A compass needle is not always balanced parallel to the 6u;+z4kz vm lm-q8yyvq/icsx*(fuq0Earth’s surface, but one end may dip downward. zmu6qzvyc(u*yim0 4k ;fv xlqs8q/ -+Explain.

Draw the magnetic field lin n5sloust,chrk20y14h 2 :emnes around a straight section of wire carrying a current horio1cuk ns e:,rlm h 04n252shytzontally to the left.

In what direction are the magnetic field lines surrounding a straight wire carryk ab7u t,pm ,imxg dua,30hc;.ing a cdt g u aup,m3i0;k7,hx.bac ,murrent that is moving directly away from you?

A horseshoe magnet is held vew +aym 7xybt1yjz sr8 8h8bm*qk6kf.,rtically with the north pole on the left and south p+ya8,68bjsk b qmf 8zx*1yth myk7r.wole on the right. A wire passing 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 e l+qtu;kv txxt2) /-kax49np metallic object, or only those made of iron? (Try it and see.) Why is this9npxv /)extkq;t -txk +l42au so?

Two iron bars attract each o y4.ulcr o36vbymcitcy35h /2 ther no matter which ends are placed close together. Are both magnets? Ex.ti5b c6h3m/rylc y o yuc34v2plain.

The magnetic field due to current in wires in your home91n8j0;gll uayf s+g k can affect a compass. Discuss the effect in terms of gyukl fjg91a; s8 +n0lcurrents, including if they are ac or dc.

If a negatively charged particle enters a region of unilih7;m( 5fbpfi78q li form magnetic field which is perpendicular to the particle’s velocity, will the kinetic energy of the particle increase, decrease, or stay the samem7plif5(h;q iil 8b7f? Explain your answer. (Neglect gravity and assume there is no electric field.)

In(Fig. Below), charged pa/cs eg9fb,eh ;rticles move in the vicinity of a current-carrying wire. For each charged particle, the arrow indicates the direction of motion of the particle, and the + or - indicates the sign of the charge. For each of the particles, indicate the direction of the magnetic force due to theeg9 ;eh,f/bcs magnetic field produced by the wire.

Three particles, a, b, and c, enter a magnetic field as shown i)o0et/drjmcx qsj+55 n Fig. 20–46. What can you say abo+c5)mqjt 0 /dj5ex rsout the charge on each particle?

A positively charged particle icm k3e/:rw(m pn a nonuniform magnetic field follows the trajectory sho /:mk3emr(wcp wn 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 attrac4( a t.lvrxhl/t a magnet? Can a magnet attract an iron rod? What must you consider to rt/h la4l.vx(answer these questions?

Explain why a strong magnet held near a CRT television screen (Section 17–10) xhxvod2).s3f1 udnj 2 causes the picture to beco21 djfxdsu) 2xvo. nh3me distorted. Also, explain why the picture sometimes goes completely black where the field is the strongest. [But don’t risk damage to your TV by trying this.][/But don’t risk damage to your TV by trying this.]

Suppose you have three iron rods, two of which are magnetized but the th:0piskb 5r h km-6c h1a0bwu/hf6juy.ird is not. How would you determine which two are the magnets without using any additio-0 mh /i kyfr jk65b:b0.1h a6uucphswnal objects?

Can you set a resting electron into motion with(trjfa ko*1g 4sn 0da/ a magnetic field? With an electric 0jnaa tg/1*sk ro(4d ffield? Explain.

A charged particle is moving in a circle under the influence of a ungob ow- o+g t1r4hxp00 nmvsa23(dwr7iform magnetic field. If an electric fie g41 ovmrw7hwx od3ga2n0rp+b o(-ts 0ld 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 , ch(thzw9 hw8.tq832dverqy 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 cau.3zc8hthtew(wv,8y hqq9rd 2sed to move. Do positive and negative ions feel a force in the same direction?

A beam of electrons is directed toward a hor0z(ae c z)1ygpg(p)i eizontal wire carrying a current from left to rightcz p((pye))ga1i zge0
(Fig. Below). In what direction is the beam deflected?

Describe electric an6y.lhtzs k,k8 lq93 xbd/or magnetic fields that surround a moving electric charge.3kzl8hlyxt,q6 ks b.9

A charged particle moves in a straight line through a particular regixa6i( jpm 76edon of space. Could there de(6x6ma7 pjibe a nonzero magnetic field in this region? If so, give two possible situations.

