A compass needle is not always balanced parallel to the (t2u jnutx 9m:Earth’s surface, but one end may dip downwardm2xtt( jn9:u u. Explain.

Draw the magnetic field lines around a straight secti.ukir gl uvj6 o4r/ s4.t(dj9won of wire carrying a currenur jojl.i6gk/vu tr .s(9dw44 t horizontally to the left.

In what direction are the magnetic (h6 3rmldqo h5-s o85nh,ruizfield lines surrounding a straight wire carrying a current that is moving directly away fl qruzo d85h-r hon63i(h,s5mrom you?

A horseshoe magnet is held vertically03+tun z3t-nfdf,kqz with the north pole on the left and south pole on the right. A wire z,z3 3-f 0k udt+qfnntpassing 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 thos52 olwi7+vym0r4 m7m) tqwh xle made of iron? (Try it and see.) Why mi7tvwxm7 q yo+l420 m)lwr 5his this so?

Two iron bars attrack:x6/ p7.k )b9gffhh/s qs ev3y )pw5 )jftazot each other no matter which ends are placed close together. Are both magnez/ )./)ek7jkxvwb6of3)s5: pqy9phstghffa ts? Explain.

The magnetic field due to a6o k.ffz3pc;current in wires in your home can affect a compass. Discuss the effect in terms of currp;cfo3z6 .fak ents, including if they are ac or dc.

If a negatively charged partic-+x4wo eh z-kile 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 assume there is no electric field+zwkex-h4-i o.)

In(Fig. Below), charged particles move in the vicinity of a current-carryin)k )r *xqhap/age5n *hnd6m2e g wire. For each charged particle, the arrow indicates the direction of motion of the particle, and the + or - indicates thae qx6nhmgp) *2h5 nae)dk/* re 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. 20–46. Whak*5/w,jxtq .sxcb em6+p ev2z t can you say about the charge on each partice2s/kt,vcmwx e*.b 6j5pxq+ zle?

A positively charged particle in a none6 9o8 u.k9nc z wobizzpa691vuniform magnetic field follows the trajectory shown 9 .op9b 9 z1vo6z8wcu zn6kiaein
(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 *4at* 81ipi epsu+smu an iron rod? What must you consider to answer these questiim *+us us4p1* 8aepitons?

Explain why a strong mb9p2 g11w-v lblv; nfyagnet held near a CRT television screen (Section 17–10) causes the picture to become distorted. Also, explain why thepn9 v2y 1 lwvl;b-f1bg picture sometimes goes completely black where the field is the strongest. [But don’t risk damage to your TV by trying this.][/But don’t risk damage to your TV by trying this.]

Suppose you have three iron rods, twqpa 2uah 4,j1wo of which are magnetized but the third is not. How would you determine which two are the magnets without using apau,24jh a1qw ny additional objects?

Can you set a resting electron into e,) jagxcf;aebjst ( b,b9qd )f04-ximotion with a magnetic field? With an electric field? Expqf4x(da9ee;),f agtb)j xj0 b- cis,blain.

A charged particle is moving in a circle under the 4.osck;kh:13rmdk wj4ayly 50 s(bmeinfluence of a uniform magnetic field. If an electric field that points in the same direction as the magnetic field is turned on, describe ky r. lk5:wke 3ah0sc om1m4bdyjs4(;the path the charged particle will take.

The force on a particle in ah 0*o 5n0 w- gt:zacq0kdl-x,nz*xea r 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 caused to move. Do positive and negative ions feel a force in the same z*xw-zrn0kco el00,a-a*d g5xqhtn : direction?

A beam of electrons is directed toward a n.+1ja ml7ii chorizontal wire carrying a current from left to . nciml +a7ji1right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields that surround a moving electric char,m4(ky- vf 2fe3f 2ljnobj;jjge.jjn 2 4;j klm,yf 23ej(o-bfvf

A charged particle moves in a straigh b8jn6,*0a 3umo;rsjl8k jv1so jbti (q8nm j;t line through a particular region of space. Could thejml ,6jov b8m( 3so;jtj8;0qni1u jbs*8a n krre be a nonzero magnetic field in this region? If so, give two possible situations.

