A compass needle is ce 7c6c4v ezn0not always balanced parallel to the Earth’s surface, but one end may dip downward. 406nz7ec vce cExplain.

Draw the magnetic field lines around z3vtzwl5+d 3zqbol48e pnw 42a straight section of wire carrying a current horizontally to nd wel54q+ 8bo lwzp4zv3 23ztthe left.

In what direction are the magnebedi9i :dvs6s6iar:re 6ybga0 a/+ v)tic field lines surrounding a straight wire carrying a current that is moving direasy9ve/ air60biir :+d:ve6 )asbg d6ctly away from you?

A horseshoe magnet is held vertically with the northkd gb*wyj;q m,jilf*sz/2 e) 1 pole on the left and south p/b leji *gmdz1j yqwf,s k;*2)ole on the right. A wire passing between the poles, equidistant from them, carries a current directly away from you. In what direction is the force on the wire?

Will a magnet attract any metalb 4eloy-/ qfyvhmg6j0fc2d:)lic object, or only those made of iron? (Try it and see2ojqd0vfcy :ym6-e b4 )fglh/.) Why is this so?

Two iron bars attract each other no matter ocyvtnrv:1-i dj j/qs*-: 9gj which ends are placed close together. Aj jvs:yn/- :oid9-qt cv*gj1r re both magnets? Explain.

The magnetic field due to current in wirey1,i.n b /n1 :poqjh9jud wrv.s in your home can affect a compass. Discuss the effjr9njbnhpq idy, 1v: w. ou1/.ect in terms of currents, including if they are ac or dc.

If a negatively charged particle enters a regio(kaith(y7c . wn of uniform magnetic field which is perpendicular to the particle’s( (wt.akh7yci velocity, will the kinetic energy of the particle increase, decrease, or stay the same? Explain your answer. (Neglect gravity and assume there is no electric field.)

In(Fig. Below), charged particles move i s 99ia4zh-gzsnq*vr +n the vicinity of a current-carrying wire. For each charged particle, the arrow indicates the direction of motion of the particle, and the + or - indicates the sign of the charge. For each of the particles, indicate the direction of the magnetic force due to the magnetic f +ig9zsvra-4z h9qs*n ield produced by the wire.

Three particles, a, b, and c, enter a magnetic field as shown i 1qq,wbfw o8e5 ;ytb4ln Fig. 20–46. What can you say a,le1b5tw 4q;q fobwy8bout the charge on each particle?

A positively charged particle in a nonuniform magnetic field folln c.krp;xno ntk vqql,(m*,47 ows the trajectory sh4n oxk(;m, n*r.7c k,ptqqlvnown 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 iron rod? Wj4 n.hsq -.d kypyo,t9hat must you consider to answer thesejsy9h.oqk 4p-.ynd,t questions?

Explain why a strong magnet he; mfugaer)(,w ld near a CRT television screen (Section 17–10) causes the pict ,)u;mfr wa(egure to become distorted. Also, explain why the picture sometimes goes completely black where the field is the strongest. [But don’t risk damage to your TV by trying this.][/But don’t risk damage to your TV by trying this.]

Suppose you have three iron rods, two of w7l;)2oevywp /qsa l; *mc (axkhich are magnetized but the third is not. How would 2kc7lslp o*( e;;xa)a yvmqw/ you determine which two are the magnets without using any additional objects?

Can you set a resting electron into motion with a magesfi(o3. +y a -84tbtbp-aca onetic field? With an electric field? Explaifobp-4its3-+bet (o. aa ayc 8n.

A charged particle is moving in a circle under the influence of a u,i u 09-ofs2qu ke3dcde4/ pihniform magnetic field. If an electric field that points in the same direction as the magnetic field is turned on, describe the path the charged particle will t 0c /ief -khsdq49u,3ped i2uoake.

The force on a particle in a magnetic field is the idea behind electromg 9tl5,mb0 5koifb yj5g8nvh4agnetic pumping. It is used to pump metallic fluids (such as sodium) and to pump blood in artificial heart machines. The basic design is shown in(Fig. Below). An electric field is applied perpendicular to a blood vessel and to a magnetic field. Explain how ions are caused to move. Do positive and negative vyhl45gt8 oif5j059kgbnm, bions feel a force in the same direction?

