A compass needle is not always balanced parallel to the Earth’s surface, e+ j vl:u-cn;hb3 :i zb 9c03*quu/cr:etgcjj but one end may dip un9;i z ljt3cvrhq0c:eebu cg /*-::cubj3 +jdownward. Explain.

Draw the magnetic field lines around a saq- ,gsbb t9q,traight section of wire carrying a current horizontally to -,9a,qbqg stb the left.

In what direction are the magnetic field lines surrounding a straight wire 4 m0 kp.co1r1efbfgpi) 24go)8ecr rccarrying a current that is moving directly g ro4bcop4rec ie1f2 ))p.8fk0c1gr maway from you?

A horseshoe magnet is held ve mt hmxlz;51b54z/va srtically with the north pole on the left and south pole on the right. A wire passing between the poles, equidistant from them, carries a currenxmtm 5sz4lv zhb;a/ 15t directly away from you. In what direction is the force on the wire?

Will a magnet attract any metallic object, or only those made of irlko).c6)c c gqajjg-f;a4qd ,on? (Try it and see.) Why g)46)o c.-aj,fqk glqaj cc;dis this so?

Two iron bars attract each other no matter which ends are placed vbk 6i,xxzy+vun09 w7close together. Are both mi6x,zv y+9nvb x 0ku7wagnets? Explain.

The magnetic field due to current in wires in your home can affect jgyfd 1ouj) *2,ku )mja compass. Discu*jj1ugod )mfk 2y)j,uss the effect in terms of currents, including if they are ac or dc.

If a negatively charged particle enters a regioe.v6j+4k8 - biuv5;ipwsbm hiwlz yj5y gf :9-n 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 electrhe j.f 69 i4k5vb+luzwgj:5-yp-ivym8; bsiwic field.)

In(Fig. Below), charged particles mo.qxdmkxo a 573ve in the vicinity of a current-carrying wire. For each charged particle, the arrow indicates the direction of motion of the particle, and the + or - indicates the sign of the charge. For each of the particles, indicate the direction of the magnetic force due to the magnetic field produced by k3d.a5mxo q7xthe wire.

Three particles, a, b, and c, enter a magnetics98t cwadl5 f4l/5pa 8fst d)l field as shown in Fig. 20–46. What can you say about the charge onf8 8d94/twl)5cts llfpdaas5 each particle?

A positively chargedo w5 qp+3x6pxs particle in a nonuniform magnetic field follows the trajectory shxx5q 6 sw3o+ppown 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 as pzsth)v2i x*c05m ;d magnet attract an iron rod? What must you considerm i ;css)vpzt5*xh20d to answer these questions?

Explain why a strong magnet held near a CRT television screen (Section 174 nnprf6lr1 zml01q5e8wz c)o.dqxh ,–10) causes the picture to become distorted. Also, explain why the picture sometimes ozcrnr6qph,4 en.m1w5l 0fl8x)1z qd goes completely black where the field is the strongest. [But don’t risk damage to your TV by trying this.][/But don’t risk damage to your TV by trying this.]

Suppose you have three iron rods, two of which are magnetized but 31ua ihz5,;rj v-gxagk*vsq; the third is not. How would you determine which ixvjav1u z rk*s;-aqgg 53; ,htwo are the magnets without using any additional objects?

Can you set a resting electron into motion with a magnetic field? With an e1yh8tbd l3co3sec umi6ct 4e ae-091flectric field? Explae1cmb0yocis3ct dft e8le39a-uh16 4 in.

A charged particle is moving in a circle up ent-m x;bz16nder the influence of a uniform magnetic field. If an electric field that points in the same directm6z1pbxnet; - ion as the magnetic field is turned on, describe the path the charged particle will take.

The force on a particle in a magnetic field is tnt+.mp g .m7jihe idea behind electromagnetic pumping. Imp+g t7jin. .mt 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 ions feel a force in the same direction?

A beam of electrons is directed toward a hoanayc xyp2( n9xi5n st3+(zt)rizontal wire carrying a current from left xns2n (a t9ci(ytp 5 n3y+)axzto right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields tit*0) 5y eft1t7 vmhjfhat surround a moving electric charge. *mf7t10ie5yt)vtfjh

A charged particle moves in a straight line/8 lkvvi;x0 ,7r( khnw4en euk through a particular region of space. Could there be a nuenr8i0,w hv xv74neklk k(/;onzero magnetic field in this region? If so, give two possible situations.