If a moving charged particle is deflected sid/v5 qiw+ pee8 ;sd,ykpeways in some region of space, can we conclewy/5;qepk +ds,8 v ipude, for certain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there 2h6q *l hj1yytis 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 moving electrons invqaq fi4 5nz:. a certain region of space are being deflected by an electric field or by a magnetic field 5qz nq4:af .vi(or by both)?

How can you make a compass without using iron or other ferromagnetic matersod 8*g:2wk xcial?

Two long wires carrying equa08qkhav rkt,m yi ;;fy- jpm4.l currents I are at right angles to each other, but don’t quite touch. Describe the magnetic force onjahp0.fry84tkq y;k;,vi m-me exerts on the other.

A horizontal current-carrying wire, free to move in Earth’s gravitational3brrt)j lfz+. field, is suspended directly above a second, parallel, current-carrying wire.fz+ l b3rjt.r)
(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 9i k:jbj0a:m lattract an unmagnetized piece of iron?

An unmagnetized nail will not attract an unmagnetized paper arrgu hk:y-*u4y:65joxbbh .clip. However, if one end of the nail is in contact with a magnet, the other end will attract a paper clip. bh4* a jkgb6 :u:.uy5-yrrxhoExplain.

Two ions have the same mass, but one i.b8gx-faj c3 ws singly ionized and the other is doubly ionized. How will their positions on the film of a mass spect-c8a gb j3fx.wrometer (Fig. Below) differ?

What would be the effect on B inside a lobuck9 2l8y0 kgng 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 s yr; f9e i1azvp)2 z+in/ime)zimilar 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 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 stara )yvn9ez ei/ipimz+r1zf2 );ter doesn’t pass to the dashboard switch.

  (a) What is the magnitude of the force per meter of length on a(n.ngj 7if6isp 1 dp)1yiyen2 straight wire carrying an 8.40-A pf 6ijsy17eigdn(y .) in12pn 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 og d2irsu*bo 9qme u+5l+nqi-:f+shn)n a 160-m length of straight wire stretched between two towers carrying a 150-A current. The Earth’s magnetic fieldnq* rui++9 slu5hfbs 2m:go-di )e+qn of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  Calculate the magnitude of the magnetic forcep p;gn09 1/ni7dqtot o on a 160-m length of straight wire stretched between two towers carryinpq/0ond ;9 np71ogtt ig 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 theag0/ejr1)t*w2vo s oq maximum force on it is 0.750 ojaeo gwr*s/0)q tv12 N when placed in a uniform 0.0800-T field?    A

  A 1.5-m length of wire carrying 4qw :qlej/ w:9x.5 A of current is oriented horizontally. At that point on the Earth’s surfa /wjeqw q:l9:xce, the 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 maximum of 1.28 N when placed bett/4o w7kgl9q g ek1h0mween the pole faces q 0g9 w/lhkgok17te4m 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 be only 4xi(ggf *ogu81;zb5t q 1 tzyp35% of its maximum possible value. Sketch the relationship of the wire and the field if the force had been a maximum, and sketch the relationship as it actually is, calczg4 x5qif t pg;8yotg1(1zu*bulating the angle between the wire and the magnetic field.    $^{\circ}\,$

  The force on a wire is a maximu 3dunrbg0 xk-7,/vpqh 8 d2erom 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 “flaxuunlspw-4x0).-y 99 orq yaoat” horizontally in x 9)a0syowpy9a-q 4 lru-nx .uair because of the force due to the Earth’s magnetic field $\vec{B}$, which is horizontal, perpendicular to the wire, and of magnitude $5.0 \times10^{ -5}\;T$. What current would the wire carry?    A Does the answer seem feasible? Explain briefly.

