A compass needle is not always balanced parallel to tosenm- .+fnmz*gb 2f oa9j g6.he Earth’s surface, but one end may dip downward. Explain.majfnsogomfg n +-ez* .6 .b92

Draw the magnetic field o*+6hz54 tf.o vy)vpf aksp1a lines around a straight section of wire carrying a current horizontally*t.1 o p afyhspaofv6 4zv5k+) to the left.

In what direction are the magnetic field lines surrounding a straight wire j m4,k ws sp2z7-w-hjvcarrying a current that is moving directly skpjjw 7 2,4mhwv--s zaway from you?

A horseshoe magnet is held vertically with thj ,:vim86yzm1; 9mjw + e9yvrmlczyd*e north pole on the left and south pole on the right. A wire passing between the poles, equidistant from them, carries a current directly away from you. In what directionmmm ym+jdijvye8rc z:,99yw 6z1* l;v is the force on the wire?

Will a magnet attract any mety4 qaz*yk.:n3rswr .dxf8lg*allic object, or only those made of iron? (Try it an* dy. kys.:rgxla4n8wz *rq3 fd see.) Why is this so?

Two iron bars attract each other no matter which m4/sj9 xcy+wh;c7c cb1ph8yf ends are placed close together. Are bothwmjcbx s1 +9 p ;4fyhhc87cc/y magnets? Explain.

The magnetic field due to current in wirerdng*vnwp* ) /s in your home can affect a compass. Discuss the effect i* ng*rv/p)w dnn terms of currents, including if they are ac or dc.

If a negatively charged particle enters a region of unifo;m pvf9f9-cyncvz2bk) rof 0- rm 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 fipozvf)09rvmbcc- kn2 -f;9 fyeld.)

In(Fig. Below), charged particles move in the v rztw4;:b0(oouk 5f bricinity of a current-carrying wire. For each charged particle, the arrow indicates the direction of motion of the particle, and the + or - indicates the sign of the charge. For each of the particles, indicate the direction of the magnetic force due to the mw f(4t5o:r;z0 urkobb agnetic field produced by the wire.

Three particles, a, b, and c, enter a oq-8dfrqo9 n6 magnetic field as shown in Fig. 20–46. What can you say about the charge on 6orq8no fqd9-each particle?

A positively charged particle in a nonu fo-j9nj1tl1l:w;xa zniform magnetic field follows the trajectory shown inn;1l 9tfx-la w1joj:z
(Fig. Below). Indicate the direction of the magnetic field everywhere in space, assuming the path is always in the plane of the page, and indicate the relative magnitudes of the field in each region.

Can an iron rod attract a magnet? Can a magnet attract an iron r.q0 lpea2nz ktg5.vb6od? What must you consider .6v nag. l52t0 ezqbkpto answer these questions?

Explain why a strong mar66f j0ase1nz gnet held near a CRT television screen (Section 17–10) causes the picture to become distorted. Also, explainz0r 1fesj 6n6a 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 threepv*( ukc: 7t8vimw3 ne iron rods, two of which are magnetized but the third is not. How would you determine which two are the magnets without using ai( u nw:kc83pm7ev*tv ny additional objects?

Can you set a resting electroz 2; /wrglwe w//tzvr3n into motion with a magnetic field? With an electrg tw;wl2/ zz/ewv3r/ric field? Explain.

A charged particle is moving in a circle under the influence of a (85txe/0 +ysgtf ns jbb4pkk6uniform magnetic field. If an electric gtbsbn+jx54ky68/f ktpes (0 field that points in the same direction as the magnetic field is turned on, describe the path the charged particle will take.

The force on a particle in a magnetic field is the idea behind mae 3m7iu; w8aelectromagnetic pumping. It is used to pump metallic fluidea aw87 ;umim3s (such as sodium) and to pump blood in artificial heart machines. The basic design is shown in(Fig. Below). An electric field is applied perpendicular to a blood vessel and to a magnetic field. Explain how ions are caused to move. Do positive and negative ions feel a force in the same direction?

