 deflection6q/ . d7)vwn8cntfi djckx*1u of the electron beam near the center of a TV screen due to the 7xvjdtn*8qf.d kw c)c i/1 6unEarth’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) istl n6 te3 //lqz vy8so-o;vkl) 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 eac/ko tnls);-qe /ltol6 zv 3v8yh 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, loca(klm d,f;a1 k59pq lrrted at the corners of a square of side l, carry k(95ld,fm1 pqk;r larequal 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 steering”;;w7f)d/5yuz5odg eail2uz vt 00o l)u 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 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 peluuvua 0w;0)o5d5y2iodgzl/f ) 7t zrotons traveling at $ 1.0\times10^{7 }\,m/s;$ be bent?    $^{\circ}\,$

  The magnetic field B at the center of a circular coil ofppa.u3s :l wu 64qwxb* wire carrying a current I (as 6w*sw :x3puauqbl .4p 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 the9nw1kvezc hyy m ::4yq.n 4r9-g) lwny magnetic field is about 1G($ 1\times10^{ 4}\;T$) Imagine a simple model in which the Earth’s field is produced by a single current loop around the equator. Roughly estimate the current this loop would carry. [Hint: Use the formula given in Problem 80.]    $ \times10^{ 9}\;A$

  You want to get an idea of the magnitude of magnem z*u38vp ,ayhtic 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 u my3zv p8a*h,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, tsp 5l2rtch8w9, 6:xc:mzorc3e r )zyqraveling to the right at aero9,sw5zy8c6mh tcq )3zrlrc ::x2p 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 spiraljvj(5ne:p/ rx path through a gas in a magnetic field of 0.010 T, perpendicular to the plane of the spiral, as shown in (Fig. Below). In two successive loops, at points P and Q, the radii are 10.0 mm and 8.5 mm, respectively. Calculate the change in the kinetic energy oejp j5rx:nv/(f 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 ma:sfhgp,2dg ) vgnetic field at its center. If the maximum cu,2) :hpv dsgfgrrent is 5.7 A, how many turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wwtd2wv, *+ u:zi n yfbj4d.2exires, each of diameter 0.50 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 suspension strings make an angle d2dz nj+:.fuw we y4*2x,tvbiof 3.0$^{\circ}\,$ with the vertical, what is the current in the wires?    A

  An electron enters a uniform mn; zxkfd(l ,s4agnetic 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$