A compass needle is not alwayde 4eo8 zsuf39lxbfph: ql7/-s balanced parallel to the Earth’s surface, but one7bhdluqe3f/p 4l s-:89ozxf e end may dip downward. Explain.

Draw the magnetic field lines around a stxlj t5tqtdonv ce 1: z3+d:g63raight section of wire carrying a current horizontally to the lttqon:+v:e dz363 jg5dc txl1 eft.

In what direction are the magnetic field lines su(awx7oot ly8ns ++ckwt ,s:2irrounding a straight wire carrying a current that is moving dire 7wlxk(wta: tc+2 ys+ios,8noctly away from you?

A horseshoe magnet is held vertically with theq2qpdym+ rht v); 6c-e north pole on the left and south pole on the right. A wire passing between the poles, equidistant from them, carries a current directly away from you. In what direction is th2vdp- 6qc+y hr;)mtqe e force on the wire?

Will a magnet attract ag,a3tpikt3 k; ny metallic object, or only those made of iron? (Try it and see.) Why is this so3g;t ip t,kak3?

Two iron bars attract each other no matter which ends are placed close tog5wxr4)*djr hi.u/ q bkether. Are both magnrij wrkx./q 54bu*)dhets? Explain.

The magnetic field due to currec( nwygr6l8pqi g61*6 ho vg3rnt in wires in your home can affect a compass. Dis rhi* 1 r(3n8g qg6pvwo6y6cglcuss the effect in terms of currents, including if they are ac or dc.

If a negatively charged particle enters a region of uniform magnetic field lo w2k weqjzx hyi)j.8 d5z.34which is perpendicular to the particle’s velocity, will the kinetic energy of the particle increase, decrease, w yj4.xoilw83zh )ez .5 qk2djor stay the same? Explain your answer. (Neglect gravity and assume there is no electric field.)

In(Fig. Below), charged particles mov,vm o(uyu 01qbe in the vicinity of a current-carrying wire. For each charged particle, the arrow indicates the direction(,m ob0quyuv1 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.

Three particles, a, b, and c, enter a mai/oooazuj;um l/8i,q m 37la 4gnetic field as shown in Fig. 20–46. What can you say about the charge on ai 437ma,l/8;o/o ujzo q imlueach particle?

A positively charged particle in a nonuniform magnetic ye 2gp 3+:cu;9d ixk-fpv+jb ffield follows the trajectory shown in ip 2+x:f ufv-gcb;9jdyk +3 pe
(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 mv/5oyzd m7pk/2(g hz a magnet attract an iron rod? What must you conmkm 72pg5vh dz/yz /o(sider to answer these questions?

Explain why a strong magnet held near a CRT telev-e /,3jbrtr q2u yu)xyision screen (Section 17–10) causes the picture to become distorted. Also, explain why the picture sometimes goes completely black where the field is the strongest. [But don’t risk damage to your TV by trying this.][/But don’t risk damage to your TV b j-3e)tqyyxru 2r ub/,y trying this.]

Suppose you have three iron rods,zrkg*z;rt qnia9 c- 25 two of which are magnetized but the third is not. How would you dga ntik5*rz -czqr;9 2etermine which two are the magnets without using any additional objects?

Can you set a resting electron into motion with a magnatq:u ax 6y ;+qmemyff3qi xcb i5km:p84r(/, etic field? With an electric field? Explq5cy :r6t84bx3ym(i;kf apfaqiqu + me/:x m,ain.

A charged particle is moving in a circle under the influence of qs rf p3eua2n+ha 694b/ sb,pga uniform magnetic field. If an electricasu9s p f4aqerb+bhp,6gn/23 field that points in the same direction as the magnetic field is turned on, describe the path the charged particle will take.

