A compass needle is not always balanced parallel to the Ear4 d.jbkxflsj 2 /z7,:eue/nwpth’s surface, but one end may ld,. jbjwf2/ sx7 k4eenpu /:zdip downward. Explain.

Draw the magnetic field lines au7plk j5 mv/9suw1gg 7round a straight section of wire carrying a current horizontally to the lef7p1 klwms j7gv 9g5uu/t.

In what direction are the magnetic field lines surrounding a stry,mbc:(x8oc sj( wuu 7aight wire carrying a current that is moving dire s7ub 8yw:cc( omjux,(ctly away from you?

A horseshoe magnet is held vertically witha)0)* otmdfw2kdj 3ox the north pole on the left and south pole on the right. A wire passing between the poles, equidistant from them, carries a current directly a 3 *02fmxt)aodj)okwd way from you. In what direction is the force on the wire?

Will a magnet attract any metallic oz6c7gloq/b ) r 8cqrvr;p*yk: lndm3.bject, or only those made of iron? (Try it aq:r7q / vocdr r.p;z*c)k8l n 6y3bmlgnd see.) Why is this so?

Two iron bars attract each other no matter which ends are place:tj7p11tfk gg 2u eke9d close together. Are both magnets? Explakj:2p1ef te k7 9ut1ggin.

The magnetic field due to current in wires in your home d/-r b6qif; wm-s0f efcan affect a compass. Discuss the effect in terms of curre;qf ri bdef-w-s06/m fnts, including if they are ac or dc.

If a negatively charged partic b;5+j tpldc4y cb64llle 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 electrbp y 4;ll4 c+cdb6tlj5ic field.)

In(Fig. Below), charged particles move in the vicinity of a current-carry(g ppz,,5mimuq(kt k2 87hxvt ing wire. For each charged particle, the arrow indicates the direction of7 g,,m ktxp uq(hpzt(iv82 m5k motion of the particle, and the + or - indicates the sign of the charge. For each of the particles, indicate the direction of the magnetic force due to the magnetic field produced by the wire.

Three particles, a, b, and c, enter a magnetic field as shown in Figkb j/rleh: 7 olo*x-0f. 20–46. What can you say about the charge on each particlel/0h7-lxf eorb j*:ok?

A positively charged particle in a nonuniformdqy.),ojjq* sz(0cj r magnetic field follows the trajectory shownq*do,( )jcq.rjzj ys0 in
(Fig. Below). Indicate the direction of the magnetic field everywhere in space, assuming the path is always in the plane of the page, and indicate the relative magnitudes of the field in each region.

Can an iron rod attract a magnet? Can a magnet attract an vbeyu44)w- +rwu8qe47txv tl iron rod? What must you consider to a)q-+urwx y w vbee7l4tu4v 84tnswer these questions?

Explain why a strong magnet held near a CRT television sox6-p-ceqy3j creen (Section 17–10) causes the picture to become distorted. Also, explain why the picture sometimes goes completely black where the field is the strongest. [But dcx -o3j-qy6epon’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 bue1d 1ts4mrc sw lc;r/(t the third is not. How would you determine which two are the magnets without using any additional obtlr /r1e m;sw14s c(dcjects?

Can you set a resting electron into mot8 * mfn +1x5yskmie0ytion with a magnetic field? With an electric field? Explain.x85myy10 tefnk s+mi *

A charged particle is moving in a circle under the influence of i7di. * ptkt4vh- wgn9a uniform magnetic field. If an electric field that points in the same direction as the magnetic field is turned on, describe the gd -7ipik9vw4nt.h*t path the charged particle will take.

The force on a particle in a magnetic field is the idea behind electromagnw6 b4zu mmb5xtcx8 )l)etic pumping. It is tb6xlw8xb )zc4 ) mm5uused 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 direction?

A beam of electrons is directed towardzb4b dha v93pqzcyke53+m 0j) a horizontal wire carrying a current from le9p0b3)zqdv jm 4y5bk3ea cz+ hft to right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields k:bam;7p:qfnq aar40 that surround a moving electric charge. apq:4nk;a0fb q7amr:

A charged particle moves in a o 3ph43rjixiybynm5):d b:t 4 straight line through a particular region of space. Could there be a nonzero mi t:3by3dyrm4:b j4 po5nihx) agnetic field in this region? If so, give two possible situations.