A beam of electrons is directed toward a horizontalr9)ykszm plym b:pb9h/ds0 ++ wire carrying a current from left to rig h 0:rky) d+smp9mlsy9b pb/z+ht
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields that surround a moving electric chargnltwt /b,5rlg2: iu2oe.nt ogblw,/:5ilt r 2u2

A charged particle moves in a straight lin a)w8up5xg rg0)cs2 kue through a particular region of space. Could there be a nonzero magnetic field in this region? If so, give two possible situa)u spu)kwcx0a2 g 58rgtions.

If a moving charged particle is deflected sideways in some region of space, ccw (bkqbzk4(6 5) lzfjo9ea9nan we concludeb 4k5nb )aqzo6 w cezfj9(k9(l, for certain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is a uniforxk+p kkpnb4yrf5: sd(dlmm )(o s1q/4m 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 sp *z/sni1ig6jyan+s 3 lace are being deflected by an electric field or by a magnetic field (or by bls1y saz ij+gn3*n 6/ioth)?

How can you make a compass n .i0 hn,ffd.ywithout using iron or other ferromagnetic material?

Two long wires carrying equal currents I are at right angles to 9ygdcm :it9f ,;wf smz8z*-tteach other, but don’t quite touch. Describe the magnetic forsd; w8*9c,f: zgty -zmimtt9f ce one exerts on the other.

A horizontal current-carrying wire, free to move in Earth’s gravitational as rnbsokacd .xwp;;c* .8o27g ,g7 emfield, is suspended directly above a second, parallel, current-carrm;gxocnew 7gaok7p ;rb 2,*css ad8.. ying 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 attractuo)nu m(xq 2x8xc/-g4rf(fodih pq 57 an unmagnetized piece of iron?

An unmagnetized nail will not ./znixzn j:gmr0(zd*5 (dru oattract an unmagnetized paper clip. However, if one end of the nail 0rjuz ndod 5 :(./zzg( rnim*xis in contact with a magnet, the other end will attract a paper clip. Explain.

Two ions have the same mass, but one is singly ionized and the other is doubly r+ 9 ixqev hfchibdp9;u (:/6gio96fhg:vqx/idc( ;iru9beh +p nized. How will their positions on the film of a mass spectrometer (Fig. Below) differ?

What would be the efcdx +( 83fw5f9v hpfuofect on B inside a long 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 toz y:ikw,sy(*y x ;stfk 5j)ze9 a solenoid is a relay . A relay is an electromagnet (the iron rod inside the coil does not move) which, when activated, attracts a piece of iron on a pivot. Design a relay to close an electrical switch. A relay is used when you need to switch on a circuit carrying a very large current but you do not want that large current flowing through the main switch. For example, the starter switch of a car is connected to a relay so that the large current needed for the starter doesn’t passy;t9j xkiz)fkywe5z:sy * (s , to the dashboard switch.

  (a) What is the magnitude of the forcfmw4p* wqd5rs8dt 6y3e per meter of length on a straight wire carrying an 8.40-A current when perpendicd3sw6t8yf *q54wmpr d ular 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 magnitud71;x u5h tvlwke of the magnetic force on a 160-m length of straight wire5xw7v tkluh 1; stretched 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 160-m length of straight wire0gm rvf4fx1piz xnmt- 7) 5ub, stretched betx -vmfgz 75utb 4pn1mi),xf0r ween 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 /hqo *)srb8rz3ny1yl.80 m long if the maximum force on it is 0.750 Nzb8yh nyor3) qr1s*l/ when placed in a uniform 0.0800-T field?    A