The force on a particbhk/*t *cty)rle in a magnetic field is the idea behind electromagnetic 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*htcty k) /r*b 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 dir kuf-6wd.vw,.fk 0qd mected toward a horizontal wire carrying a current from left to right dffq,-. 0dwk6u. mwv k
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields thateq ad62wr +hr1 surround a moving electric charge.herq+wrd 621a

A charged particle moves in a straight tbz0nld wn0hp;mk )z *t+8v+x line through a particular region of space. Could thzm*dx 0lwt0 pn) nv+8t;+ khzbere be a nonzero magnetic field in this region? If so, give two possible situations.

If a moving charged particle is deflected sidewayy6ns3zv4m e /xs in some region of space, can we conclude, for certain,46y mx sn/e3zv that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space .+)nsj hdkhn i .9;qfuthere is a uniform magnetic field $\vec{B}$. Outside this region, B = 0 Can you inject an electron from outside into the field perpendicularly so that it will move in a closed circular path in the field? What if the electron is injected near the center?

How could you tell whether moving elemcgbvz936(ji pwul; /xi2u+w ctrons in a certain region of space are being deflected by an electri3wj +vi2;i9 ubw(pcz/um6 gl xc field or by a magnetic field (or by both)?

How can you make a compass witho:i.llse aj-i; hcan7exs+7s0ut using iron or other ferromagnetic material?

Two long wires carrying equal currents I are at ri+xz,nk; l5bb.j ob:c;(zm-zn(e .5sn l rh yiaght angles to each other, but don’t quite touch. Describe the magnetic folz-., (s xn:bm5 y( cr zha5obnzb.jni e;;+klrce one exerts on the other.

A horizontal current-carrying wire, free to movet.x(,feni8 k6lp dx 1iqi3pi ; in Earth’s gravitational field, is suspended directly above a second, p1 6i kp qxetpx8i(3ld.if;,niarallel, 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 + 1br0wssv 8yoweb0 a,an unmagnetized piece of iron?

An unmagnetized nail will not attract an unma1-3df aq 8csjilz57g hgnetized paper clip. However, if one end of the nail is in contact with a magnet, the other end will attrag3- l8ah5df s7 zicqj1ct a paper clip. Explain.

Two ions have the same mass, but one is singly ionizejoe 8*/ctf6kije:t(( oflz7zd and the other is doubly ionizz6j(:ifjzfo 8/elkeot* ( 7cted. How will their positions on the film of a mass spectrometer (Fig. Below) differ?

What would be the effect gjc12i mvyx/ )n/w ,nwon 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 to a solenoid is a relay . A relok a w /)phxdcr3n3t6c;b0c2vay 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 o0t/cwvcxpb3 ;2rh6)a k 3cndswitch 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 leng d hy56.tihsdijz) ,1tth on a straight wire carrying an 8.40-A current when perpend. it,6 yhh1tzj)5sd diicular 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 qg)h70st5;fm jp5 0hv qei;an4*t odut7wx-v of straight wire stretched between two towegu5fwdttvq0;*i0-757t x j)san4 qehpmh ;vors 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 x1+qo,xp i3/*p qv* duayih.h;b,cu j of the magnetic force on a 160-m length of straight wiredy3,.1oqpcqx*auv, ii ph/;b* u +x jh 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

  How much current is flowing in a wirey ot)s+b- 8bxu 4.80 m long if the maximum force on it is 0.750 N when placed in a uniform 0.0800-T fiely)8uxs+ bot -bd?    A

  A 1.5-m length of wire carrying 4.kdh v-ycyswk( y/d+/5 60slgp5 A of current is oriented horizontally. At that point on the Earth’s surf/p lyy gk-5y c/+ ds(k6wds0vhace, the dip angle of the Earth’s magnetic field makes an angle of 38 $^{\circ}\,$ to the wire. Estimate the magnitude of the magnetic force on the wire due to the Earth’s magnetic field of $ 5.5\times10^{ -5}\;T$ at this point.    $ \times10^{-4 }\;N$

  The force on a wire carrying 8.75 A is a maximumgp mi:ti-*6tl3-yzf)l r lz1r of 1.28 N when placed between the pole faces of a magnet. If the pole faces are 55.5 cm in diameter, what is the approximate tzrl-llrf6yt-i 3 pmg:zi )*1strength of the magnetic field?    T