If a moving charged particle is deflected sideways in some region of space, can;efn.x h.phq -pnfil fvx00/z 8fm9: v we fxqxnlpie.pf hn80;zv-mv:./ 9h 0 ff conclude, for certain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space thj9j+, vufdyl9a tz2 7t6:0wbs b*khisere 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 wh20wwfia gwfi9i6nl96f fi ix;p*8x2 p ether moving electrons in a certain region of space are being deflected by an electric wx6lw6pf8xp2iiaiw9i*; 9 g0fn2 fif field or by a magnetic field (or by both)?

How can you make a compas0-fe xk( /o8sesrjx5s s without using iron or other ferromagnetic material?

Two long wires carrying equal currents I are r:* bmbof/e2*xxobek;:ufu hux(3) m at right angles to each other, but don’t quiteer;h f/bob fuem:o3x :x(x)m**bu2 k u touch. Describe the magnetic force one exerts on the other.

A horizontal current-ca ynzg55ecb /9mrrying wire, free to move in Earth’s gravitational field, is suspended directly above a second, parallel, me9/ gn5y z5cbcurrent-carrying wire.
(a) In what direction is the current in the lower wire?
(b) Can the upper wire be held in stable equilibrium due to the magnetic force of the lower wire? Explain.

Why will either pole of a magnet attract an unm 4zwsi, u3jrtr: ,z9wcak.5obagnetized piece of iron?

An unmagnetized nail will not attract 8)ilmaabp( lp n 67b7ksw9ak 1an unmagnetized paper clip. However, if one end of the nail is in contact with a magnet, the other end will attract a paper clip.( p)kmp 6sa bnbaw7 1ll8i97ka Explain.

Two ions have the same mass, but one is singly iouly2x sp( g,d/nized and the other is doubly i2up/lyxd,( g sonized. How will their positions on the film of a mass spectrometer (Fig. Below) differ?

What would be the effect on B inside a long solenoid i:kkf* xk-igr9f
(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 so:dg)mwjxp:5- d0yux:pf-md r 1 hvt8 dlenoid 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 swdx ry5mf-h-gwm8vdtd::ud )p01pjx : itch. 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 pe198vtz7uiy rs r meter of length on a straight wire carrying an 8.40-A current when perpendicular to a 0.90-T uniform magnetic field? v1r7syi8z9 ut    N/m
(b) What if the angle between the wire and field is 45.0$^{\circ}\,$?    N/m

  Calculate the magnitude83f f 4sn5ovz igskn0jwm f.*0 of the magnetic force on a 160-m length of straight wire stretched between two towers carrying a 150-A current. The Ea ngk8f5oz0 m4sj0*f3i.nfwv s rth’s magnetic field of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  Calculate the magnitude of thi1ny;i0gj p6b e magnetic force on a 160-m length of straight wire stretched between two towers carrying a 150-A current. The Earth’s min biyp;j10g6 agnetic 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 c*x4mdwvx)-ww/o zx+s s- c1z4.80 m long if the maximum force on it is 0.750 N when placed in a uniform 0.0800-T fieldo)s 1cxxw*m+wdvzxs /c wz4-- ?    A

  A 1.5-m length of wire cawi08 kzl 4lvr1rrying 4.5 A of current is oriented horizontally. At that point on the Earth’s surface, the dip angle of the Earth’s ma1vzwr48ll k0 ignetic 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 8llvgt*h (b . abs9r((a.75 A is a maximum of 1.28 N when placed between the pole faces of a magnet. If the pole faces are 55.5 cm in diameter, what is the 9 s.lh*(b(a rtvl(gbaapproximate strength of the magnetic field?    T

  The magnetic force per meter on a wire is measured t9 32lr /v s8lvh6solpxo be only 35% of its maximum possible value. Sketch the relationship of the wire and the field if the force had been a maximum,s8sl lrlp32ovx6v /9h 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 maximmc3w3 vhma fr2yx);f-um of $ 6.50\times10^{-2 }\;N$ when placed between the pole faces of a magnet. The current flows horizontally to the right and the magnetic field is vertical. The wire is observed to “jump” toward the observer when the current is turned on.
(a) What type of magnetic pole is the top pole face?  ----待选择----North PoleSouth pole 
(b) If the pole faces have a diameter of 10.0 cm, estimate the current in the wire if the field is 0.16 T. $\approx$   A(retain one decimal places)
(c) If the wire is tipped so that it makes an angle of 10.0° with the horizontal, what force will it now feel?    N