  A 1.5-m length of wire carrying 4.5 A of current is oriented t +b*6ek2f jpm5s fs; tlt.qz):zyjt/ horizontally. At that point on the Earth’s surface, the dip angle of the Earth’s magnetic field makesstp5tl6k tb/: j ;2sjzze y*)mtf+qf . 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 8cj41avq wtng +* qm6ktg,c5:f.75 A is a maximum of 1.28 N when placed between the polg4kwv+jq nt5 6t:cqa*f1c g m,e faces of a magnet. If the pole faces are 55.5 cm in diameter, what is the approximate strength of the magnetic field?    T

  The magnetic force per meter on a wire is measured to be ,ue 2njgz: 4kuonly 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 itzk2:euu,j 4ng actually is, calculating the angle between the wire and the magnetic field.    $^{\circ}\,$

  The force on a wire is a maxiek3f 3 ec+20dhfx0f ylmum 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 “floatzfpwmam l/y4 y: xu,-*” horizontally :4/map f xu,myl* z-ywin air because of the force due to the Earth’s magnetic field $\vec{B}$, which is horizontal, perpendicular to the wire, and of magnitude $5.0 \times10^{ -5}\;T$. What current would the wire carry?    A Does the answer seem feasible? Explain briefly.

  Alpha particles of charge/ 24zxxu u6shu $q\,=\,+2e$ and mass m = $ 6.6\times10^{ -27}\;kg$ are emitted from a radioactive source at a speed of $1.6 \times10^{ 7}\;m/s$. What magnetic field strength would be required to bend them into a circular path of radius r = 0.25 m?    T

  Determine the magnitude and direction of the force ob qjf6eb -o* 2kd(3myyn 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 diagram sho12*lobb ;r1wrsi u; :p x)vtucwn in (Fig. ib:ro p ;v 12rbu ;w)lxus1tc*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 directi,yz1qo2o.d ;yli xc9p+xd b8non 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 vertically upward with*nv, i,r(lwupl- x n;z 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) pxh)(;mrz/z vgl+vm 8 oroton enters a 0.20-T field, in a plane perpendicular to the field. What is th+/xgm;(r8 vzoh )l mvze radius of its path?    m

  An electron experiences the gre vlqq)ftz39s *atest 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 ofeajzi4ua 1* a90da lm1 a beam of electrons that go undeflected when passing through perpendicular electri4z9lm d1aueja a1a*0i c 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 mak, h; g+hzs fp+z2hsg9ss 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 i)toj/sykczqg,pggyfa:y +3i+5.7 brequired for a particle of charge q moving with constant speed v to make one circular revolution in a uniform magne./+zi) 3bq7 jf, yg5 sag tpiygo:ykc+tic field $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge q mouc .12 w(7x-( npq ak:0s/jmj uxhyasdves in a circular path of radius r in a uniform magnetic field B. Show that its momentum /uk(aqxxy0a 1 m2jpw.s( j:7nhsd-cu is p = qBr .

A particle of mass m anduxig9l q,44mm charge q moves in a circular path in a magnetic field B. Show that its kinetic energy is proportional to m 4gq4xiul,9m$r^2$, the square of the radius of curvature of its path.

Show that the angular momenj /z2qp rca8sa0h: f7htum of the particle in Problem 21 is $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves with a speed of 160 m/s perpenpl*4bn0axeig7pa ,x3s t2g84(i 5xsh ae ajq1dicular to the Earth’s magnetic field 8gi s5 17sa4e*0bt xgil2p ea h(4 x3pnjqax,aof $5.00\times10^{-5}\mathrm{~T}$, 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 they5+k f)n6dpwd 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 sp6 4mxb1 k ,)heqx-( akt d(p(jiuwxn2reed $\nu=2.0\times10^5\mathrm{~m/s}$ 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-A current. How2e yhsxc4/fg 0 strong is the magnetic field 6sc g/f2hy x40e.0 cm away from it? Compare to the Earth’s magnetic field. $B_{cable}$   $ \times10^{-4 }\;T$ the field of the cable is about    times that of the Earth.

  If an electric wire is allowed to produce a magnetic field no largem. */mv;va/) wvtnaltr than that of thvl/.)t v;w*mt va ma/ne 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 m;a9nczkgy 18 carries current I out of the page toward you. Indicate, wi1ga9 8czk;y mnth appropriate arrows, the direction of $\vec{\mathbf{B}}$ at each of the points C, D, and E in the plane of the page.