If a moving charged particle is m(m7h7k+s-qjba s t z(deflected sideways in some region of space, can we conclude, for certain, th-kts7 h s(7m(q z+ajbmat $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular regi p(v rs ;3d(mypu,gp;i0pyi *mon of space there is a uniform magnetic field $\vec{B}$. Outside this region, B = 0 Can you inject an electron from outside into the field perpendicularly so that it will move in a closed circular path in the field? What if the electron is injected near the center?

How could you tell whether moving electrons in a certain region of space are nrwi58w3l2k dh h, ;jkmyd 2.mc: fsh6being deflected by an electric field or by a magnetic82.,w 53nml2mdk;dkj :cw6yrh s hh fi field (or by both)?

How can you make a co9j(;jp 9)cej;x +bz 9ldjvfhmmpass without using iron or other ferromagnetic material?

Two long wires carrying equal currep7szn7cbszj3c4 zwss+9/ +b*kr h b4lnts I are at right angles to each other, but d wlzb+ csz4bb kpch/*r793s 7z+sn4j son’t quite touch. Describe the magnetic force one exerts on the other.

A horizontal current-carrying wire, free to move in Earth’s gravitationcdhzg jj66u. )-omfu:al field, is suspended directly above a second, parallel, zfu jhcd6m)-o: g. ju6current-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 cof i *vv-kmuu up- ,-g+-m,y hxn.u/jmagnet attract an unmagnetized piece of iron?

An unmagnetized nail will not attract an unmagnetized paper clip. Howevltbi+m),*. dmnc5c c der, if one end of the nail is in contact with a magnet, ti* m5,c .c+mntd lbdc)he other end will attract a paper clip. Explain.

Two ions have the same mass, but one is singly ionized and the other igvm e+u gsn-0/s doubly ionized. How will their positions on the film of a-sm0e/gun+v g mass spectrometer (Fig. Below) differ?

What would be the effect on B inside a long solenoid q23g,o l0 4lphanuvm0 5h1k y+okbm)iif
(a) the diameter of all the loops was doubled,
(b) the spacing between loops was doubled,
(c) the solenoid’s length was doubled along with a doubling in the total number of loops?

A type of magnetic switch similar to a solenoid is a relay . A relay0g)x )kch4t/+ 2m bhx( evzcc9go gw:a 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 w zt4/hxw h+xg cgo0c)() gcva: ek9b2mhen 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 magnitu +oad vs2oe-k5de of the force per meter of length on a straight wire carryi5 ek2va- sod+ong an 8.40-A 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 on bik;/u p,1r4opqu/+0btm zsua 160-m length of straight wire stretched between tw1o0t;r+/ubpus iz4k, / mqupbo 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 ohl/h-(27rkgv4 ew+myi 7dj kq +mzxl2f the magnetic force on a 160-m length of straight wire stretched 22k7wv-+4 d( xk7hzljqym+g/ mheli rbetween 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 +ldtt rj(py -amign6q(:i0j. long if the maximum force on it is 0.750 N when placed in a uniform 0.0talm- i(:dt j6 n.0(+ry jiqpg800-T field?    A

  A 1.5-m length of wire carrying 4.5 A of current is oriented horizontally.(a5yx4h)9yo 497*fm pbze6qc m uzndz At that point on the Earth’s surface, the d9z()4 n5a9h eozx4mb*ufqp 6ymc7zyd ip 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 between 0 swxgf ck--3thxu :7bthe pole faces us-b3fh7cg 0 wt-xk:x 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 o;xm/z n113z9 mqbmvvr n a wire is measured to be only 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 betwe39zr m z xmn/v1;qm1vben the wire and the magnetic field.    $^{\circ}\,$

  The force on a wire is a8 2fqshfl tkt+l3f)) m maximum 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 “flowdn q o/shp*y )80)nkia((kpujfwk-: at” horizontally in air beca *wi(a)dpkjpn/:y0o qn(fus) -khkw8use 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 charge /8obpd (vitj) $q\,=\,+2e$ 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 forc u2cnk0wfg* .+kryru2e 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 fomcvwz9(-ras )u4( yd*zval* jr each diagram shown in (Fi-(4a)wyz c9zvmulv*r jd* (asg. 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 directnwob539xm+eya h f4-vion 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 projecvm28g 6dhh u5iw9 g2 k92eafgrted vertically 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 energdaw rovl,,z 38*n)p bvww5mj ;y) proton enters a 0.20-T field, in a plane perpendicular to the field. an8 *m,zvd , 5l3w)ow wrp;bvjWhat is the radius of its path?    m