A beam of electrons is directed toward a horizontal wi6ud jqao 8 a0g9jugr-lu0vk20bct7 k9 re carrying a current from left to right od gka 0 89 u6c 2ub0-jtgrqvlau0k79j
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or mplol2t mc9+dn)*u;lnagnetic fields that surround a moving electric charge.o* );+c9mlndnu 2t llp

A charged particle moves in a straight line thro9mxtyd;kh5 0qia( f ksk).6hough a particular region of space. Could there be a nonzero magnetic field in this region? If so, give two possible situ)9 mh.ay65iq kx(kho ;ftdk0sations.

If a moving charged particle is deflected sideways in somelnsk.8 8jtw+q jwfo /6 region of space, can we con kw +swl8t/68jfn. joqclude, for certain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is a uniform magnetic fieldq9iji28) krn c $\vec{B}$. 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 siu*,wg) abrd :h 2)qsmoving electrons in a certain region of space are being deflected by an electric field or by a magneti,a i s* 2q:ug)dwh)srbc field (or by both)?

How can you make a compass without using iron or other ferromagnetcaixr/ 2fvj3 8ic material?

Two long wires carrying equal currentsfinza ni9( 9n) I are at right angles to each other, but don’t quite touch. Describe the magnetic force one exer)9ann z f(9iints on the other.

A horizontal current-carrying w pku 3w+d9 a m1;tqx.q ugpgaz(n8-+nqire, free to move in Earth’s gravitational field, is suspended directly abxgq8umd;(+t -q 1ngz+ p9kpnu.qa aw3ove a second, parallel, current-carrying wire.
(a) In what direction is the current in the lower wire?
(b) Can the upper wire be held in stable equilibrium due to the magnetic force of the lower wire? Explain.

Why will either pole of a magnet attract an ;.apejmq. g6zunmagnetized piece of iron?

An unmagnetized nail will not attract an unmagnetized paper clip. Howr bsudxg4a sfb*raq5 v 2p2.58ever, if one end of the nail is in contact with a mag8rarp.2fs2 b s5da* q54vuxg bnet, the other end will attract a paper clip. Explain.

Two ions have the same mass, but one is singly iq7k922qvd r *c *nbevcv tsktkf9+m*3onized and the other is doubly ionized. How wil9k7m93*2vvs +td v*bkrckt fenq*2cq l their positions on the film of a mass spectrometer (Fig. Below) differ?

What would be the effect on B inside a lonq a-euet(ki/zlv0 -l** jxuu8g 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 ;2ihe25cgnxm pj5t ( rw6)fuvsimilar 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 eg hnr 5)i;x jcw 2562(etfvumpxample, 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 theeg 0ny3 ef ,6g.b5wahk3zm)qk force per meter of length on a straight wire carrying an 8.40-A current whefb0e kqk3hgawz e6yg)35n. m,n 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 magne,7wxgprb-v(i tic force on a 160-m length of straight wire stretbrv (,7xgwi p-ched 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 16k m0(+z q l5zj8-itrpua-sf+u 0-m length of straight wire strer+tz z 5akl+-0qsf8pm -iu( ujtched 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 force on it is z7z,ehuw .kl.0.750 N when placed in a uniform ezhk lzu,7. .w0.0800-T field?    A

  A 1.5-m length of wire carrying 4.5 A of current is oriented horizontally. At tx(4; d ku,yehthat point t x h4e;u(kyd,on the Earth’s surface, 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 be0y gz2y ywrs*el-6ry+p r:nm3tween the pole faces of a magnet. If the pole faces are 55.5 cm in diameter, what is the approximmr*yln+pw3 rs e :yz2yr-y0g 6ate strength of the magnetic field?    T

  The magnetic force per meter on a wire is measured to be only2m7c r4esypm(l)c8 th 35% 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, calculating the angle between the wire and the magnetic fyc ecm7 4m82pt )lhsr(ield.    $^{\circ}\,$

  The force on a wire is a maximum ofbh9 k6;n9r otuj2m )zv $ 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” horizontar7g2 tzj z(wg ao*q,j0lly in air because of the force due to the Earth’wr7gz ojj ,*aqz(0g2ts magnetic field $\vec{B}$, which is horizontal, perpendicular to the wire, and of magnitude $5.0 \times10^{ -5}\;T$. What current would the wire carry?    A Does the answer seem feasible? Explain briefly.

