A compass needle is ws w,upp69oz 6not always balanced parallel to the Earth’s surface, but one end maw, p 9upsozw66y dip downward. Explain.

Draw the magnetic field lines around a straight section of url5 u3 3g0hiswire carrying a current horizontally to the 5hiu sr0u3l3g left.

In what direction are the magnetic field lines surrounding a straight wire carryoe4 5czpoe .o2,(g updlu pv9+ing a current that is moving directly away from o ezo.egpu+ v49uo(2 clpp5d,you?

A horseshoe magnet is held vertioq ba5wu1t862 hnmul:cally with 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 away from you. In what direction is the force on the wlutw1o b8nqham6: u5 2ire?

Will a magnet attract any metallic object, or only those made of iron? (Try it 1b6n g xxa/ ltbo+7pe4antagn 4bb/6xpl+e x1o7 d see.) Why is this so?

Two iron bars attract each other no matter which ends are pl2ktcdnfzxycp s;rr2;4.h) +vind 1m. aced close together. Are both magnetsks2rfn)4r;ncci2 x; . zy d+1t.dvp mh? Explain.

The magnetic field due tosexa-9ia;7-tqj sfp ) current in wires in your home can affect a compass. Discuss the effect in terms of currents, in a)7t;xa- qs9pfi- jsecluding if they are ac or dc.

If a negatively charged particle enters a region of uniform magnetisu-om 513egdq c field which is perpendicular to the particle’s velocity, will the kinetic energy of the particle increase, decrease,uogq1- 5 m3sde or stay the same? Explain your answer. (Neglect gravity and assume there is no electric field.)

In(Fig. Below), charged particles move in the vicinity o4- t+ p-ams9frip ,fcgy;8r tdf 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 magnetic field produced by the wire.st4fprid9p +;gc- t8 -m,yra f

Three particles, a, b, and c, enter a magnetic field as i 7audb9s l*2ot p8x5dshown in Fig. 20–46. What can you ss5dx2* b dl pt8i7ao9uay about the charge on each particle?

A positively charged particle in a nonunil42:bn ib7k w bpzbgrxr* tw83 cm+d9,(wh,laform magnetic field follows the trajectory sho,:g wrwda+zmb 2wb 3,ik bcx7trlnb 94 lh8(p*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 attract a magnet? Ca ;0 -8 dzn*j7iem)hyvchc-wpln a magnet attract an iron rod? What must you consider to answer the 0vp h)jw- z8*7e;li- dycnhmcse questions?

Explain why a strong magnet held near a CRT television scrqp(te12 yc2mp een (Section 17–10) causes the picture to become dispc2p2qe1mt (y torted. 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 ma u-)n8uyab cbui8 m)(66y lsfignetized but the third is not. How would you determine which two are the magnets )myafu cbb()n8yi uu6l -68iswithout using any additional objects?

Can you set a resting electron into motion with a magnetic field? Wi (bqwmdsze ,*+p4h 4mcth an electric fie( m+*44 w qpzb,edshcmld? Explain.

A charged particle is moving in a.mtfm0rrn rfwgamq//3 3 hs96 circle under the influence of a uniform magnetic field. If an electric field that poi f6 msgmra 3./0qtf9rhr/m3wnnts in the same direction as the magnetic field is turned on, describe the path the charged particle will take.

The force on a particp) l7 8nbx ;v-qlgv-ynyt1 *kxle in a magnetic field is the idea behind electromagnetic pumping. It is used to 7 ny y1gxkvxb)8p* n;l--qlvtpump 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 ;ap,8 sacl58; tmkixgtoward a horizontal wire carrying a current from lei5sg ca a;lt8xp;8,m kft to right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields that surround a .6i1lt/t*w bqlargy8 moving electric charge.lr6 t/ i*aw8b.t lyq1g

A charged particle moves i2dm; -akz m;ron a straight line through a particular region of space. Could there be a nonzero magnetic field in this re - rd;;2kmzaomgion? If so, give two possible situations.