  An electron experiences the greaye6tgzt0jw2 - ;5gpou+wu0i utest 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 k 31aqgf qt,0pelectrons that go undeflected when passing through perpendicular electric and magnetic fi3p,fat1 g kq0qelds 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 masa6.gbx itq1f3acm+5 vs 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 cha)xn/: s(uft+t guq 4knd /(isw. bv/ayrge q moving with constant speed v to make one circular revolution in a uniform magnetic fiel(+. 4yfbikx ( q/wng/dnat)vt s:/ usud $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge q moves in a circular path of radius r in a ,9xubipm9y ch 3; hev-2i0vt iuniform magnetic fiev-; v i23 0yhh x9,pmu9ticbield B. Show that its momentum is p = qBr .

A particle of mass m 0dn*bvp o. 2ec2fx8pz -fwou)and charge q moves in a circular path in a magnetic field B. Show that its kinetic energy is prop2 pv* 20nbfw8oep . )zd-ouxcfortional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momentum of the particle in Problem x 7bxq9tb89sokm))ey 21 is $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves with a speed of 160 m/s perpei i9ao s ,j+t)w l.uyy-ta1up/ndicular to the Earth’s magnetiolyyjaw)-a/ u9,.t+ 1sipuit c field of $5.00\times10^{-5}\mathrm{~T}$, If the bullet possesses a net charge of $13.5\times10^{-9}\mathrm{~C},$ by what distance will it be deflected from its path due to the Earth’s magnetic field after it has traveled 1.00 km?    $ \times10^{-7 }\;m$

  Suppose the Earth’s magnetic field at r1yesn p9emac 1a7.gtag:l5( 17g4h 9fsqsz rthe 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 spe3wl*,7j 5zd)-gy bpcihs qcinm)yr(6 *c6wxged $\nu=2.0\times10^5\mathrm{~m/s}$ 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 vehiclbf7 m)*ff;atoevt3* yr l.p:ze carries a 65-A current. How strong is the) :*t bfpaly f. t;vzef*om7r3 magnetic 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 t 0kh3a.eom 9jlo produce a magnetic field no larger than that of thee03.mljo9 ak h 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 straight12wdarmry0e58) j k in wire carries current I out of the page toward you. Indicate, with appropriate arrows, thedm nw8r5y1eri 2)0jka direction of $\vec{\mathbf{B}}$ at each of the points C, D, and E in the plane of the page.

  A vertical straight wire carryi +5q 5s1vu3 tbtfsjr1rng an upward 24-A current exerts an attractive force per unit lengvu 1qs 35tr1t+jbfs5rth 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 direction of the force between two parallel wj) xx o9-wgi fkr1ltjv)0;wo5c-v/fyires 35 m long and 6.0 cm apart, each carrying 25 A in the same dire 9/xo1t5)fkvi ;fj )l-r-owy cjvx0wgction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic field is being carri +wcol,3j:necpirq:/ ed out 1.00 m from an electric cable. What is the maximum allowable current in the cable if the experim,o :w+ c n3cep:r/jqilent is to be accurate to $\pm1.0\%?$    A

  A power line carries ai z3 :a60t3dkpsu)j myskal6* current of 95 A along 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 fieil0yuj3d :*za)sk6s 6a pkm t3ld of about $\frac{1}{2}G$?    $ \times10^{-6 }\;T$ The field of the cable is about    % that of the Earth.(retain two decimal places)

  Two long thin parallel wires 13.0 cm apart carry 25-A cyr(c9 -sdidiq 3-t x0kwgge* 6urrents in the same direction. Determine the magnetic field at point P, 12.0 cm f ts- yxrq*w9dg3e cdi(g0k-i6rom one wire and 5.0 cm from the other(Fig. Below).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18 cm due south from a straight vertical wire ca 3caz trzt4uf1;b72gzww0d 0.pm 0pqwrrying a 35-A current downward0m71wzz bwpdw0 f3 4g0ruta. cqz;tp 2. 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 2ni 05p8q+ kb0telii) p2.0 A of current due north. What is the net magnetic field 20.0 cm due west of the wire if the Earqi+k5)p 8li0pein b t0th’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 protons passd6kvh)/k z(t)2ynres 8 g7 nrmes 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 magnetiw2hrrr r1l8 o/tf.d4pc field midway between two long straight wires 2.0 cm apart i/hr 8o t4. rwr1lfp2drn terms of the current I in one when the 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 1u.d -1dd lgmfl.jt( 4m4 wttkfrom, an instrument. If the insulated wires are of negligible diameter but are 2.8 mm apart, what is the magnetic field 10.00 cw du- t4dm114lk( fml tj..dgtm 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 pl 2a54uw 3k :kzij6dibdane of the two wires shown in (Fig. Below), parallel and just to the right. If it carries 25.0 A upward, what force per meter of length does it exert on each of the other two wires? Assume it is 2.8 mm from the nearest wire, center to cent2jda kkz:43i65 di bwuer.
$F_{near}$ =    $ \times10^{ -2}\;N/m$  ----待选择----attractrepel 
$F_{far}$ =    $ \times10^{ -2}\;N/m$  ----待选择----attractrepel 