  Alpha particles of charge noi)jrw;e k y(h9,y :araako- t9n 70s$q\,=\,+2e$ 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 directie qbp9d2gt 6cwb.kk7(on 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 ofh(o cxq4 .2;vq1+b-m q(omhh9ycf7izbf3itb the force on a negative charge for each diagram shown in (hi v4c+hm- bom(.tib; h1 ffy7qb2cxq (zo39q Fig. Below), where $\vec{v}$ (green) is the velocity of the charge and $\vec{B}$ (blue) is the direction of the magnetic field. ($\otimes $ means the vector points inward. $\ odot $ means it points outward, toward you.)

Determine the direct lh3j9gggxziq9k;g7 6ion 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 verticaarf(;av+w zofc0gnm9 d(n/h 8lly 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) protonhlt5* 5p pbsq-;as7en enters a 0.20-T field, in a plane perpendicular to the field. What isae7h;b p* pq-5nsts5l the radius of its path?    m

  An electron experiences the greatest force a. bevhg- hwa z1;f7.mls 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 thatoqi - p3hio/u, go undeflected when passing throuopoui,hq -3 /igh perpendicular 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 atom whose micy4; ou f1q+kass 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 T7gnryn(,5lt yed *epm-h,eo36y 7 lg h required for a particle of charge q moving with constant speed v to m l ,n,6g(rnel3d7-gey5y7hoy * petmhake 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 circular path of ryp. vb;he. ;cnadius r in a uniform magnetic fiepy.. v enhb;c;ld B. Show that its momentum is p = qBr .

A particle of mass m and charge q moves ikh-py);yf6ql spg: i (n a circular path in a magnetic field B. Show that its kinetic energy is pro i)6s;kyh:lyp(gpq-f portional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momentum of the particle if s2s ota+ .zwg+qxk6 b4ke)k)n 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 perpendiculdtziqaq :i0(ou ,aa8a0zl9 ozi8+8x yar to the Earth’s magnetic field lauiiydaz8a9aoit(z,0z8o0q x8+q: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 fiel i3nd b,*p) 4b(nygrcbl:-yp ld 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 speesk5lx 71 e 3.mlbd:8)i wnmupfd $\nu=2.0\times10^5\mathrm{~m/s}$ 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 stalh(0m -yy)hdouo/qr o+led vehicle carries a 65-A current. How strong is the magnetic field 6.0 cm away from it? Co /yydhqh-o+uorm (0 o)mpare 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 that o vc.b+u.7sf vdu(r/k ab:j 8nrf t/bka ujuv8 c:+vs.db7 f(.rnrhe Earth $(0.55\times10^{-4}\mathrm{~Т})$ at a distance of 25 cm, what is the maximum current the wire can carry?    A

In (Fig. Below), a long straight wire carries current Ics0 2o.mssz,2(ppa q5ju blt+ out of the page toward you. Indicate, with appropriate arrows, theb+s2q p2s .sm0c5aluo (, jtzp 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-A current exerts an attractive fo8 /p5/vi 9pskdm( ,9pnwpi(m 0v.uziblv rem)rce per uni9 (vm.5likbd0/i wpvmmpun9s ),rep( v 8zp i/t 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 ae yz2-yhe;hu0 dn7p5i nd direction of the force between two parallel wires 35 m long and 6.0 cm apart, each carrying 25 A i5deh z ye-pn 02y7;uihn the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic field is being e a.zem .00iag3 t3zpud,6 m9j zej0srcarried out 1.00 m from an electric cable. What is the maximum allowable je upij603 .de,rmaz g9.s00zt e3mzacurrent in the cable if the experiment is to be accurate to $\pm1.0\%?$    A