If a moving charged particle is deflehq1v:1out gewlv3s88 cted sideways in some region of space, can we conclude, for certain, thaw8qes1gvt vh o l38:1ut $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is a uniform magnetic fixq lqirpb576nm -w9il. ah))qp: uhk7eld $\vec{B}$. 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 spahc)l. q:wo r84 i d-wqtb:mip2ce are being:l8: icq 2)rwqmpi .-bodth w4 deflected by an electric field or by a magnetic field (or by both)?

How can you make a compasst)-c*-xpmh kz pk t2sy+ m/9ns without using iron or other ferromagnetic material?

Two long wires carrying equal currents I are ato1 )jds 5vym6d right angles to each other, but don’t quite touch. Dj do )1vd6y5smescribe the magnetic force one exerts on the other.

A horizontal current-carrying wire, free to move in Earth’s g1af8j mt pqu3s-gez 2)ravitational field, is suspendf 1a )3t8qj-m2segp zued directly above a second, parallel, current-carrying wire.
(a) In what direction is the current in the lower wire?
(b) Can the upper wire be held in stable equilibrium due to the magnetic force of the lower wire? Explain.

Why will either pole of a magnet attract anrr;mj dq05d*(s:cwpy unmagnetized piece of iron?

An unmagnetized nail will not attract an unmagnetized paper cprvmo *yd b *,uw/te;*qts-d7+a zl( sh;p/mqlip. However, if one end of the nail ismu7bazds -,*hm;v q+ to ;epd*(/w* tpry/lq s 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 t5cda9j +y9t8ru +1ji:tnzbl nhe other is doubly ionized. How will their positionnu8tj+jz 59ia1 y:b rdt9c+lns on the film of a mass spectrometer (Fig. Below) differ?

What would be the effect 5 zq/.zysmw 9dob q zv*/)trv1on 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 swdf+q gt7oa+0j: 89r hdltye:h itch similar to a solenoid is a relay . A relay is an electromagnet (the iron rod inside the coil does not move) which, when activated, attracts a piece of iron on a pivot. Design a relay to close an electrical switch. A relay is used when you nt:q9dh h + +djlg:rfo 8y7tae0eed to switch on a circuit carrying a very large current but you do not want that large current flowing through the main switch. For example, the starter switch of a car is connected to a relay so that the large current needed for the starter doesn’t pass to the dashboard switch.

  (a) What is the magnitude of the force per meter of : rf(k,izj( srmrx6z; length on a straight wire carrying an 8.40-A current when perpendicular to a 0.90-T uniform magnetic f j(zr,6z:k(;mxfri srield?    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 of straight wq.cda*p 5bh2e8ckfze7/ .d dy ire stretched between two towers carrying a 150- .d y25cfeed *cqb7pkd.ah/8zA 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 o8dowmgz90m) df straight wire stretchedmdwo9g 80 zm)d between two towers carrying a 150-A current. The Earth’s magnetic field of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  How much current is flowing in a wire 4.80 m long yb:sc 72dgho )arvh g5wml3:7if the maximum force on it is 0.750 N w mla wyg737):c2sbvhhg 5rod: hen placed in a uniform 0.0800-T field?    A

  A 1.5-m length of wire carrying 4.5 A of current is oriented horizontally1xsh hv;wj1n/3y4 hw jo zzz0jv92;kc. At that point on the Earth’s surface, the dip angle of the Earth’s mag20hx hjs j k 3wznoz1wvc /jz;94h;1yvnetic 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 maxim l k* w3rm/,7fbl4hmcnum of 1.28 N when placed between the pole faces of a magnet. If the pole faces are 55.57mfrm wcl/4lk3,* h bn 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 only 35% of its may:/fv sgvf+kg 8/ogq *ximum possible value. Sketch the relationship of the wire and the field if the force had been a maximum, and sketch the relationship as it acv/*:k g/qf fgo8yg+svtually is, calculating the angle between the wire and the magnetic field.    $^{\circ}\,$

  The force on a wire is a m qaff5qz,)7 xfsl rc(+aximum 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-dianx041ummu 9f ameter copper wire could just “float” horizontally in air because of the forcem xa u0f41mnu9 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 charghp 7*rew)w*w ktn +f7re $q\,=\,+2e$ 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 :fdim0 +r13qg:sd uh non 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 shown in (b*p1 kq8cb 6euFig. Belowkbp1b 8q 6uec*), 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 direction ofe 6wzh-iw z-w+y pof(4 $\vec{B}$ 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 wn3dj/ qqaj77-all1 bi ith 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, in a plane perpegb7- 8s fl-kbwndicular to thf- s7w- l8bgkbe field. What is the radius of its path?    m