  A vertical straight wire carrying +,okln0t:uigm p/ob 9 an upward 24-A current exerts an attractive force per unit lengtb0n/o 9 :ipg u+tk,olmh 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 directz-f1x re* ufe8ion of the force between two parallel wires 35 m long and 6.0 cm apart, each carrying 25 A in the same di1-8eu*zf frx erection.    N  ----待选择----attractiverepulsive 

  An experiment on the E; ;aqo) gswab0arth’s magnetic field is being carried out 1.00 m from an electric cable. What is the maximum allowable current in the s bw;ag;q)o 0acable if the experiment is to be accurate to $\pm1.0\%?$    A

  A power line carries a current of 95 g7e;mhd ;xyjuj- iy2, A along the tops of 8.5-m-high poles. What is the magnitude of t7y;d;h-jg,i2x ujme y he magnetic field produced by this wire at the ground? How does this compare with the Earth’s field of about $\frac{1}{2}G$?    $ \times10^{-6 }\;T$ The field of the cable is about    % that of the Earth.(retain two decimal places)

  Two long thin parallel wiresm*bkno* cy/(qt e87zl 13.0 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(Fig. B* z*lm(ct7 q/ bokney8elow).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18 cm due south from a straight( c/y 2/7 wmi zouznrhf3z8jh4 vertical wire carrying a 35-A current dr/2u7 fzy cm8zh iow34/j(hz nownward. 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 4 vtg7 jdo43iy2fy2, jnwvsc* 22.0 A of current due north. What is the net magnetic field 20.0 cm due west of the t4y4w v3 7*i, vsc2gfjon2djy wire if the Earth’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 pa2v c0;e m-gd1adjcwc 3e7qpl-sses 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 c7 pkzpv- fp9.cm apart in terms of the current I in one whenpvc 7 -pfz9.pk 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, andzmjf x/16jad8, z (gqw from, an instrument. If the insulated wires are of negligible diameter but are 2.8 mm apart1 6j aqx/z fdwjm(8g,z, what is the magnetic field 10.00 cm from their midpoint, in their plane (Fig. Below)? Compare to the magnetic field of the Earth.
   $ \times10^{-6 }\;T$ The field of the wires is about    % that of the Earth.(retain two decimal places)

  A third wire is placed in the plane of the two wires showmj60i2scxl -hs h+/4)dm y hi ff*jg5nn 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 5m fg2c f*4h jxi-s6ynhh+isdl0j/m) 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 cpyeg (q/lv8; 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 sa8k h)qhro/e5k me plane as a straight wire, as shown in (Fig. Below). There is a current of 2.5 A i8khhkr5/qo )e n 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. lw;c; fgsa0 *yA second wire, made of 2.5-mm-diameter copf;* wl;yscag0per wire and parallel to the first, is kept in suspension magnetically 15 cm below (Fig. Below).
(a) Determine the magnitude and direction of the current in the lower wire.    A the current is to the  ----待选择----leftright 
(b) Is the lower wire in stable equilibrium?  ----待选择----not in stable equilibrium in stable equilibrium 
(c) Repeat parts (a) and (b) if the second wire is suspended 15 cm above the first due to the latter’s field.

  Two long wires are oriented so that s vw(ov 0n2/ pzak/.ukthey are perpendicular to each other. At their cloz2o(v k.u wp/n0sa/v ksest, 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 one carries 5.0 A?    $ \times10^{-5 }\;T$