If a moving charged particle is deflected sideways in some regiou:jrkupfxf3j2 19 r9rn 1qz86g,lufm n of space, can we concludel13fm k 6,qz2p :gfu u8rxfnr99j ujr1, for certain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is a uniform mx2;cu/o d,ebp3wlp9lh,er bk *l( 2qhagnetic 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 utp/z 4k yve+-certain region of space are being deflected by an electric field or by a magnetic field (or evkpzuyt-/4+ by both)?

How can you make a compass without using iron or other ferromagnetir+ *1dgtx6(w7u fsq pkln -blur- )m)kc material?

Two long wires carrying equal cuyw +ea60zepx6yuhisuts *7ys;p0q. erh)d+ ( rrents I are at right angles to each other, but don’t quite touch. Describe the magnetic force one exerts on the o6qi*.er+ )00e (deh xut7p6y+zwsupy s sha;yther.

A horizontal current-carryiena9agq au q)h/(wz ..ng wire, free to move in Earth’s gravitational field, is suspended directly above a second, parallel, e / )a.qunz.w(qg ah9acurrent-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 unmagnetized piece239j)v v xnwmhameo56 of iron?

An unmagnetized nail will not attract an unma5 x24ujgy2z/ :iy5kt pycjz v6gnetized paper clip. However, if one end of the nail is in contact with a magnet, the ozji5 g4c2yt2j6/kxyv:5pz y uther end will attract a paper clip. Explain.

Two ions have the same mass, but one is singly ionized and t0 5z bas dqb;)riov61whe other is doubly ionized. How wri0bzo1d 6vbwa; q)s5 ill their positions on the film of a mass spectrometer (Fig. Below) differ?

What would be the effect on B inside a losx* dh-vh217o-dez:m6j xjzon ;-m m hng solenoid if
(a) the diameter of all the loops was doubled,
(b) the spacing between loops was doubled,
(c) the solenoid’s length was doubled along with a doubling in the total number of loops?

A type of magnetic switch similar to a snu 844 to;rfdvolenoid 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 r8t4;4fo dvn ua 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 per meter of length on a straight wiref8h:k,d-o dkk carrying an 8.40- 8ddkk f-k,:ohA 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 a 160-m length s7 x2)t3 jc8 cp1s:hv.mkpc9knymym, of straight wire stretched between two towers carrying a 150-A cuvcx s 2 mnpyjs c9ctmk)mh3 17,:pk.8yrrent. The Earth’s magnetic field of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  Calculate the magnitude of the magnetic force on a 160-m length of stgyq0p cyb hpp-(/3s vpa 9j7zsa(o8l8raight wire stretched between two towers carrypa y(z3 p7g vs qcp-p sh8aj(lyb0o9/8ing 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 a -9cfm2hsa n-aj9( aq4.80 m long if the maximum force on it is 0.750 N when placed in a q s9faa-2(ma- hnjc a9uniform 0.0800-T field?    A

  A 1.5-m length of wire carrying 4.5 A of ca)au v/j (xn8murrent is oriented horizontally. At that point on the Earth’s surface, the dip angle of the Earth’s magnetic field makes an angle xau(anm/8 )vjof 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 ./v v1n 9i3m)z xwmmcif(9tqpthe pole faces of a magnet. If the pole faces are 55.5 cmm/(w 9ifizpx m n.v1 )9mqvc3t in diameter, what is the approximate strength of the magnetic field?    T

  The magnetic force per6lvd gi4( 9ckwc l5j6l meter on a wire is measured to be only 35% of its maximum possible value. Sketch the relationship of the wire and the field if the fl6 i k cdgv6j4(59lwclorce had been a maximum, 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 mq7i *7,q8g k ),mp7aht5wztctcm*z tyaximum 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 “flo , dotj6u*f5 vmkar4*kat” horizontally in air because of the force due to the Earth’s mak mu5r 6tf4d, kvao*j*gnetic 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 y3w.(h j kywx)q7wd (a$q\,=\,+2e$ 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 th,z u ug-4akyp ezp/-7be 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 diagramq50an g4t 7sba shown in (Fig. Below), wb7qa5a s4gn 0there $\vec{v}$ (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 direction of:be85uir q ivq ixhir1/d3o7( $\vec{B}$ for each case in(Fig. Below), where $\vec{F}$ represents the maximum magnetic force on a positively charged particle moving with velocity $\vec{v}$.