  Suppose a straight 1.00-mm-diameter copper wire could just “float” hor 09coie56mmqtsps ./g izontally in air because of the force due to the Earth’s magnei.mtcg p q95s 6o/ms0etic 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 chacye 5j; /ldml/rge $q\,=\,+2e$ 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 iy4rmmu/fkix6h/h :9 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 each diaq iaeuo 21plkhv8s .-4gram shown in (Fig. Below), wh4 s-1ov uiel8ahp2qk.ere $\vec{v}$ (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 directio8g.(x6 o nazuup qz4va- qxa.)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 verth6drmbw a4 .3z4ew1 ewically 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) prhx1wo hve*x3 7w z .9rx:ky8scoton enters a 0.20-T field, in a plane perpendicular to the field. What is the radius of x yreh:x 7 o1kz*3 wc.h98wvsxits path?    m

  An electron experiences the 3xzh5f2 ylx3b greatest 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 os0m ij *qn;zuw *pqc51zp8sm/ji8 kf0ka*7u df a beam of electrons that go undeflected when passing through perpendiculw*pk/8m* 0idu0q8f k5zuzcmjs a; pn7q j 1is*ar electric and magnetic fields of magnitude $8.8 \times10^{3 }\;V/m$ and $3.5 \times10^{-3 }\;T$, respectively? What is the radius of the electron orbit if the electric field is turned off? $F_E$    $ \times10^{6 }\;m/s$ $F_{max}$   $ \times10^{ -3}\;m$

  A doubly charged helium atomz8 imgx+bzl+.oi e ..t whose 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 charge q moving with constan f3. yi)0ehannt speed v to make one circular revolutieah3n)i y0n .fon in a uniform magnetic field $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge q moves in a circular path of radius r in a uniform mg27i +9czu5 zwnjw)- . yhwtfqagnetic field B. Show that its momentum is p = qBr zh2q9w-w fg.)tjuyzw +5in7c .

A particle of mass m and charge q moves in a circular path vqcn((0vv+qe 3wbm5c in a magnetic field B. Show t +v q0qcvcw(3b5e( vmnhat its kinetic energy is proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momentum of the particle inwpfgth da5 *,:ni(f :p 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 Earth’zo7 hca1;91l8hla s )wqjien 5s magnetic fwqn18l ;ho9sje )a la7 1i5czhield 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 the equator has magnituq *c9:goyh5rtk- s.iede $0.40\times10^{-4}\mathrm{~Т}$ 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 koxf dg+(4pv0uq1 ,w v$\nu=2.0\times10^5\mathrm{~m/s}$ 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 stalleg .usf lbh1;;v6d ksj 2r*fw(nd vehicle carries a 65-A current. How strong is the malfd;bk(us*s.n hv6frw g;2 1 jgnetic field 6.0 cm away from it? Compare to the Earth’s magnetic field. $B_{cable}$   $ \times10^{-4 }\;T$ the field of the cable is about    times that of the Earth.

  If an electric wire is allowed to produce a magnetic field no larger than t)gvt21h q.zz fzpb79mhat of the Eartz )gqbzp.9 vz2htmf17h $(0.55\times10^{-4}\mathrm{~Т})$ 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)k05h e byn1zn out of the page toward you. Indicateenzb)hyn51 0k , with appropriate arrows, the direction of $\vec{\mathbf{B}}$ at each of the points C, D, and E in the plane of the page.

  A vertical straight wire carrying an upward 24-Aw -y omviep 3qt: 7qjr:ls)rn:ri4d30 current exerts an attractive force3emrd3:t:7v:on 0iqy j rw -qrl4s)ip per 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 diecnf;jkj;ef 8 ;jrkgbi4+h4 n,01wqirection of the force between two parallel wires 35 m long and 6.0;qgjn0 w+hci,;rfej jki en484kfb1; 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 out 1.00 n0 -k)6 lfy t)wf xvqq.ze44rsm from an electric cable. What is the maximum allowable current in the cable i4etnf)6qqvsfzyl w-).r kx04 f the experiment is to be accurate to $\pm1.0\%?$    A