  An electron experiences the greatest ford lr;u6i:ki1 9ma; qofce 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 electrons thatg0im: :jh;8w3 cjozes go undeflected when passing through perpendicular electric a h je038cg:;wijs mo:znd 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 mass isfoy1z-3to sq 6 $6.6 \times10^{-27 }\;kg$ 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 requiredeylwgkcu1 g:l,). h i( cvm-7q for a particle of charge q moving with constant speed v to make one circular revoluti,i7c u1w)qll cm v-y: gg(h.keon in a uniform magnetic field $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge q moves kgkzy0c s5t:7in a circular path of radius r in a uniform magnetic field B. Show thkyg 7sz5k:c t0at its momentum is p = qBr .

A particle of mass m and charge q moves in a circular path in a magnetic f0kd.fevytymkt. 0 22 )o5cbos ield B. Show that its kinetic energy is proportional to o. k.0d)oc 2 mt2v0fyskbety5$r^2$, the square of the radius of curvature of its path.

Show that the angularb8b- s 6+ida.ddtu a,f momentum 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 perpendic4+b g+ar f:2 na.1nm4ko wgdvuular to the Earth’s magnet1+:dgv m4gw.nn o2ua4r+b ka fic 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 magnef1n/x-pfdej*: 1 vfa gt kxf5+tic field at the equator has magnitude $0.40\times10^{-4}\mathrm{~Т}$ and a northerly direction at all points. Estimate the speed a singly ionized uranium ion $(m=238\mathrm{u},q=e)$ would need to circle the Earth 5.0 km above the equator. Can you ignore gravity? $F_B$    $ \times10^{ 8}\;m/s$ $\frac{F_B}{F_g}$    $ \times10^{8 }\;$

  A proton moving with spel zd+;3w 9wkkns o(s:led $\nu=2.0\times10^5\mathrm{~m/s}$ 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 ipum k/ li ;0+*cpb ,4.xlgi1mzre g o2.optb,a stalled vehicle carries a 65-A current. How strong is the mag *+ oei;ti,1op. mg04pl2c mz/bxbgkrupi.,lnetic field 6.0 cm away from it? Compare to the Earth’s magnetic field. $B_{cable}$   $ \times10^{-4 }\;T$ the field of the cable is about    times that of the Earth.

  If an electric wire is allowed to produce a magnetic field no lar7lo6 qua r,l.2aueyo2 e; owvksl:xa9:u8x s3ger than that ooq 69 ulu 8suolr32.xx; ee,ay::2vwao7kaslf the Earth $(0.55\times10^{-4}\mathrm{~Т})$ at a distance of 25 cm, what is the maximum current the wire can carry?    A

In (Fig. Below), a long straight wire carries current I out of the pag9 1jv)k,p av 8t8u,eonxfot7ae toward you. Indicate, 1e aoxov a, vuj,p88n)tf kt97with 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 carryingka 6y0j-e0 srm t9t7ru an upward 24-A current exerts an attractive force per unit lengt ms9taru 0rk7y-0t6ejh 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 p0c 3zz3 tlj*td2 xg*bt;ca0axj0ud o2arallel wires 35 m long and 6.0 cm apart,*0xat2zl g0tczj2 d3dat; ou3jc*0bx each carrying 25 A in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic field is being carriedn4cvuw nhe:v42(yja , out 1.00 m from an electric cable. What is the maximum allowable current in the cable if the experiment is to be accuratanvw4: e4chyv n2,uj(e to $\pm1.0\%?$    A

  A power line carries a current bul d moe:2d0n+bf/ ii724nkqof 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 with2m47n2bi :edbf0nqoi +uk /l d 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 1mi6jjn *my0kcm apart carry 25-A currents in the same direction. Determine the ma0*ij6j 1knmy mgnetic field at point P, 12.0 cm from 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 vertic0; /lwvr9r q3vyrms65e2c xocal wire carrying a 35-A current downward. In what direction does the compass needle point at this location? Assume the horizo 2y;5/ xrqr c vw9r6mces0lv3ontal component of the Earth’s field at this point is $0.45\times10^{-4}\mathrm{~T}$ and the magnetic declination is 0$^{\circ}\,$.    $^{\circ}\,$ N of W