  Alpha particles of chargt i:we ;od1bhsj 4:hl;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 electns,wpw0b9hvlv+s -v2m0 iv v1 ron 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 ab*(s sf0jha f4 negative charge for each diagram shown in (Fig. Bahfjf(4 b0*ss elow), 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 directioup832tal-u dt n 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 mpkn8/a n 7opdmz/*b s p9e+b:r5 (dwevertically 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 r ,ae43e+abu lenters a 0.20-T field, in a plane perpendicular to the fie3, rle4 uba+eald. What is the radius of its path?    m

  An electron experiences the g 1.)8oq6 c hzqm;bdqylreatest force as it travels $2.9 \times10^{6 }\;m/s$ in a magnetic field when it is moving northward. The force is upward and of magnitude $7.2 \times10^{-13 }\;N$. What are the magnitude and direction of the magnetic field?    T ----待选择----EastWest 

  What is the velocity of a beam of electrons that go undeflec/1 3q;; t;4 qieuob w+wezdllcted when passing through perpendicular electric and magnetic fields of mage+wtwe3u; q1 /d; 4;cozi bqllnitude $8.8 \times10^{3 }\;V/m$ 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 whzuca,4 4 mumq7nt18vgq-vc8 fose mass is $6.6 \times10^{-27 }\;kg$ is accelerated by a voltage of 2100 V.
(a) What will be its radius of curvature if it moves in a plane perpendicular to a uniform 0.340-T field?    m
(b) What is its period of revolution?    $ \times10^{ -7}\;s$

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

Show that the time T required for a particle of chtged*hui+h5kq ,im3vyc ) 8wi)t 3d4iarge q moving with constant speed hd) g3dmv*uit+kwi8,i3ic e)q t5y h4v 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 moves in a circulkxxi, .90ua3ze d:yzk ar path of radius r in a uniform magnetic fiea. x:3,xzd k0kyzeu9 ild B. Show that its momentum is p = qBr .

A particle of mass m and chargr. pb8 jsm9ko*-rzd- re q moves in a circular path in a magnetic field B. Show that its kine9 rjr8 r p.k-zs*do-bmtic energy is proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momentum of the pdba13lx v;o ;f4iq31m3s dendarticle 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 to the E/h.7ddjx) wstarth’s magneticd .7x/d) tswjh 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 ft 1thzw5sic zc0gk lq5n6 0m*s(/i9fe ield 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 speed i do9,eqngy9 ($\nu=2.0\times10^5\mathrm{~m/s}$ 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 veh+ s2zqg-kqjxa 48th(;rx fa8om.gjn4 icle carries a 65-A current. How strong is the magnetic field 6.0 cm away from it? Compare to the Eanatfk2-gm4(xqj4 sxj+ha 8z grq8 o;.rth’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 lart 4c fd-:5kvs 2vfvxe-ger than that of the Ear5xvf -kf:vc 4v es2-dtth $(0.55\times10^{-4}\mathrm{~Т})$ at a distance of 25 cm, what is the maximum current the wire can carry?    A

In (Fig. Below), a lot zdnnha 5t -7x:fd57ye ;.rdvng straight wire carries current I out of the page toward you. Indicate, with appropriate arrows, the :t77x5.hdt ven-zfydrna d5; direction of $\vec{\mathbf{B}}$ at each of the points C, D, and E in the plane of the page.

  A vertical straight wire a rpwum tt65hd06m ;4rcarrying an upward 24-A current exerts an attractive force per unit lhw45drrttmm;6 0 a u6pength 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 magnit3oixdf uuihj ml12e 95jvv7jbi+55u 2ude and direction of the force between two parallel wires 35 m long and 6.0 cm apart, each carrim i2 19f5oih352x u5jju ve7bldv+u jying 25 A in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic field is erd k5fs)hdaf53q r2 j38j*pa being carried out 1.00 m from an electric cable. What is the maximum allowable current in the cable i5q3h3d)ake5f2r r aj 8p*jfsdf the experiment is to be accurate to $\pm1.0\%?$    A

  A power line carries a current of 95 A acd. 2doipvso063a2x clong the tops of 8.5-m-high poles. What is the magnitude of the magnetic field produced by this wire at the groundcpdo2csv6d a0x3i o2. ? 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 wf66.im u(btekor 5-dg9 0fsc 25-A currents in the same direction. Determine the magnetic field at point P, 12.0 6-gsk0(twcf eidm .b 56f 9roucm from one wire and 5.0 cm from the other(Fig. Below).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18acv6sb hs -h* cd s0:j)5mwdh) cm due south from a straight vertical wire carrying a 35-A current downward. In what direction does the compass needle point at this location? Assume the horizontal component ow sdh:d)hhcm-)vjb5a c0*6 ssf 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 mapy,h f/c5yzk 5d . :l5hcv mns4r49lrmgnetic field 20.0 cm due west of the wire if the Earth’s field there poi9 4nykvrhlsm,/h r c5lf m5 45p.cdyz:nts north but downward, 37$^{\circ}\,$ below the horizontal, and has magnitude $5.0\times10^{-5}\mathrm{~Т}?$
   $ \times10^{-5 }\;T$
$\theta$ =    $^{\circ}\,$ below the horizontal