  Two long straight parallel wires are 15 cm apart. Wire A car(rkvwx +u9w0qries 2.0 A current. Wire B’s curr wv09krwx+u (qent 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 o-e / m-z1:afglr7z oa3.8 cm from 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 wire M is opposite to that in wireaze m 1-zfag7-/:oorls 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), determiney4 um/qp3g1nx the magnitude and direction of the magnetic field at the midpoint of the side of43xgn m1y/q up the triangle between wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, cg, 7vm.pu4w0 okkog*ra35 ofera; ;sa distance d apart, carry equal currents I in the same direction. One wire is at x = 0, thef ew43. ,7ups ror*0 oom;kgacva;gk5 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 ck9 nnux zn5:dvba6)y-arries a current of 2.0 A. Calculate the field inside near the center. zy-)v:adu5nn9b n6kx    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in d2zdsw2j (j9zc b 6 incrun;(26vd.pbziameter is to produce a field of 0.385 T at its js 2z 9c z(jw66ncrb;i p(bdvu2d n2z.center. How much current 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 g5c1kz-abbw ,jp srbm809g4 dib:zu .is 33 A. A 3.0-cm-long straight wire r.gu 4gzbi-:91d ,b bpja0cs5kwz mb8cuts through the center of the solenoid, along a diameter. This wire carries a 22-A current downward (and is connected by other wires that don’t concern us). What is the force on this wire assuming the solenoid’s field points due east?    N

You have 1.0 kg of copper and wqxhrh5)ns/ ,eant to make a practical solenoid that produces the h )5/x,sehrqn 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, length, and so on.

A toroid is a solenoid in the sh-: nooi 5ri,jdape of a circle (Fig. Below). Use Ampère’s law alon5j- d,ro: ioing the 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 magnetic field bwq hbfqs) +9mnlv)rb q. gwfv+d(7:i/etween the conductors of a coaxial cable (Fig. Bef+h7q+v (nqvsirmq:d)gb /w f bl9 w).low) 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 4ej,;fkal/2ptfc n 7g with its face parallel to the magnetic field betw ,a fgt2c ;l/7pfejn4keen 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 f(abq oe17q x6zor a $53.0 -\mu A$ current. What current will give full-scale deflection if the magnetic field weakens to 0.860 of its original value?    $\mu A$

  If the restoring spring of a galvanometer weakens by 25% o c2 y6,vqg1jqlr;i h:over the years, what current will give full-scale deflection if it original2h61 cvgqy;rq ,:ojlily required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 1tj -3g o+zb:k1 9 wrfif:0lyur2%, by what factor does the output torque changjrwo+rf0 itg:f:1yz -b lu k93e?

Show that the magnetic dipole moment M of an electron orbiting the proton nucleu rmw2 p-ey(p*/7iwwrzg97 wc7uco4 ldslcd*pz m g ( yew2w7urp-79w7/rowc4i of a hydrogen atom is related to the orbital angular momentum L of the electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter and containing nine loops 72 olt/mlm h ud;muv8,lies flat on the ground. The Earth’s magnetic field at this locatio,m7duo l 2/hvt8;lummn 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 in a 0.566-T magnetic fielcwk,- atkv* 1md. What value of electric fiel,*-twkkc vam1d could make their paths straight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germaninaiz x19it9c yj,1 rao4e6 ,iqum 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 ato,te1i1 aini9 4,q6 jo9xyzcramic mass of 76 u. What are the atomic masses of the other isotopes?

  Suppose the electric field 1/i+c um/ 0u6hei:wf,u4 5y y;oexf9x pumlad between the electric plates in the mass spectrometer of (Fig. Below) is fmu/ xe/1ae:lmioi u, 5ypfcuw06xh 9u4dy;+$2.48\times10^4\mathrm{~V/m}$ 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 bwp)/hb 0* sbwh0znr 9aeing used to monitor air pollutants. It is difficult, however,/wspznr a 0h9b)bhw*0 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 ions by a voltage V .wjz afu p g1ndh;q;d8 ck5(r(before they enter a magnetic field B. The ions are assumed to start from rest. Show that the mass of an id; g(a q8z;5ju.wpk(f1crdhn on 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 meterf*8mu-prrp 6 fw(z cy4, and a 25-A current flows through the wire. If the permeability of4c p*68fru prm (f-zwy 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 640 tu6rjyzaz 4 nh;e /ym;rr1;di.rrns of wire. The magnetic field inside the solenoid isjyr n .zrym ze;1ai;/r 64;dhr 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 momentur,e tlk8h6jw+d 7e2 ekm $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 saieh8t3 y 7drh p-:/+fp v+)lclf8 pcivme kinetic energy upon entering a region of colpehpdv ) +hrvf 8yf-pi7c3i8 l:c+t/ nstant magnetic field. What is the ratio of the radii of their circular paths?   