  A long horizontal wire carries 22.0 A of curr/j:y5tr9,wtm 4x lj on 2ncvr-ent due north. What is the net magnetic field 20.0 cm due west of the wire if the Earth’s field there points nortx,:nj tylc 4/5w-2 mnotrjrv9 h 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 passes a given point in n-nvgq,cmx(94c6 bj zspace 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 betzbj69 7zo 8vdab/l*xtu;o im;ween two long straight wires 2.0 cm apart in terms of the o/m9;z6l u7iz;btdvbax j*8ocurrent 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, an,4hi93or9 ablcnua 0wd from, an instrument. If the insulated wires are of negligible diameter but are 2.8 mm apart, what is the magnetic field 10.00 cm from thawl9i c30h4 ubn9 roa,eir 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 p2 q+,nai gku3the plane 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 n2kpa+u 3iq ,gother 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 pointcdl*,+ :m ck*o nyhgar wk) 7ov-b;z7hs 23$^{\circ}\,$ E of N outdoors. However, when it is placed 12.0 cm to the east of a vertical wire inside a building, it points 55$^{\circ}\,$ E of N. What are the magnitude and direction of the current in the wire? The Earth’s field there is $0.50\times10^{-4}\mathrm{~T}$ and is horizontal.    A  ----待选择----updown 

  A rectangular loop of wire lies in the same plane as a straight witk7 u:l5bxs, kxpa yy8 4sp9v/re, as shown in (Fig. Below). There is a current of 2.5 A in both wires. Determine the magnitude and direction of the net force o/yb4:5, p xplutv8 s 9s7akyxkn the loop.    $ \times10^{ -6}\;N$  ----待选择----away from wiretowards wire 

  A long horizontal wire carries a current ofr8up2wrh. pl. 48 A. A second wire, made of 2.5-mm-diameter copper wire and paralllpr u2r8h.. wpel to the first, is kept in suspension magnetically 15 cm below (Fig. Below).
(a) Determine the magnitude and direction of the current in the lower wire.    A the current is to the  ----待选择----leftright 
(b) Is the lower wire in stable equilibrium?  ----待选择----not in stable equilibrium in stable equilibrium 
(c) Repeat parts (a) and (b) if the second wire is suspended 15 cm above the first due to the latter’s field.

  Two long wires are oriented so that they are perpendictuj:uc mj549a2i )yrmular to each other. At their closest, ta tu4m:ij 9)crj m2yu5hey 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 carries 2.3ms*4dlp4dt*h o5hg p 0 A current. Wire B’s current ishp3d4d5s p 4hm*l*g ot 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 from one another. (Looking along th*(7cb5cwg1xtq ;qeln em, 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 wires N and P (Fig. Below). Determine the magb x c;l(qgc7e*nq15 wtnetic 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), determiny(aei26 ;jmd je the magnitude and direction of the magnetic field at the midpoint of the side of the triangle between w6m(;deajy ij2ire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, as:szr cy17.o* ofk0eu distance d apart, carry equal currents I in the same dk*o.s cer: uyfzo 7s01irection. One wire is at x = 0, the other is at x = d, (Fig. Below). Determine $\vec{B}$ along the x axis between the wires as a function of x.

  A thin 12-cm-long solenoid has a totah qpsz,yx 2;1ql of 420 turns of wire and carries a current of 2.0 A. Caly 2xq1,pq;zhs culate the field inside near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameter is to pro;vsa:btr r0d1a 5 hp* zr9sj)yduce a field of 0.385 T at its center. How much current should the solenoid carry if it has 975 turns of the widtp5 zys*:v a9r0 );arhs jrb1re?    A

  A 550-turn solenoid is 15 cm long. The current in it is 33 A. A e pdp1dz .8-6wvjdil -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). What is the force on this wpe8divl z d-wp.16 -djire assuming the solenoid’s field points due east?    N

You have 1.0 kg of copper and want to make a practicawzr3.e6b c)vz l solenoid that produces the greatest possible magnetic field for a given voltage. Should you make your copper wire long and thinb.rvz6 e zw3)c, short and fat, or something else? Consider other variables, such as solenoid diameter, length, and so on.