  An electron is projected vertically upward withn 8 qjyg:tes; v06jnps24bs7pfl( 6u)qu m 6ss a speed of $1.7 \times10^{6 }\;m/s$ into a uniform magnetic field of 0.350 T that is directed horizontally away from the observer. Describe the electron’s path in this field.    $ \times10^{-5 }\;m$

  A 5.0-MeV (kinetic energy) proton enters a 0.20-T field,1m iehu )n 7u)-whr; qzqd):zm in a plane perpendicular to the field. What is: m )ze7zw)mq;run1 qdi)-hhu the radius of its path?    m

  An electron experiences the greatest force as itw. vtk4gep)) ;rp3y lm travels $2.9 \times10^{6 }\;m/s$ in a magnetic field when it is moving northward. The force is upward and of magnitude $7.2 \times10^{-13 }\;N$. What are the magnitude and direction of the magnetic field?    T ----待选择----EastWest 

  What is the velocity of a beam of electrons that go undeflected when passinjx8mh. 2eqavgpk:.*ig through perpendicular electric and magnetic fie*vkh xm.8aje:pgiq .2 lds 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 masswlg/z,h xl 68jpry4l/ 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 cek) srg:px9- eonstant speed v to make one circular revolution in a uni:px krges )-e9form 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 uni zcdy(ga 6y99 wkai*m)form magnetic fizwa6a)i k 9c9dym gy*(eld B. Show that its momentum is p = qBr .

A particle of mass m and charge q moves in a circular path in aw2nch,. x2y4aw 1ad xj61bly l magnetic field B. Show that its kinetic energy ia14nxw1cbl yy wxl2dja. ,26h s proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momentum of the parti5 6np 0j( mkrzbe9ln-ecle in Problem 21 is $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves withc .2m8 vmab nlcpn;56k a speed of 160 m/s perpendicular to the Earth’s magnetic field ofcmp kc 8n;anl.v265b m $5.00\times10^{-5}\mathrm{~T}$, 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 magnitude bxp*yj569+)2acb q(hg bnbdn $0.40\times10^{-4}\mathrm{~Т}$ 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 spee.z h de*4 j,byte7yc 3lwpo6.id $\nu=2.0\times10^5\mathrm{~m/s}$ 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 vehicle carries a 65- t:,fk6r.ru(q3utw gls/vc .x A current. How strong is the magnetic field 6.0 cm away from it? Com3.tqsclt6 k, gu(v:x/ .rufrw pare 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 nst-ani7ez* l5 o larger than that of the Eart ln t*-a5s7eizh $(0.55\times10^{-4}\mathrm{~Т})$ at a distance of 25 cm, what is the maximum current the wire can carry?    A

In (Fig. Below), a long straight wire car. jp4r0dw4q h/o-0ogfj bu0obries current I out of the page toward you. Indicate, with appropriqo04h 4.ru 0jw oopf0dgbb-j/ ate 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-A current exerts an at 6o f9qcsawp9/fq6+ez(sb/fto2 /ldxtractive force per 6tw6 qq/czb2ef/+9o flx af( dso/9p sunit 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 direction of the 5p7 el9t zz,pl -ugc(uforce between two parallel wires 35 m long and 6.0 cm apart, el-l( ,7 upcez59putzg ach 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 m from a+lcm 0ld,t q6n l(1skyn electric cable. What isdyl c06(m,lq+n kts1l the maximum allowable current in the cable if the experiment is to be accurate to $\pm1.0\%?$    A

  A power line carries a cktib9;(d ta(x/zbn, ourrent 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 dotx9t,kon; b /a(( zidbes this compare with the Earth’s field of about $\frac{1}{2}G$?    $ \times10^{-6 }\;T$ The field of the cable is about    % that of the Earth.(retain two decimal places)