  A power line carries a current of 95 A along6vffcag29oov . f 7hc; the tops of 8.5-m-high poles. What is the magnitude of the magnetic field produced by this wire at the ground? How does6a fcvhf. ooc9 ;2vf7g 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 xpad+7yr+:v 8b8x knd13.0 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(Fi8 nxvk:+ayxb+7d8rpd g. Below).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18 cm due south from a straign(uab r1b*2 skht vertical wire carrying a b*busrkn(1 2a35-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 carries 22.0 A of current due nortm 95wicz:j:2ow l/u gdg snl*/h. What is the net magnetic field 20.0 cm due west of the wire if the Earth’s fi zj9ducl w*omg2lgw: 5: is//neld 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 ofv c t2; olx8;wllt rnzx;fm +6ht(,j/z protons 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 g1o1lgwy;;picm apart in terms of the current I in one when the other carpl; ;gioy11wg ries 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, +2.t03of,fuzevr a+d)m zj zdpgij- 5and from, an instrument. If the insulated wires are of negligible diameter but are 2.8 mm apart, what is the magnetic field 10.00 cm from their midpoint, in their plane (Fig. Below)? Compare to the magnetic field2-d je 5+zo ig f.za3mv,+r)tpjdfz0u 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 thea.k fqio+ s6:w plane of the two wires shown in (Fig. Below), parallel and just to the right. If it cas+6.:kwoqi f arries 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 poin)vjp6lnf0 l5nc*l xnx,g;qf6 ts 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 p bfht0a )l0:7-.pbeoj 7spywas a straight wire, as shown in (Fig. Below). There is a current of 2.5 A i 7y eos.-:atwhlbp0j p0)7fbpn both 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, ma 8u .a1k,k8mz3: 0 hpkfyjetjrpsg q:9de of 2.5-mm-diameter copper wire and parallel to the first, is kept in suspensionyjhzg830:jkkuekq, 8s r19: fmtp. p a 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 l)r qfu81 emt6igsoc)vk. z0 jk--dm9 are perpendicular to each other. At their closest, they are 20.0 cm apart (Fig. Below). What is the magnitude of the magnetic field at a point.vfs ztgekcl-i ) )u1rm-8o q06d9k mj 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 current.mxafg7 rt0 . jcbw*jc*kew+o3*gujwo0 -m 9s , Wire B’s current is 4.0 A i,ubcew.m* r aw*-7jcsto jgjk 0 +fomxg3*0w9n 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 k3tft1;a).w.lr qpjh 3.8 cm from one another. (Looking along them, they are at . 3.;qa k)lhptrj wt1fthree 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 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), deterf7zcy) x kmur82qe th83f)o)p mine the magnitude and direction of the magnetic field at the midpoint of the side r8t82mqux)y37foz) pckeh f) 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, carr8 34,rkjxadw t.v )kejf)f i3qy equal currents I in the same direction. One wire is at x = 0, the other is at x = d, (Fig. Below). Determin 3)fr 4v)xdfji3.8aj,wkke tqe $\vec{B}$ 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 and carries a / jd32+xbwyx:w03lxl:ji zte current of 2.0 A. Calculate the field inside near the cente 0w y:3 ezbw3tlxjd2xj/xl: i+r.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.2n f(zehbzq fe r33/6d39cdvb85 cm in diameter is to produce a field of 0.385 T at its center. How much current should the solen 6b3fbqrd9c8z 3 n/f3(v dheezoid carry if it has 975 turns of the wire?    A

  A 550-turn solenoid iusi c0-(ifeahc5fai l64g43u s 15 cm long. The current in it is 33 A. A 3.0-cm-long straight wire cuts through the center of the solenoid, along af6 e0c3iug4sahl c5fu-i(ia4 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 copperj:o6xnkvh s .4.a7i6m,i yei s 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 i, h6sm six6.navjo:7k . ey4ifat, or something else? Consider other variables, such as solenoid diameter, length, and so on.