A toroid is a solenoidn9 zb1gl9i k iee0d:k8 in the shape of a circle (Fig. Below). Use Ampère’s law along the ci ik1kl9bg ze9d:en 08ircular 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 between the conductors6 pj0rhws :ewn*rbvam8a q 7lz5(:op jf5x z39 of a coaxial cabl:3jrm5 pza0j 95*p r(sf 6wbvln azoe8w7xh: qe (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 ua(ekw nvb 43dt/z9:5pg ;btl ;pr)rjof wire 22.0 cm on a side is placed with its face parallel to the magnetic field between the pole pieces of (bgtz/d;pbvn j ;ut9a5w4lep:) krr3a 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 fom q370;ykk+dv7v aoo v2zc,ub r 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% ojmgovd d30xm9n7o : t 8v)0tv9.dg zxqver the years, what current will give full-scale 0x9nvmd t0v9d. mdq7 zo8 gxvto:j3)gdeflection if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by what factor does the o c5 8etfl xe:t0/yq ,nmdk1u-zutput torque changeczl,f/qx 0eye8tt 5:1m u nk-d?

Show that the magnetic dipole moment M of an electron orbiti506nyo 1qlah dqb7: ofng the proton nucleus of a hydrogen atom is related to the orbital angular momentum L of thef 1 lodn qqh7:ybao650 electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter and containing nine loops lies flat on te a6i :x80x.b lnpqs6fs+9aqkhe ground. The Earth’s magnei0qa9xpql6 :s68a fek.+s xbntic 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 in a 0.566-T magnetic fielod 9iyhj/ p*2id. What value of electric field c* ho yp2/iidj9ould make their paths straight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atoms have radii of curvature equal t+uns1:7ihd2q( ncumv o 21.0, 21.6, 21.9, 22.2, and 22.8 cm. The largest rad2qh1+n :iun m7d(suv cius corresponds to an atomic mass of 76 u. What are the atomic masses of the other isotopes?

  Suppose the electric field between the electric plates in the mass sd 9pp*t: a3)zk/1qob ,(d pfk1xdksls pectrometer of (Fig. Belowfap: 1to)zkb * /qd xl 3dssk9,pdp(k1) 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 difficult, h:1 auqc t:4itvowever, tot::q 41iucavt 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 before they enter z70 lye c9kcd:fc nr*8a magnetic field B. The ions are as :clr f8c9d zkey*nc07sumed 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 wir7*izlz+7 kulb e per meter, and a 25-A current flows through the wire. Ifb+ z*uklizl7 7 the permeability of the iron is $3000\mu_0$ what is the total field B inside the solenoid?    T

  An iron-core solenoid is 38 cm 6wtax d)r/jain8gygbmi ;bxf51,1w8long and 1.8 cm in diameter, and has 640 turns of wire. The magnetic field inside the solenoid is 2.2 T when 48 A flows in the wire. What is the )5xwyjt ng w16ia8 x/fmg,i; r1b db8apermeability $\mu$ at this high field strength?    $\times10^{-5}\mathrm{T}\bullet\mathrm{m/A}$

  Protons with momentucj g4ks1 g5ip,m $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ are magnetically steered clockwise in a circular path 2.0 km in diameter at Fermi National Accelerator Laboratory in Illinois. Determine the magnitude and direction of the field in the magnets surrounding the beam pipe.    T

  A proton and an electron have the same kinetic energy jr; 8avz1(.pes(wma hupon entering a region of constant magnetic field. What is the ratio of the radii r ae8(j ap(1;s. vwzhmof their circular paths?   

  The power cable for an electric trolley (Fig. Below) carries a horizontal y,q 63 l02)ezinyrda lcurrent of 330 A toward the east. The Eayi6,3q)lnzy l20 de rarth’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 whicd2 cyh1z+ x7rn+p6qpth has acquired a net charge of $1550\mu C$ and moves with a speed of 120 m/s perpendicular to the Earth’s magnetic field of $5.0\times10^{-5}\mathrm{~T}$.    $ \times10^{-6 }\;N$

  Near the equator, the Earth’s magnetic field points almost horizontally.2md6eaon jo 5 to the north and5no.ead62 moj 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, whck3:*n-ssphj )2w jz47oay xbose 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. Belowjdt )/x1e. ldj). 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 perpendicut1j)d .d jlxe/lar 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 wire is* -a1upilnl36ugonn9*b duz 4mo51no 1.00-mm-diameter 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. Calcu dgonu 65uu z134lm i1-nao*p*9bolnn late the required current flow in the suspended wire.    A