  A power line carries a current of 95 A 3/pzn8w1;hsoi*i nf xep iw65along the tops of 8.5-m-high poles. What is the magnitude of the magnetic field produced by this wire at the ground? How does this compare with the Earth’s field of about s8in 6i1p5fi/ x* ezw3pnohw;$\frac{1}{2}G$?    $ \times10^{-6 }\;T$ The field of the cable is about    % that of the Earth.(retain two decimal places)

  Two long thin parallel wires 13 vuwwm,;f7c j1.0 cm apart carry 25-A currents in the same direction. Determine the magnetic field at point P, 12.0 cm from one wire and 5.0 cm from the other(Figw,wcmu 7vj ;f1. Below).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18 cm due south from a stra.q 4 1gy1ns1eb+8q lfk,m0xc+tzuk ri ight vertical wire carrying a 35-0lucs. iq bqg,+km1nr fk8z14y1 t+xe A current downward. In what direction does the compass needle point at this location? Assume the horizontal component of the Earth’s field at this point is $0.45\times10^{-4}\mathrm{~T}$ and the magnetic declination is 0$^{\circ}\,$.    $^{\circ}\,$ N of W

  A long horizontal wire carriefef 3fxjb94ldk7 wz ,3s 22.0 A of current due north. What is the net magnetic field 20.0 cm due west of the wire if the w,bf3dzk ex9 f7l4f3jEarth’s field 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 p- 6xjethzd1 q /sn4u*a1c;mvrrotons passes a given point in space at a rate of $1.5\times10^9\mathrm{~protons/s~}.$ What magnetic field do they produce 2.0 m from the beam?    $ \times10^{ -17}\;T$

Determine the magnetic field midway between two long straight wires 2.0 cm apa7+odhztz8.i k)s uce o;4t .jjrt in terms of the current I in one when the other carries 15 A. Assume these cuutkochjz ..i) s+ dzt47eo;j 8rrents are
(a) in the same direction,
(b) in opposite directions.

  A long pair of wires conducts 25.0 A of dc curref;j z1g 9hl+eent to, and from, an instrument. If the insulated wires are of negligible diameter but are 2.8 mm aparej9; 1+elgzhft, 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 placoxgm /g4ly;6 b7mi1 shc(g)i hed in the plane of the two wires shown in (Fig. Below), parallel and jus m7l6) /g(yc;1hxh g4 bsiimgot to the right. If it carries 25.0 A upward, what force per meter of length does it exert on each of the other two wires? Assume it is 2.8 mm from the nearest wire, center to center.
$F_{near}$ =    $ \times10^{ -2}\;N/m$  ----待选择----attractrepel 
$F_{far}$ =    $ \times10^{ -2}\;N/m$  ----待选择----attractrepel 

  A compass needle points 23zyrulylp,6s2(8t7t t ls0 n(n$^{\circ}\,$ 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 l x 1+t+1br+pee+pu2hifn2v /lvqf 8z vies 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 and direction of the net fo/exr++u2f h e1v++b 2i lp1vnptv z8qfrce 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 b:(el2k sx u.;l m6ubtd)kydk bz /m11wire, made of 2.5-mm-diameter cdmz1k eybdkmu;6) x(/b bl:s1u2tk .lopper 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 are perpendicular to each otherwb kunx-qz12+vj2w o 9. At their closest, they are 20.0 cm apart (Fig. Below). What is the magnitude of tvbw jon1+qz2 wxu92-khe 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 apar :v qw/ksvm+rl/x q;3jt. Wire A carries 2.0 A current. Wire B’s current is 4.0jr3lw+vkvsq m:q //;x 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 anothe6p9: : frqamhlr. (Looking along them, they are at three corners of an equilateral triangle.) The current in each wire is 8.00 A, but its direction in wire M is opposite to that in a:p9rql6:fmh 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 magnituxvzk c)h4s5; ude and direction of the magnetic field at the midpoint of the side of the triangle between s cuk5hx);v4zwire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a diss fi4t.r9 xp*xtance d apart, carry equal currents I in the same dit9xr. isf4* pxrection. 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 so(j:h+n9 huaurx i9pf 5lenoid has a total of 420 turns of wire and carries a current of 2.0 A. Calculate the fij(rah:+ 9p9nufx5 iuheld inside near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoiqgi9f z5*0jqfd 1.25 cm in diameter is to produce a field of 0.385 T at its center.*j5 0f9 fgqqzi How much current should the solenoid carry if it has 975 turns of the wire?    A