A toroid is a solenoid in the shape of a circle (Fig. Below*stvr;l f-dlt oaz w1(k.wpp,z6uz) (). Use Ampère’s law along the circular path, shown dashed in (Fig. Below a), to determine that the magfl ;s(azpwd,(uz1w*zr 6tv-ko lp) t.netic field
(a) inside the toroid is $B=\mu_0NI/2\pi r$ where N is the total number of turns, and
(b) outside the toroid is B = 0 .
(c) Is the field inside a toroid uniform like a solenoid’s? If not, how does it vary?

(a) Use Ampère’s law to show that the magnetic field between the conductorf hys,ak ky 9l:18a;yls of a coaxyk89y;y: kflals1h , aial 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 wir,xo544lti;u7mcu s0 wvm rm+hss+a l1e 22.0 cm on a side is placed with its face parallel to th i1u7 +l0sumr;hotwm5la4 css,vx+4 me magnetic field between the pole pieces of a large magnet. When 6.30 A flows in the coil, the torque on it is $0.325\cdot N$. What is the magnetic field strength?    T

  A galvanometer needle deflects full scale for av f-+ b+ ykpi/ti2:rys $53.0 -\mu A$ 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, what: moaadm9 )b k5s3) fcq+3gycf current will give full-syk3 sabc5 m)f a:f3 dmo+q9gc)cale deflection if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by what factor does the out9gm o3nbfn/r3 (7qmvy put torque chanqrv/ fn9n3gy7 obm(3mge?

Show that the magnetic dxvjfdb 8/,+ xhipole moment M of an electron orbiting the proton nucleus of a hydrogen atom is related to t, xv jxb+f8/dhhe orbital angular momentum L of the electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diamete0sc *djm; uq8dr and containing nine loops lies flat on the ground. The Earth’s mag80;qddjucs *mnetic field at this location has magnitude $5.50\times10^{-5}\mathrm{~Т}$ and points into the Earth at an angle of 56.0$^{\circ}\,$ below a line pointing due north. If a 7.20-A clockwise current passes through the coil,
(a) determine the torque on the coil,   $\times10^{-5}\mathrm{m}•\mathrm{N}$
(b) which edge of the coil rises up: north, east, south, or west?

  Protons move in a circle of radius 5.10 c q isx9a niqpm.x;hw)z-5j e 6.uz(wy)m in a 0.566-T magnetic field. What value hx.jeywz)xq( an-p.quzi9 6w) ; 5simof electric field could make their paths straight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atoms 9pi 5w+a xfs0 rx.x8c6usd;w9l6i tki have radii of curvature equal to 21.0, 21.6, 21.9, 22.2, and6a 8+ .x9 6kswx5isdf9u ;ci ti0wrxpl 22.8 cm. The largest radius corresponds to an atomic mass of 76 u. What are the atomic masses of the other isotopes?

  Suppose the electric field bhe5 em3i4w 0vzetween the electric plates in the mass spectrometer of (Fvh 50me wi4e3zig. 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 m w8kdfd w p-xpec*b5dfq**j/4onitor air pollutants. It is difficult, however, to separate molecules with nearly eqkppfdqeb4dw -x*5fj c/*w 8d*ual 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 voltageg22qs0mt6tt p:e+ btu V before they enter a magnetic field B. The ions are assumed to start from rt6tbqp:se+ m g0tut22est. 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 c50intx wr6*m h-ri8nvurrent flows through the wire 5wri xr0h68 mi-nntv*. If the permeability of the iron is $3000\mu_0$ what is the total field B inside the solenoid?    T

  An iron-core solenoid is 38 cm long and 1.8 cm in diame lw r 3ft-p:)vev ;17hhxlf.gater, and has 640 turns of wire. The magnetic field inside the solenoid is 2. herxv-flwt71 hv)a.pl 3:fg;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 momentumdsbdc4yy9:g ai1ae: 5 $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 electrw;l7mq:,hj o(ctb8 i3gx y-td on have the same kinetic energy upon entering a region of constant magnetic field. What is the ratio of the radii of their circulardg-httb , o jcqy3;xm7l:w8i( paths?   