  The magnetic force per meter on a wire is measured hl6h;lfmv3.v 9 zueq2 to be only 35% of its maximum possible value. Sketch the relationship of the wire and the field if the force had been a maximum, anqvvm9 2;. z6lhhe3luf d 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 maximum o 9 x)c:w so5x3gvrox8cf $ 6.50\times10^{-2 }\;N$ when placed between the pole faces of a magnet. The current flows horizontally to the right and the magnetic field is vertical. The wire is observed to “jump” toward the observer when the current is turned on.
(a) What type of magnetic pole is the top pole face?  ----待选择----North PoleSouth pole 
(b) If the pole faces have a diameter of 10.0 cm, estimate the current in the wire if the field is 0.16 T. $\approx$   A(retain one decimal places)
(c) If the wire is tipped so that it makes an angle of 10.0° with the horizontal, what force will it now feel?    N

  Suppose a straight 1.00-mm-diameter copper wire could just “float” 0q n6xvg jcn+l )hr yr7nas1)-horizontally in +6n) xn0)ayrrlgn7c h 1vsq- jair 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 chargewdryh 5c0l9 ,e $q\,=\,+2e$ 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 on an electr1q*)-ug +cheta/hp r(phty-h on 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 diagra:ce+0 xsex efi0e9x,im shown in (Fig. Below), where x+i, xsxfe0 0:i9e ece$\vec{v}$ (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 o/+xzotc me:+hyu qf4w+p7(6y t-lf hr f $\vec{B}$ 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 a spee -i9z2va 3qrdkd 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 8 x9sn2n s3/nchnu( pfenters a 0.20-T field, in a plane perpendicular to the field. What is the radius of it32hnpnnsnc u/xf (s89s path?    m

  An electron experiences the greatest for-g9pd5 x9i r x ,- r8grky)a7cn(nkwsrce 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 that go undeflected when passing thrz1ax a ox. kbyw4811cpough perpendicula axw. ckz184 op11baxyr electric and magnetic fields of magnitude $8.8 \times10^{3 }\;V/m$ and $3.5 \times10^{-3 }\;T$, respectively? What is the radius of the electron orbit if the electric field is turned off? $F_E$    $ \times10^{6 }\;m/s$ $F_{max}$   $ \times10^{ -3}\;m$

  A doubly charged helium vy5j5 4mf mf+*y mq/v-ec.sm aatom whose mass 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 yik h;2td4a6 3dlvj,ez y+kve (l7z)ja particle of charge q moving with constant speed v to make one circular revolution in a uniform magnet7,k e)ev(lz2zy46a; 3hj iv tlkjd+y dic 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 uniform qx4 rygjr9)f4 magnetic fieldg)r r xq9f4jy4 B. Show that its momentum is p = qBr .

A particle of mass m and chaz-)dh/ku3)ro69m : ldgpg v zkrge q moves in a circular path in a magnetic field B. Show that its kinetic energydd/6 gkz o-vmpl 3)gh)r9kzu: is proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momentu eayc /t.w,bodxpkyi8 12il0.m 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 perpendicular to the Earth’ r+ztbw- 3s 9s9w8o0(mewkcs ls magnetic 93 m8st0l+bow9wzsr cw- ks(efield of $5.00\times10^{-5}\mathrm{~T}$, If the bullet possesses a net charge of $13.5\times10^{-9}\mathrm{~C},$ by what distance will it be deflected from its path due to the Earth’s magnetic field after it has traveled 1.00 km?    $ \times10^{-7 }\;m$