  Two long thin parallel wires 13.0 cm apart carry 25-A cumj*hv58 ldp) b2 ghd c9epq39trrents in the same direction. Determine the magnetic field at point P, 12.0 cm from odd9lmb93pphv) qcjet582*gh ne 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 straighp+cbr i *8qs;syscyd1elp 89 4ty 0t8lt vertical wire carrying a 35-A current downward. In what direction does the compass needle point at this location? Assume the horizontal component of the Earth’s field at this0 s q9pl*byp8 s+itte rycyc;ds88l14 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 cur nma)6s2is(v uxbf1e)rent due north. What is the net magnetic field 20.0 cm due west of the wire if the Earth’s field there points north but down)b)x m2a6 ensv u(if1sward, 37$^{\circ}\,$ below the horizontal, and has magnitude $5.0\times10^{-5}\mathrm{~Т}?$
   $ \times10^{-5 }\;T$
$\theta$ =    $^{\circ}\,$ below the horizontal

  A straight stream of protons passes a givel+cys1sqpq 1-ha)ch 7n 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 magneticmm/fj:2szq;mm2, bmiwq+s,w3 j*jl e field midway between two long straight wires 2.0 cm apart in tewml, ,mibwf3 qqz* j/ :ejmmms2;2+ jsrms 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 25.09k;x) -ja qcasryke,) A of dc current to, and from, an instrument. If the insulated wires are of negligible diameter but are 2.8 mm apart, what is the magn;cakrk)ex-aj sy,q9) etic field 10.00 cm from their midpoint, in their plane (Fig. Below)? Compare to the magnetic field of the Earth.
   $ \times10^{-6 }\;T$ The field of the wires is about    % that of the Earth.(retain two decimal places)

  A third wire is placed in the plane of the two wires shown in (Fig. Below), pa-x+vgr 4 ktos8rallel 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 +s4v-or8t xgkother 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 xyq qy*6 2a*ef23$^{\circ}\,$ 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 qa-fgwua63z dsm(y 6( 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 dire6( (wfsgayq6ud3 -z amction of the net force on the loop.    $ \times10^{ -6}\;N$  ----待选择----away from wiretowards wire 

  A long horizontal wire carries 3h0 lo:bdu*pk a current of 48 A. A second wire, made of 2.5-mm-diameter copper wire and parallel to the first, is kept in suspension mbpdhu 3 0:k*loagnetically 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 pez p j7so;3u0mmbml+lf*nx+4 arpendicular 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 ml+abz m 0fnm+x ;4oj p*ulms37idway 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 apvnxy n758 kfyb e6ol2zc667 bnart. Wire A carries 2.0 A current. Wire Boe bxlbf68nyc n7yv6z576k2n’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 cm fro el cxa:l9c5e d1by-u6m one another. (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 9e l-1 :x65a dyeculbcwire 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 themyc 8gk /no91ani*uc6 am3 pxm8boy33 magnitude and direction of the magnetic field at the midpoint of the side of the u 3mc68i*amoy8 g1n3kp 9mx oncb3y/atriangle 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 cur4zsy0)c*t jrfro8 ;hi rents I in the same direction. Orj r8si y*h;zft0o 4)cne wire is at x = 0, the other is at x = d, (Fig. Below). Determine $\vec{B}$ along the x axis between the wires as a function of x.

  A thin 12-cm-long solenoid has a total of 420 turns of wire and carries a 9jxiw4 jbth ,n,*in+pcurrent of 2.0 A. Ca hn9bjnipxiwt+ *4,,j lculate the field inside near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 c/0/pw w u0zwnldfg 4s8m in diameter is to produce a field of 0.385 T at its center. How much currenfs0 u0n pw//8 zg4dwwlt should the solenoid carry if it has 975 turns of the wire?    A

  A 550-turn solenoid is 15 cm long. The current in it is 33 A. Amqnwecvy q1p+9r 7/*y 0eecj*pxy7k8l g25dq 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 thp778 2pmg *ec1v+ 0w5xrjyc/ 9 yqqedykqeln*at don’t concern us). What is the force on this wire assuming the solenoid’s field points due east?    N

You have 1.0 kg of copper and want to make a practical solenoid that produces fz:+ s mq3plo:the greatest possible magnetic field for a given voltage. Should you make your copper wire long and thin, short and fat, or something else? Consider other variables, such as solenoid diameter, le:mz3f+q:p ls ongth, and so on.