  A straight stream of protons passes a given point in space at a ra3 s31rajws7 8fk.wjxq te of $1.5\times10^9\mathrm{~protons/s~}.$ What magnetic field do they produce 2.0 m from the beam?    $ \times10^{ -17}\;T$

Determine the magnetic field midway between two long straight g(lc myyjl 8s6o34mw hx:pne:)f:lc0e skm,1wires 2.0 cm apart in terms of the current I in one when el s8:1nh:x(mw mfo6lmce3 ,)ls gy04 cypk:jthe other carries 15 A. Assume these currents are
(a) in the same direction,
(b) in opposite directions.

  A long pair of wires conducts 25.0 A of dc current to, and from, an instr4m *a ax*k dtuvx(b902 csmu hbh6h2x(ument. If the insulated wires ar 4mv*(0k9 htuax2xb *sbadx 6h(2uc mhe 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)? 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 (Fig. Below)s57 ydyv4na5 4. bv8zawkfh+n, parallel and just to the right. If it carries 25.0 A upward, whd ybw4vvafz +ay5k 4785snn.hat force per meter of length does it exert on each of the other two wires? Assume it is 2.8 mm from the nearest wire, center to center.
$F_{near}$ =    $ \times10^{ -2}\;N/m$  ----待选择----attractrepel 
$F_{far}$ =    $ \times10^{ -2}\;N/m$  ----待选择----attractrepel 

  A compass needle pointb;j9(*js( wutgh k2 zxs 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 wir.nlprod1:qy0 e lies 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 magq :np1od0r yl.nitude 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, made of 2.5-mm v p:zkj5 w24y/,bq,pzkdut,d-diameter copper wire and parallel to the first, is kept in suspension magnetically 15 cm below (Fig. Bel:jy,,25vu/kz wbdkppqt,4 zdow).
(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 th- 6 qxkzn8v-xx/0 yrxhat they are perpendicular to each other. At their closest, they are 20.0 cm apart (Fig. Below). What iv06--nx/8rky xzx qxhs 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 aparce+ mo)atx (o0ckwi8:t. Wire A carries 2.0 A current. Wire B’swo+0i o xa8et(c ):mkc 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 are 3.8 cm from one another. (Looking aybuu3 zu4g f 6 ;suvz83nkd3d/-3o cgklong them, they are at three corners of an equilateral triangle.) The current in each wire is 8.00 A, but its direction in wire M is opposite to that in wires N and P (Fig. Below). Determine the magnetic force per unit length on each wire d3 d8kbuz o3zfkduygvgn suc/-;34 63uue 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 magnit0 b;rr3bkn2jiude and direction of the magnetic field at the midpoint of the side of the triangle between wire M and n 3r kjr0b;ib2wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a distance d apart, carry equal currenth qqzn(8hsfz t ;dbdh 3+1p4-nik,x4ns I in the same direction. One dn4n+8dib sx-3znp4h,hqz;t ( 1fh qk 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 total of 420 turns of wire a6 r jr5r7/itrd bk9/bmm/ 1hncnd carries a current of 2.0 A. Chrb7j9rkr/ c m1 mdir 5t/b/6nalculate the field inside near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameter is to produce a field of *4go j(fcic0hfddp**0.385 T at its center. Ho(j fdd4g*ihcpc 0o f**w much current should the solenoid carry if it has 975 turns of the wire?    A

  A 550-turn solenoid is 15 cm long. The8lw1jqbu+. br current in it is 33 A. A 3.0-cm-long straight wire cuts through the center of the solenoid, along a diameter. This wire carries a 22-A current downward (anwlr b1 .u8+bjqd is connected by other wires that don’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 producesyu3wpst :+b)4 f ifyl4 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 diametb 3iy): 4ptf4fsl +wyuer, length, and so on.