  A 550-turn solenoid is 15 cm lbx2wmyf c,i(+ong. The current in it is 33 A. A 3.0-cm-long straigh 2yw,(f cbim+xt wire cuts through the center of the solenoid, along a diameter. This wire carries a 22-A current downward (and is connected by other wires that don’t concern us). What is the force on this wire assuming the solenoid’s field points due east?    N

You have 1.0 kg of colgla iez l1:(wz*, k p:v1ss6a0mlw). sm7p mypper and want 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, s.l*appzy0:z a7v :i1ge smw k l(1,lm 6lmssw)uch as solenoid diameter, length, and so on.

A toroid is a solenoid in the shape of a circle (Fig. Bel( i kr/x:rdp:cow). Use Ampère’s law along the circular path, shown dashed in (Fig. Below a), to determine that the magnetic fir:dx:rkic (/peld
(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 magnetid(8+gg7j7oh o4qzuu y c field between the conductors of a coaxial ca+7gjuqyo8g 7 h( 4duzoble (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 zkacp4*z29egdr; z a 7a side is placed with its face parallel to the magnetic field between the pole pieces of a large magnet. When 6.30 A flows in the coil, the torque on iaz;2 z k47daz*9rgep ct is $0.325\cdot N$. What is the magnetic field strength?    T

  A galvanometer needle def3u mqi-vz.yp9)5s rgk zgl6km 3pd r.+lects full 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, wh-vhb, y2r(f.xv2ppjfai+)8 uln :zg oat current wi:g.f j oun8v-( 22 yxbh+ai)ppvfl,z rll give full-scale deflection if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by what factor does the o u9;m02ftzr z/lck n8lutput torque changenu;/m f 082kzll9rztc?

Show that the magnetic dipole moment M of an electronly*)jkok o7/efztb9 h 5*6kka orbiting the proton nucleus of a hy)yl6atj/ kk9h oo kf*k 7zb5e*drogen atom is related to the orbital angular momentum L of the electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diamet1r tw9q 8n f1p /h8q7vmt2nm hmg1vn4uer and containing nine loops lies flat on the ground. The Earth’s magnetic field at this location has magnitumvhh7 4rt1n891fp8 q umvm12wtn g/q nde $5.50\times10^{-5}\mathrm{~Т}$ 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 cmbz u*7u3mkcp+ al 8;js in a 0.566-T magnetic field. What value of electmuc sk3b8l p7; a+jzu*ric field could make their paths straight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germaniumjpg/,1y8(o6 pkcy zad.ao, uz atoms have radii of curvature equal to 21.0, 21.6, 21.9, 22.2, and 22.8 cm. The largest radius corru/aj,gc .1y 8yd6ppzoa, (kz oesponds to an atomic mass of 76 u. What are the atomic masses of the other isotopes?

  Suppose the electric field between the electric plates in the mass 4gju,1m;7 5 kas +txqe*/u ,xwouhr4dp(ewr kspectrometer of (a ej4k(ruue4wmu1; r po+ q,tx*7,sxgk/5w dh 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 monwhdrzht zl7p56 jq/38itor air pollutants. It is difficult, however, to separate molecules with nearly equal mass such as CO (28.0106 ujwz p/zdl7hr 83hq6 5t) 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 a)btmvrp . o vt0f/ 8.zysy+mp9ccelerates ions by a voltage V before they enter a magnetic field B. The ions are assumed t8v.rvy9osbp/f+0y )tmp z .tm 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 has 430 loops of wire per meter, and a 25-A current flowse(wm u-)h* snj t - e*)mwhn(ujshrough the wire. 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 inrerthl;t7:if:h- )p *trns0 r diameter, and has 640 turns of wire. The magnetic field ins ns:e-0pl 7;i r*ftr:rht)htride the solenoid is 2.2 T when 48 A flows in the wire. What is the permeability $\mu$ at this high field strength?    $\times10^{-5}\mathrm{T}\bullet\mathrm{m/A}$

  Protons with momentuzr s, (.wrv5trr v9gc)m $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ are magnetically steered clockwise in a circular path 2.0 km in diameter at Fermi National Accelerator Laboratory in Illinois. Determine the magnitude and direction of the field in the magnets surrounding the beam pipe.    T

  A proton and an electron have the same kinetic energy upon enteringa4glg) i ee(v /gwe6zwgc21 6x a region of constgxc ge (a 6w21ge )zv/e6wlg4iant magnetic field. What is the ratio of the radii of their circular paths?   