A toroid is a solenoid in the shape o ck7e+p*y )ghjf a circle (Fig. Below). Use Ampère’s law along the circular path, shown dashed in (Fig. Below a), to determine that the mag*yec7jgkp +)hnetic 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 betweq c,a0ktwxx .5en the conductors of a coaxial cable (Fig. Below qc0x t.,ak5xw) 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 ofz ffk if4y7+ 8/d,k-a(zgokn z wire 22.0 cm on a side is placed with its face parallel to the magnetic field between the pole pieces of a+z( na8fdyfo-f/7izkz4 k,gk 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 f6a t0z qvd7/m bqycrf;6/iy)dull 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 weaku9oe af c77:f x. rwwcwew33l) dgbp-9ens by 25% over the years, what current will give full-scale deflection if it originally requirpweg9we) d:.fo9a3wbc3u-cw7 f r l x7ed $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by what factor does the outpongbrt4-*t9b ut torque changenbg*49o-rt bt ?

Show that the magneticd2n6i yth*s: yj8xo 5o 1dva0f dipole moment M of an electron orbiting the proton nucleus of a hydrogen atom is related to the orbital angular momentum L of the ed6 j fni* xs10y h5d:tvy2oao8lectron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in f/.5p 0 (xyze1kuq l-fh/ ijv+vkybp.diameter and containing nine loops lies flat on the ground. The Earth’sq ypelfpv.b(/x 0.u jf/v1yz i-+hk k5 magnetic 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 cm in3lcl. 2moc2kz a 0.566-T magnetic field. What value of electric field could make their pathcc.mk 2l 2ol3zs straight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germand*4 1ol.eb06* qbs qin2rtes sium atoms have radii of curvature equal to 21.0, 21.6, 21.9, 22.2, and 22.8 cm. The largest radius corresponds to an atomic mass of 76 u. What are tq 6ln.tr o0sebe14ss** bi2qdhe atomic masses of the other isotopes?

  Suppose the electric field between the electg.ddvilq.*c :6 mr c8fric plates in the mass spectrometer of (Fig. Belolf v .:6d*qgm 8.cdicrw) 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. It7 sw8 n+dk6rb:8d p56nxb,j j y7wgquq is difficult, howerp :j+ 8yn6ud7k qb,8w6 7xs nd5jqwgbver, to separate molecules with nearly equal mass such as CO (28.0106 u) and $N_2(28.0134u)$. How large a radius of curvature must a spectrometer have if these two molecules are to be separated on the film by 0.50 mm?

One form of mass spectrometer accelerates ion-9iv8wdgz w9e 3eq9bbs by a voltage V before they enter a magnetic field B. The ions are assumed to sta8zb9wdwb g9 eeq-93iv rt 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 9otgw +3: cfzj430 loops of wire per meter, and a 25-A current flows through the wire. If the permeabilw fj9oc3 :zt+gity 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 diameter, and has 64jubq2n +og+ 1l0 turns of wire. The magnetic field inside the solenoid is 2.2 T when 48 A flows in the wire. What is the permeabilityq2gu+ objl+1n $\mu$ at this high field strength?    $\times10^{-5}\mathrm{T}\bullet\mathrm{m/A}$

  Protons with momentuyyyqg 6q942m 4s4d vzyhsd857dzdk w2m $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 entem4/6ffef/mtin fr +3k ring a region of constant magnetic field. What is the ratio of the radii of their cir/ff ni/mm3tr64f f ke+cular paths?   