A toroid is a solenoid in the shape of a cir6kyfxukw yo+x /. m- v0nt3(tycle (Fig. Below). Use Ampère’s law along the circular path, shown dashed in (Fig. Below a), to determine that the magy+6 t(oxywxf0y-t/kk u3.n v mnetic 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 magn ar2 fl4xaz3;j xp-4uwetic field between the conductors of a coauxwa4f jx42a- ;lpr3z xial 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 j k6tph l2ds t)o:* sddf0gntmr4n)k*c ,81et placed with its face parallel to the magnetic field d:rk 180n dthsofp))t njt**e tsld24, mcg6kbetween 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 s(6; vc3 rv 90(bchh yby.gzonfull scale for a $53.0 -\mu A$ current. What current will give full-scale deflection if the magnetic field weakens to 0.860 of its original value?    $\mu A$

  If the restoring spring of a galvanometer weakens by 25% over the years,5 abpea/kbykxz4 2j .3 what current will give full-scale deflection if it originbak2 3 za/4p xby5ejk.ally required $36-\mu A$ ?    $\mu A$

If the current to a motoy1x3:pjvg29jb e 3* k7pbdqd pr drops by 12%, by what factor does the output torque changevbjk3bg7:3q pd p*ej129xy pd?

Show that the magnetic dipole moment M of an electron gq50b sdo;r8ysgrx 76 orbiting the proton nucleus of a hydrogen atom is related to the orbital angular do5ggry0r8 qsb7 6 xs;momentum L of the electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter and containing nine loops liesfdd 5prtlc(9pxj36p0 flat on the ground. The Earth’s magnetic field at this loca0df 6x (rcpd3pj59pl ttion 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+ry irjmw r;s ./we;k, in a 0.566-T magnetic field. What valr .my;r/i+wrejs;w, kue of electric field could make their paths straight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atoms have radii of curvature equas h c6+8vaw3c 20rgd(jh0k (gow.rxr7opbm5vl 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 ocrrxh v2 50( 0cgo (op3768bdwwrakvj.s+hgmf the other isotopes?

  Suppose the electric field between the electric plates in1jveaaqvq)*--0pee 4p8ka ji the mass spectrometer of (Fig. Belowje q8apaeev04)p iqa*k--v 1j ) 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 .xe nkqk-/g6w),dpggto monitor air pollutants. It is difficult, however, to sep.kk /) g-6,xgwqe pgndarate molecules with nearly equal 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 befo.0j fsm(26wxm h y3qvire they enter a magnetic field B. The ions are assumed to start from rest. Show that this3hx.v20 (mmy6qw fje 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 solenoidm+ug(g d,7pxa has 430 loops of wire per meter, and a 25-A current flows through the wire. If the permeabili7md pggau(, +xty of the iron is $3000\mu_0$ what is the total field B inside the solenoid?    T

  An iron-core solenoid is 38 l85 7ml -ss92cxztstyek9 ot.xh* c2t cm long and 1.8 cm in diameter, and has 640 turns of wire. The magnetic field inside the solenoid is 2.2 T when 48 A flo8htmzk*cl sx2 y o.9-2t ctle9xts57sws in the wire. What is the permeability $\mu$ at this high field strength?    $\times10^{-5}\mathrm{T}\bullet\mathrm{m/A}$

  Protons with momentumhc* y ,7l0ktwt-dh f)w;xs9qr $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 hau)n n:mk v)f(5p rgwf8ve the same kinetic energy upon entering a region of ffg8mr5 p(n)vuwn) :kconstant magnetic field. What is the ratio of the radii of their circular paths?   

  The power cable for an electric trf*md/j g;mm b5olley (Fig. Below) carries a horizontal current of 330 A toward the east. The Earfb5d m j*mm/;gth’s magnetic field has a strength $5.0\times10^{-5}\mathrm{~T}$ and makes an angle of dip of 22$^{\circ}\,$ at this location. Calculate the magnitude and direction of the magnetic force on a 15-m length of this cable.    N the force on the wire is  ----待选择----southerlynortherly  and   $^{\circ}\,$ above the horizontal .