  A compass needle points 23 * y9 3lvhf-pb4lgqw,o ,v/ddq$^{\circ}\,$ E of N outdoors. However, when it is placed 12.0 cm to the east of a vertical wire inside a building, it points 55$^{\circ}\,$ E of N. What are the magnitude and direction of the current in the wire? The Earth’s field there is $0.50\times10^{-4}\mathrm{~T}$ and is horizontal.    A  ----待选择----updown 

  A rectangular loop of wire lies in the same plane as a straight n.vftm;,m0 cqq6ga8f wire, as shown in (Fig. Belowq ftma8c m6qngf;0, v.). There is a current of 2.5 A in 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 a7;+ph+p 7pwa 2uinwrr5- c whw current of 48 A. A second wire, made of 2.5-mm-diameter copper wire and parallel to the first, is kept in suspension magneticrr 5+p7h awi -pwunc+ phw2;w7ally 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 other. .02hyiu :abw: :xllg0 g)haa tAt their closest, they are 20.0 cm apart (Fig. Below). What is the magnitude of the magnetic field at a point midway between them if the top one carries a current of 20.0 A and the bottom oney.h0g :ai l:0tw ug)bala2hx : carries 5.0 A?    $ \times10^{-5 }\;T$

  Two long straight parallel wires are 15 cm apart. Wire A carrieoro83e 3bapme*y sn( 6s 2.0 A current. Wirbsyn83mo ae *peo(63 re B’s 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 ckf bqhp3y tn/ ;( mr)ln1sfo af+9kf75m from one another. (Looking along them, they are at three)n1qsnb+hyfmpl9 k ok (5ff7r at/f3 ; 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), determine the magnitude and direction of the magneticfh ayy4ow9r91uh ihch4,q )6e field at the midpoint h,4uaf 19)hoch6yy9rqhi w4e of the side of the triangle between wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a distance d apart, carry equal currents I -yyh1 fi ij-.)b3xpjq0wky-an7 c,bbin the same direction. One wire is at jf-3b1,p aiyh.bwk7ycx bqn-ij-y0) 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 totalw: 5eqqymqqq3q+88wm of 420 turns of wire and carries a current of 2.0 A. Calculate the field inside neawe+8qq mq:qm3 qw58qyr the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameter is to prasz, 0b(nh . va;jtqocn v)2/hoduce a field of 0.385 T at its center. How mucth (bz vja;, v/acn2n)sqho. 0h current should the solenoid carry if it has 975 turns of the wire?    A

  A 550-turn solenoid is 15 4o+vcj au-:zv1 igzni y-b) 2ycm long. The 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 (and is connected by other wires that don’t concern us). 1viz2zib a4v -gjnc )y :+-uoyWhat is the force on this wire assuming the solenoid’s field points due east?    N

You have 1.0 kg of copi3d ff3(w ry781zzpat per 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 variati3(81 7z3r zffdwpyables, such as solenoid diameter, length, and so on.

A toroid is a solenoid in the shape of a circle (Fig. Below). Use Ampè2alaa/2vvk 93-gy) b*kh nyyure’s law along tb9nu)32h /lgk ay*2v vyakya -he circular path, shown dashed in (Fig. Below a), to determine that the magnetic field
(a) inside the toroid is $B=\mu_0NI/2\pi r$ where N is the total number of turns, and
(b) outside the toroid is B = 0 .
(c) Is the field inside a toroid uniform like a solenoid’s? If not, how does it vary?