Two stiff parallel wires a distance l apar5/pfq5x lvz xfb5jiaq+.8*2g-pcvc. 0tnwlit in a horizontal plane act as rails to support a light metal rod of mass m (perpendicul.l5pzxtqjiv 2x f- ap0 q 5g*v/ +cw5nfi8.cblar to each rail), (Fig. Below). A magnetic field $\vec{B}$, directed vertically upward (outward in the diagram), acts throughout. At t = 0, wires connected to the rails are connected to a constant current source and a current I begins to flow through the system. Determine the speed of the rod, which starts from rest at t = 0, as a function of time
(a) assuming no friction between the rod and the rails,
(b) if the coefficient of friction is $\mu_k$.
(c) Does the rod move east or west if the current through it heads north?

  Estimate the approximate maximum deflection of the electron b d4+f zn8ylo)oeam near the center offyo dn +ol)48z a TV screen due to the Earth’s $5.0\times10^{-5}\mathrm{~T}$ field. Assume the CRT screen is 22 cm from the electron gun, where the electrons are accelerated
(a) by 2.0 kV,    mm(Round to the nearest integer)
(b) by 30 kV. Note that in color TV sets, the CRT beam must be directed accurately to within less than 1 mm in order to strike the correct phosphor. Because the Earth’s field is significant here, mu-metal shields are used to reduce the Earth’s field in the CRT.    mm(Round to the nearest integer)

The cyclotron (Fig. Below) is a device used to accelerate elementary :i;pex ky*)giparticles such as protons to high speeds. Particles starting at point A with some initial velocity travel in circular orbits in the magnetic field B. The particles are accelerated to higher speeds each time they pass through the gap between the metal “dees,” where there is an electric field E. (There is no electric field inside the hollow metal dees.) The electric field changes direction each half-cycle, ie*x gy:)p;i kowing 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 b2m9uk beu6o+ d9:n4 uuv/rk bwires, located at the corners of a square of side l, carry equal currentsrmuv:u d2 /9b46 +ken9u ubokb $I_0$ 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 d1/8swwjwpw ys 2b(l*) n z*mfuseful 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 prots m yjps*d*w (wf8zlb1wn2/w)ons. 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 capmsgr- iq786grrying a current I (as in Fig. B gmqg8rsip76 -elow) is
$B=\frac{\mu_{0} N I}{2 r},$
where N is the number of loops in the coil and r is its radius. Suppose that an electromagnet uses a coil 1.2 m in diameter made from square copper wire 1.6 mm on a side. The power supply produces 120 V at a maximum power output of 4.0 kW.
(a) How many turns are needed to run the power supply at maximum power?    turns
(b) What is the magnetic field strength at the center of the coil?    $ \times10^{-4 }\;T$
(c) If you use a greater number of turns and this same power supply (so the voltage remains at 120 V), will a greater magnetic field strength result? Explain

  Near the Earth’s poles the magnetic field is aboue1*ms:)ll8 kdh be:lut 1G($ 1\times10^{ 4}\;T$) Imagine a simple model in which the Earth’s field is produced by a single current loop around the equator. Roughly estimate the current this loop would carry. [Hint: Use the formula given in Problem 80.]    $ \times10^{ 9}\;A$

  You want to get an idea of the magnitude of magnetic fields produced by overh-x:-kfdsmsvm0rl* y 9ead 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,*fs0rm lx-vdm yk 9:s- 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 ma,(78;bak y6hi:aab nfw fua ut4; n6r,l tm*rfke a beam of electrons, traveling to the right at a t f(4 nf rwm8 ;6yuu7ia nt,ah;ba*frl 6,akb: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 throu4 b9t4e/ronk kgh 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 and Q, the radii are 10.0 mm and 8.5 mm, respectively. Calcuk4 4okr /bnet9late 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 v5dlalkj4fgl6 1t/jkz*yzj7f.v 15 (wd; hcxa 0.30-T magnetic field at its center. If the maximum current is 5.7 A, howc.f;dz(71yv*jl jg4/hlka x k5f wzld5tj1v 6 many turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, each of diameter 0.50 mm, kbfb :;,1m5g2s hduzi2 7exvacarry the same current but in opposite directions. They are sus;h bia7g 1 z52sfb v2:ed,xumkpended 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 unyd, x:*db dx s en s(h1tkj-gc6y,v(8jiform 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$