  Calculate the force on an airplane which has acquired a net chh -,dmr7wqf2yb sp.4 o ul 9:/nysiyb1arge 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 horizoj0;h jrf6hv a(bj22j tntally to the north and h2ahvjrfb jtj2;0( 6 hjas 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, wv9 cj9qbdux9m;/s j2k)h2dmf hose 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” 6 q5la/fdree/ 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 length L = 22cm, a mass of 1.5 g, and is placed in a field of 1.7 T, what constant current flow is needed to acceleqedela/6r f 5/rate 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 w(0 s+/szg;5zb soymm pire and is suspended in air due to the two magnetic forces from the bottom two wires. The current flow through the two botto 0m m zssz/p5b+;(ysogm wires is 95 A in each. Calculate the required current flow in the suspended wire.    A

Two stiff parallel wires a distan p7uq6kwy/, 3qm c0b daj+pnftch6v43ce l apart in a horizontal plane act as rails to support a light metal rod of mass m (perpendicular to each rail), (Fig. Below). Apamq 7c36/nfcu dq k6t,+h jbw 3vy40p 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 (xuh(ey* zs2 nmaximum deflection of the electron beam near the center of a TV screen due to tze((y us2nx* hhe 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 usea vwtb+i*7x n,w )f*hrd 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 half-cycle, owing to an ac volta+ fat*irb7x , vn)wh*wge $V=V_0\sin2\pi ft,$ 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 paralle4lwmof6 (6yx t2b vn*1b 3xzwil wires, located at the corners of a square of side l, carry equal cu6z416l nxmb23x(bf*v yiw t owrrents $I_0$ 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 acce hwr3c0l .eo)ylerators 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 with the speed that the magnetic field is designed for? If the field extends over a region 5.0 cm wide and has 0 rheo3.)lcyw 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 (qxsv/kn:-v- 3ds, qv jwsn4z the center of a circular coil of wire carrying a current I (as in Fi:3-svjq z/ d qxw-s4snn(vk,vg. 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 1G;s9gez1pccqbcn)) h 7($ 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 produced j )9vxuns4hyfr0o/gyvb 7 c q;qpyi0):s,7 g yby overhead power lines. You estimate that the two wires are each about 30 m above the ground and are about 3 m apart. The local power company tells you that the lines operate at 10 kV and provide a maximum of 40 MW to the local area. Estimate the maximum magnetic field you might experience walking under these power lines, and compn,py/i:jcsqr vu ys7))gy hfx;qyo00 9b 4v7gare 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 makeo3/adxor1 wk2k,vb f + a beam of electrons, traveling to the right at a speed ofx,rdfk k3v+ o/wb1o 2a $4.8 \times10^{ 6}\;m/s$ 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 gaz-k0jozbi p0u /8cv psh /)mh7s in a magnetic field of 0.010 T, perpendicular to the plane of the spiral, as shown in (Figpuim zh80-vo z /hksb0pc /7)j. 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 of the proton as it travels from P to Q.    $ \times10^{-20 }\;J$

  A 32-cm-long solenoid, 1.8 cm in di1*z biscsf+ f2ameter, is to produce a 0.30-T magnetic field at its center. If the maximum current is 5.7 A, how many tsfcsz1 +2*fib urns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, each of diameter 0.50 mm, carryop *9a4q xaa:u the same current but in opposite directions. They are aapu9*4oaq x: suspended by 0.50-m-long strings as shown in (Fig. Below). If the suspension strings make an angle of 3.0$^{\circ}\,$ with the vertical, what is the current in the wires?    A

  An electron enters a unifof*w yit75zn 7t p4n*zudx:2i zrm magnetic field B = 0.23 T at a 45$^{\circ}\,$ angle to $\vec{B}$. Determine the radius r and pitch p (distance between loops) of the electron’s helical path assuming its speed is $3.0 \times10^{6 }\;m/s$. See (Fig. Below).
r $\approx$    $ \times10^{-5 }\;m$ (retain one decimal places)
p =    $ \times10^{-4 }\;m$