  The power cable for an electric trolley (Fig. Below) carries a hom y9cq) pii )qw:ye/4orizontal current of 330c/q4)p)ywiome9 y: iq 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,tc 2la22c5zygysruj2 p;v o 0 has acquired a net charge of $1550\mu C$ and moves with a speed of 120 m/s perpendicular to the Earth’s magnetic field of $5.0\times10^{-5}\mathrm{~T}$.    $ \times10^{-6 }\;N$

  Near the equator, the Eart2sgd /.zt8msdh’s magnetic field points almost horizontally to the north and has 2t /m8z dsg.sdmagnitude $B=0.50\times10^{-4}\mathrm{~T.}$ 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 mas get j9uy 6;le7mb+ti2s 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 large current mo 70u0ecebtl9kii19jq5 fxc 6 pves 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 accelerate the bar from rest to 28m/s in a distance of 1.0 m? In what tf9e01p9c kjqbl7x0uci 6e5i direction must the magnetic field point?
   A
the magnetic field must be ----待选择----updown 

  In (Fig. Below) the top wirsfc32izdg 3d6sz+b -agw8 h :pe is 1.00-mm-diameter copper wire and is suspended in air due to thsbfg za8ih3s 2zp cdg 6-3:wd+e 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 apart in a horizontal ,/i 1 kn aqm(hxl4s (ne,kak5fplane act as rails to support a light metal rod of mass m (pera(nke/ lak4i(h5kmxn, ,qfs1 pendicular to each rail), (Fig. Below). A magnetic field $\vec{B}$, directed vertically upward (outward in the diagram), acts throughout. At t = 0, wires connected to the rails are connected to a constant current source and a current I begins to flow through the system. Determine the speed of the rod, which starts from rest at t = 0, as a function of time
(a) assuming no friction between the rod and the rails,
(b) if the coefficient of friction is $\mu_k$.
(c) Does the rod move east or west if the current through it heads north?

  Estimate the approximate maximum deflection of the el95t6 x5h 0b38so-qndgsr hib mectron beam near the center of a TV 6rhst5o08i- sb5bhxq g dm3n9 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 accelerat. xsc:1-v 4 pptffmr(ie 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 fiepvmfs 4x1 fc r:i(pt-.ld 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 w j i amaxe,30f:rp6q:bires, located at the corners of a square of side l, carry equal currenafr3: 0xmap,j: q6ieb ts $I_0$ 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 pdkpgho r ae: 22n,-0i p;5gckin particle accelerators for “beam steering”; that is, the magnetic fields can be used to change the beam’s direction without altering its speed (Fig. Below). Show how this works with a beam of protons. What happens to protons that are not moving with the speed that the magnetic field is designed for? If the field extends over a region-od;pkg22c, kphgi:e0 5p nra 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 wire cay+j8eykg qbu kl+x ,:*rrying a current I (as in Filgj ,e*u8kbx y+: yk+qg. 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 fi s,o* /k1l- kv/mw(kjma8rhu teld 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 magnetic fields produced by overhead gtx; j-kl1;9wsrsk0i: ux*px 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 atlg9 s*j;1x -sw;k 0iurxpk: xnd 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 op ,n0utt+kc-gw p2fm;f electrons, traveling to the right awp0t+ u-p, cngtm;2 fkt 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 0.010 a 7px;btv0bu(T, perpendicular to the plane of the spiral, as shown in (Fig. px0 tvb a;ub(7Below). 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 diameter, is to produce a 0.30-T magneti+osaey-s2 8q.dv q1 se2bppt1c field at its center. If the maxims2e8s-q. aq s 1pbtepvy1 +d2oum 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 meo (iam g-nykz 3wq2b(xh/ 27y9lujb :+dbj5 cm, 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 angldh92(/c 3-uk 7ljzbya :xm5 iebw+2go qbyj( ne of 3.0$^{\circ}\,$ with the vertical, what is the current in the wires?    A

  An electron enters a uxub1u-7h oy9rgpa3o5 m b/ 0fmrlu)+yniform 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$