(a) Use Ampère’s law to show that the magnetiex bmw185f iot:pq 95xc field between the conductors of a m9pix85bx1:e5tof w q coaxial 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 placed with its face parallel zx8 jh,rv0owfs9)/uf+nms(k ;5 wkt w s: b,ptto the magnetic field between the pole pieces of a large magnet. When 6.30 A flomrb9 wv ,sz tn sk0 j):/8x,s kt;5wpf(u+fhwows in the coil, the torque on it is $0.325\cdot N$. What is the magnetic field strength?    T

  A galvanometer needle deflects full-m /qaih )povbeb.-*j 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 *.vsrjo5lzez(7k ;xsrb6 dd 0weakens by 25% over the years, what current will give fxk*bj7ze6 vsd( zl.r; 5r0sdoull-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 ou.3rkecqvzhaq43opt , b m2.a)tput torque changzbp.m 4k2c )q,q 3ev.t3rhoa ae?

Show that the magnetic dipole moment M of an electronomucxr1i w) *a-/fl:r orbiting the proton nucleus of a hydrogen atocxo-ufar m )/rl*1:w im is related to the orbital angular momentum L of the electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in dia5 j2hoyjc1m 0zmeter and containing nine loops lies flat on the ground. The Earth’s magnetic field at this location has magn j5m2j chz1oy0itude $5.50\times10^{-5}\mathrm{~Т}$ 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 circlek z. r8hjm5ut/ of radius 5.10 cm in a 0.566-T magnetic field. What value of electric field could make their paths straigj khrm85/t. zuht? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atoms have radii of curvature equal to 21mi eoy t2b9on9h (6kp..0, 21.6, 21.9, 22.2, and 22.8 cm. The largest radius corresponds to an tmeoo29i .k( h9pn6y batomic mass of 76 u. What are the atomic masses of the other isotopes?

  Suppose the electric 7ivhox:z+ 8wmpz 8 hgl/vd5e+kb 54okfield between the electric plates in the mass spectrometer of (Fig. Below)+5hxk/i4wh7ged zm+ 5oo8lz v8: k pvb is $2.48\times10^4\mathrm{~V/m}$ and the magnetic fields $B=B^{\prime}=0.68\mathrm{~Т}.$ The source contains carbon isotopes of mass numbers 12, 13, and 14 from a long-dead piece of a tree. (To estimate atomic masses, multiply by $1.67\times10^{-27}\mathrm{~kg.}$)
How far apart are the lines formed by the singly charged ions of each type on the photographic film?
$2r_{13}$ - $2r_{12}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)
$2r_{14}$ - $2r_{13}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)
What if the ions were doubly charged?
$2r_{13}$ - $2r_{12}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)
$2r_{14}$ - $2r_{13}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)

A mass spectrometer is being used to monitor air pollutants. It is diffilg4a*77k 6glp( d ecazcult, however, to separate molecules elz*l77(a pg dgkc6 a4with 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 volnp*- ,q*tmicb tage V before they enter a magnetic field B. The ions are as-tcp,m*nqb* isumed to 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 kirh8pw rh9gg4/ v/v4a 25-A current flows through the wire. If the permeability of thvgh/ wkr iv9h8 44gp/re iron is $3000\mu_0$ what is the total field B inside the solenoid?    T

  An iron-core solenoid is 38 cm long and 1.8 cm in diameter, and has 640 td u+xna4vd;mof5i; 4 m xnf6;turns of wire. The mt n 6fovixd544d;;an; xm+ ufmagnetic field inside 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 momentutz(f0bh( q c0wm $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 up7m+pj :yj2d.wen;ru+ lcl2ivon entering a region of constant magnetic field. What is the ratio of tycj+r mi l2e7ju wl2nd.p :;v+he radii of their circular paths?   

  The power cable for avm4a0ss * a: s:dkhs9dn electric trolley (Fig. Below) carries a horizontal current of 330 A toward the eastm0sh:av sd*4s :9sk da. 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 hasvv o1rl 8*s*yc 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 Eartkxdiqta x, op6p52j9il6 * vu5h’s magnetic field points almost horizontally to the north5qd ilto p ji9u*a v6xp2x6k5, and has magnitude $B=0.50\times10^{-4}\mathrm{~T.}$ What should be the magnitude and direction for the velocity of an electron if its weight is to be exactly balanced by the magnetic force?    $ \times10^{-6 }\;m/s$  ----待选择----eastwest 