  The power cable for an electric trolley (Fig. Below) carries a horizont ned1ws6pxin(js. .*fal current of 330 A toward the east. The Earth’s magnetic field has a strength1.s.wdjp* (ex6nins f $5.0\times10^{-5}\mathrm{~T}$ 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 w/ meyz0*ja a7phich 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 Earthb9nb)po g .cq s1(;dn pa 6ttl+v ye-lh(l(m9d’s magnetic field points almost horizontally to the north and has magn novht.b; 9( (qdgels( b9t1adp)l py-c+m6l nitude $B=0.50\times10^{-4}\mathrm{~T.}$ 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 :ty(8kl ctrr2p a(*wb mass is $6.6\times10^{-27}\mathrm{~kg},$ is accelerated by a voltage of 2400 V.
(a) What will be its radius of curvature in a uniform 0.240-T field? $\approx$    m (retain three decimal places)
(b) What is its period of revolution?    $ \times10^{-7 }\;s$

  A sort of “projectile launcher” is shown in (F05uz:f bsq pg7ig. 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 accelb 05fs7:zuq pgerate 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 is509/g,9y5xtc hbiwrzs.hj z b suspended in air due to the two magnetic forces from the bottom two wires. The currentzzbwr50, t9hj/sbxch5g 9i.y 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 distancx2:rfcxy k. b jn6dp4;t. a3tp :1y5fu/mr bkre l apart in a horizontal plane act as rails to support a light metal rod of mass m (perpendiculryj 6a 3 d5xppkmr2:yx..rbb4n kfu; ct:1tf/ar 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 electron beam near thedtbup+n 8 oc.8 center of a TV screen du+tup8 bno8cd. e 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 1hc67 9/74aczk f b p 1hrw*rasrotbi.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 t s4b71p6/r1cachia.rh7oz* f9wr kbac 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 wi8ccr7 paj,.ph res, located at the corners of a square of side l, carry eq.pa 8cjp,hcr 7ual 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 veky9ui8z o66 /db.8rqf josws7ry useful in 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 dkzyui/qo f8bjos s6wr9687.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 protons traveling at $ 1.0\times10^{7 }\,m/s;$ be bent?    $^{\circ}\,$

  The magnetic field B at the akwyb-+byy ani +gi+ 3; ncj73center of a circular coil of wire carrying a current I (as in Fig. Bg+ 7bbi ajyky+nay-c33;i+n w elow) 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 abou;ipsxm2w9tdy* v tw jgb6; pe;v+xy01t 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 o9 ;uijd/lbhclnpp xd8 x/10i 7verhead power lines. You estimate that the two wires are each about 30 m above the ground and are about 3 m apart. Ti87l9x ;lxi1n 0 /cpd/hbdupjhe 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 tlvo xbr10b+ *field would make a beam of electrons, traveling to the right at a spee o rl+*0t1xbbvd 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 magnetox v ka3m8jd33ii p72 dr+xsn3ic 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 radiii3 nsx2x3o +7pdjri 3d3 8kamv 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 produq pv6;rs htap.g3sb 87ce a 0.30-T magnetic field at its center. If the maximum csq7;s8 bh6 ppv.a3r tgurrent is 5.7 A, how many turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires.y9w ru d3gix :;wlmi/, each of diameter 0.50 mm, carry the same current but in opposite directions. They are suspended by 0.50-m-lodr:;wi3ulywm 9ix /g .ng strings as shown in (Fig. Below). If the suspension strings make an angle of 3.0$^{\circ}\,$ with the vertical, what is the current in the wires?    A

  An electron enters a uniform mlyc73x dqy)kdv/b/lhq 1)d .tagnetic 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$