  The power cable for an electric trolley (Fig. Below) carri g8immn2xb(y *es a horizontal current of 330 A toward the mm*yi2g nx8(b 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 has te itm we8.nk+(i4k9l acquired a net charge of $1550\mu C$ and moves with a speed of 120 m/s perpendicular to the Earth’s magnetic field of $5.0\times10^{-5}\mathrm{~T}$.    $ \times10^{-6 }\;N$

  Near the equator, the Earth’s magnetic gq i)k9pei /6qfield points almost horizontally to the north and has magni i)6/pe9q qgkitude $B=0.50\times10^{-4}\mathrm{~T.}$ 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, wha-u .ii8:y:ddyz v xe.+ldpe6gim9 vb- is( .rose 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 launat rvq39fsmx3+/zoe( cher” is shown in (Fig. Below). A large current moves in a closed loop composed of fixed rails, a power supply, and a very light, almost frictionless bar touching the rails. A magnetic field is perpendicular to the plane of the circuit. If the bar has a length L = 22cm, a mass of 1.5 g, and is placed in a field of 1.7 T, what constant current flow is needed to accelerate the bar from rest to3ftq/9xmv3(rsaz + e o 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-diampc i nzjl)e)y+ l4r 4g7ip*m)eeter copper wire and is suspended in air due to the two magnetic forces from the bottom two wires. The current flow through the two bottom wires is 95 A in each. Calculateiry l)i7j)pm 4)4 e*zlgn+ec p the required current flow in the suspended wire.    A

Two stiff parallel wires a distance l apart in a horizonbb(h*dlp 5q c:b: :qq5dkn s,dtal plane act as rails to support a light metal rod of l,b:(*:ps qqn : dkbhc55dqbdmass m (perpendicular 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 e:hke 3ppsw/9o k00nldeflection of the electron beam near the center of a TV screen due to the Eare/ep0 3kl 0pnk:h9w soth’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 partic4lh32nw-ck hs ogj6p0fbaf n;1ss;p; les 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 spewa p1k-n3;ffhnbjs 6c2psgo40 ; s;l heds each time they pass through the gap between the metal “dees,” where there is an electric field E. (There is no electric field inside the hollow metal dees.) The electric field changes direction each half-cycle, owing to an ac 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 the corners of a sqhl-ub/u k0x p)uare of side l, carry equal cubh /0xp ulu-)krrents $I_0$ perpendicular to the page as shown in (Fig. Below). Determine the magnitude and direction of $\vec{B}$ at the center C of the square.

  Magnetic fields are very useful in parti96(usw .;1pyiuhab x ncle 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 5.0 cm wide and has a magnitude of 0.33 T, by approximately what angle will a ben suxwb 6.(ay uh19i;pam of protons traveling at $ 1.0\times10^{7 }\,m/s;$ be bent?    $^{\circ}\,$

  The magnetic field B at the center ofrlca6 motg* ho ctgp321x7 3t+ a circular coil of wire carrying a current I (as in Fig. Below)2lxg* tc3 p6t moa3orgh7+ct1 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;4k19h3zaum:q xb 47rfd )whh q nfbn+eld 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 nnm.(k jj(o:a produced by overhead p.( noakj njm(:ower lines. You estimate that the two wires are each about 30 m above the ground and are about 3 m apart. The local power company tells you that the lines operate at 10 kV and provide a maximum of 40 MW to the local area. Estimate the maximum magnetic field you might experience walking under these power lines, and 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 9(yf jfk)5z1ldby 5 cdof electrons, traveling to the right at akfz y9ycbdl )(551fj d 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 spiq,k1dhv jgb:* ral path through a gas in a magnetic field of 0.010 T, perpendicular to the plane of the spiral, as shown in (Fig. Below). In two successive loops, at points P anddv:h ,g*1kqb j 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 magneti42q outx.eg5 86whprwc field at its center2p urh o8. weq56tg4wx. If the maximum current is 5.7 A, how many turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, each of diameter ums;+zuas/v m t9s +s40.50 mm, carry the same current but in opposite directiont z uamsmss;+9+us v/4s. 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 uniform magnetrslezdo*n-pmu n2/4 8 ic 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$