  The power cable for an electric trolley (Figw1s7u2zeisfh7kr 6 : l. Below) carries a horizontal current of 330 A toward the east. The Earsez ukwf1h2 il776s :rth’s magnetic field has a strength $5.0\times10^{-5}\mathrm{~T}$ and makes an angle of dip of 22$^{\circ}\,$ at this location. Calculate the magnitude and direction of the magnetic force on a 15-m length of this cable.    N the force on the wire is  ----待选择----southerlynortherly  and   $^{\circ}\,$ above the horizontal .

  Calculate the force on an airplane which has acquired a net charu 3isey1kp6k5 +wc su3ge 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 Ear(y :qb/f hdl qag)2d)dth’s magnetic field points almost horizontally to the north and ha hdy fq() l)g2:aqdbd/s 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 heli;8tj 9 .zx3olk ueg.sosu nz81um atom, whose 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 (Fig. Below). A la10( ww nmpfsd+rge 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 mpw(nw 1+0fsd 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 wire is 1.00-mm-diameter copper 8lxha+ o v0xw)ava(+*venih *s6 uen7 wire and is suspended in air due to the two magnetic forces from thlnxe7h*vs)+ nwo8+*eav6u vxa( 0hai e bottom two wires. The current flow through the two bottom wires is 95 A in each. Calculate the required current flow in the suspended wire.    A

Two stiff parallel wi: hbxvx(f5wrsi z8(9 kres a distance l apart in a horizontal plane act as rails to support a light metal rks:r8i(vxz9f xw (5hbod of mass 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 macefz4ejyqlp f( ;1 rc6q7/ d;uximum deflection of the electron beam near the center of a TV screen duz ce (6;7j1/e;l pfdcuf4qyqre 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 accelerate elementary jw px05c+ fnp-n 3nqd4particles such as protons to high speeds. Particles starting at point A with some initial velocity travel in circular orbits in the magnetic field B. w0jpp3c 5fn4 dnx+nq-The particles are accelerated to higher speeds each time they pass through the gap between the metal “dees,” where there is an electric field E. (There is no electric field inside the hollow metal dees.) The electric field changes direction each half-cycle, owing to an ac 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 corn 4)tgf/ ih5hseers of a square of side l, carry equage th4h5) /ifsl 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 very useful in particle accelerators for “beam steeri,2ax6 g nggh4hg:qo +) bagv8nng”; that is, the magnetic fields can be used to change the beam’s direction without alteringg:42gnqaah+ 8vo6h g , xgn)bg 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 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 a c5) tnh ua;)c2yzaeb9wurrent I (as in Fig. Below) ehnb5w;a )) y2atu9czis
$B=\frac{\mu_{0} N I}{2 r},$
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 mal9d x+o40 ssmt:g.nfvla, n r9gnetic 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 the magnitude of magnetic f r.k-tj-s pur7ields 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, and comrt ks-ur7j.p -pare 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 of electrons, traveling tox mmvlat 0,h3ea6er0) the right rle hm3a6xt0ev,)m0a 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 magnetic fidhc);l xr7cj) kb3t:aeld 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 the change in the kinetic energy of the proton as it travels from P to ) : )trdjc;lcxk a73hbQ.    $ \times10^{-20 }\;J$

  A 32-cm-long solenoid, 1.8 cm in dibj13y pzg: cd )6s3ytiameter, is to produce a 0.30-T magnetic field at its center. If the maximum current is 5.7 A, how many turns must the solenoid h33 :cjsdzg6 yt ipb1)yave?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, ey0yv*5i /ujb1qbgijt*dt:,yl pjb 08ach of diameter 0.50 mm, carry the same current b /btjlt :8ij*yq,* 0vbbg5u yi0y1jd put in opposite directions. 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 magnetic field B =19py aah64l3a w cub+o 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$