  A doubly charged helium atom, whose mttakmczg/ 1n7)nc.v6 ass 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 shownt.; qalhg (f d;fx+2gw 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 touchin ;hgx;taqd lf.g fw2+(g 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 direction must the magnetic field point?
   A
the magnetic field must be ----待选择----updown 

  In (Fig. Below) the top ewrgpycgq- 8 r6c/0id l2 lxj2b)2i) cwire is 1.00-mm-diameter copper wire and is suspended in air due to the two magnetic forces from the bottom two wires. The curree) x2g0lji2b8ccy2l-/ 6wgprqrc)dint 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 plane act as rs0l ng mmhm-;4pzg((vf g r0k,ails to support a light metal rod of mass m (perpendicular to each rail), (Fig.s, m ;(nlg4p0mh(r-fgk v0gmz 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 maximu b.jkxuc.7 yi+f9z)k am deflection of the electron beam near the center of a TV screen due to the Euj7b+. )a.y k9ck ixfzarth’s $5.0\times10^{-5}\mathrm{~T}$ field. Assume the CRT screen is 22 cm from the electron gun, where the electrons are accelerated
(a) by 2.0 kV,    mm(Round to the nearest integer)
(b) by 30 kV. Note that in color TV sets, the CRT beam must be directed accurately to within less than 1 mm in order to strike the correct phosphor. Because the Earth’s field is significant here, mu-metal shields are used to reduce the Earth’s field in the CRT.    mm(Round to the nearest integer)

The cyclotron (Fig. Below) is a device used to accelerate elementary part-h,x)kul 3rt0k1dcs* nmz j e0g+c/t ty 7lxf*icles 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,” wherec0l-)t t7l xn1d0/ 3u*tehfm ysk*k+zjcxgr, there is an electric field E. (There is no electric field inside the hollow metal dees.) The electric field changes direction each half-cycle, owing to an ac voltage $V=V_0\sin2\pi ft,$ so that the particles are increased in speed at each passage through the gap.
(a) Show that the frequency f of the voltage must be $f\,=\,Bq/2/pi m,$ where q is the charge on the particles and m their mass.
(b) Show that the kinetic energy of the particles increases by $2qV_0$ each revolution, assuming that the gap is small.
(c) If the radius of the cyclotron is 2.0 m and the magnetic field strength is 0.50 T, what will be the maximum kinetic energy of accelerated protons in MeV?

Four very long straight parallel wires, located at th8s)azhe :7sn ty272j z-opruse corners of a square of side l, carry equal cuj)p2-o8he7 7yass usr n 2z:tzrrents $I_0$ 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 usefulf, ml*(8e+.z8hmvpldoxse k9 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 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 vol+m. , e(fe8hmd * 8sxkz9lpregion 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 carrying qf otp)p yixf3 n8/3l;csfv ((a current I (as in Fig. Beq;v3x3( fp8y lficsft (p/o) nlow) 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 magnethbqc,8ur gv*d,el* sjb 7l 6s8ic field is about 1G($ 1\times10^{ 4}\;T$) Imagine a simple model in which the Earth’s field is produced by a single current loop around the equator. Roughly estimate the current this loop would carry. [Hint: Use the formula given in Problem 80.]    $ \times10^{ 9}\;A$

  You want to get an idea of utdxyt3 *1ry- 2.ftvw the magnitude of magnetic fields produced by overhead power lines. You estimate that the two wires are each about 30 m above the ground and are about 3 m apart. The 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, art1-d.u3ftxt w2*y vynd 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 magneti 8e3hj eedeer(r k,r3:c field would make a beam of electrons, traveling to the rigee3 , :rrjed8kre3h e(ht at 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 magne0vzqq l sezq*rwds8q31a707yv kzn :-tic field of 0.010 T, perpendicular to the plane of the spiral, as shown in (Fig. Below). In two successive loops, at points P and Q, the radii are 10.0 mm and 8.5 mm, respectively. Calculate thea vl-8yqen*31vsqr 70 qszwzkqd7:z0 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 gznzy1/ll5)l cm in diameter, is to produce a 0.30-T magnetic field at its center. If the maximum g/ zl5 l)nlyz1current is 5.7 A, how many turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, each of diametejonu7 a* maudz 1*nazv 4h0-u2r 0.50 mm, carry the same current but in opposite directions 02 au-dmhz1v4u*n aaz 7*ujno. They are 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 uniformne0vciv dtod6 v0* 26m 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$