  Suppose the Earth’s magnetic field at the equator has mhi u,d+f7+ zf.f9;m0 imartuy agnitude $0.40\times10^{-4}\mathrm{~Т}$ 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 g0wo 96 tcl7wispeed $\nu=2.0\times10^5\mathrm{~m/s}$ 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 starg +y7vclu9r72:+f)phibd)ynt u x3 spt a stalled vehicle carries a 65-A current. How strong is the magnetic field 6.0 cm away from it? Compare to the Earth’x+rhtf 7p+buuy:ig))sv2 d7 lc3p9 ny 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*e(lumi8j eh /2+rpis to produce a magnetic field no larger than that o8r plmh2 ujis i(+/e*ef 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 , .q a4kbx sxsxfh+e30guyutwew 8-pn6g 02g9the page toward you. Indicate, with a, 0n skyu0-sw qtp .362wxbaf 9gxx48u+eehggppropriate 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 upwarmfoi+(a*wwzo//4p:z q:vu :qo b) jlud 24-A current exerts an attractive force p:4o(iu l w+*w: uqfj obvo/m/azq:zp)er unit 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 force betw(t7eqw a kv21j3cr00w drcdk6een two parallel wires 35 m long and 6.0 cm apart, each carrying 25 A in the samc2wd (q 1e6r0w 3t0akc dvjk7re direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic field is being carried out 1.00 m from ;y3n nu+4+/v w, uxqoatf5jpc an electric cable. What is the maximum allowable current in the cable if the experiment is to be accurav/wa;xjc+,qo+nutnu53 pyf 4te to $\pm1.0\%?$    A

  A power line carries a current of 95 A alon u7(7pv6uvwyvpp 2ie9g the tops of 8.5-m-high poles. What is the mag6uvu 2epvpw77(v9yip nitude of the 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 wires 13.0 cmz/p wiru9nd17j2 or5ua/7 wc e 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. Below1aj /p57i dn79e/2czrworwu u ).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18 caznmd wjua* .e,t;z1 )m due south from a straight 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 this po wam ed,jatz1u)*n;.z int 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 v yq 6hixz6i55*8eelvof current due north. What is the net magnetic field 20.0 cm due west of the wire if the Earth’s field there points north buzyv8h66il5e*viq x5et 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 protoggrmit(ft2:k(f; n;y d o-la+ns passes a given point in space at a rate of $1.5\times10^9\mathrm{~protons/s~}.$ What magnetic field do they produce 2.0 m from the beam?    $ \times10^{ -17}\;T$

Determine the magnetic field midway between twyrc6bwvh; b31 o long straight wires 2.0 cm apart in terms of the current I in one when the other carries 15 A. Assume thh31b6bv rcw ;yese currents are
(a) in the same direction,
(b) in opposite directions.

  A long pair of wires conducts 25.0 A of dc current to, and frwvv 3tnxge2z3:o z s):60bnr zom, an instrument. If the insulated wires are ofzgrzw3: 30:2b)x6 tzv vnon es negligible diameter but are 2.8 mm apart, what is the magnetic field 10.00 cm from their midpoint, in their plane (Fig. Below)? Compare to the magnetic 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), par.5eiy h : c8tj)0utoi)rd7ps lallel and just to the right. If it carries 25.0 A upward, what force per meter of length does it exert on each of the other two wires? Assume it is 2.8 mm from the nearest wire, 0uri)h:5opyj.teicts d )l 87 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 23:u ln6 nxxmz1kp1)0fn.4fazh$^{\circ}\,$ 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 9 4b/0yw dkduusame plane as a straight wire, as shown in (Fig. Below). Thuyb4w d/d09kuere is a current of 2.5 A in both wires. Determine the magnitude and direction of the net force on the loop.    $ \times10^{ -6}\;N$  ----待选择----away from wiretowards wire 

  A long horizontal wire carries a current of 48 A. A seconi/h0 f7 2fkvudd wire, made of 2.5-mm-diameter copper wire and parallel to the first, is kep /27 fvhk0duift 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 dvki) (g/n c0uthat they are perpendicular to each other. At their closest, they are 20.0 cm apart (Fig. Below). What is the magnitude of the magnetic field at uv(inkd c/g)0 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 carr6y f9q(d;bz vwies 2.0 A current. Wire B’s current is 4.0 A qzf wvby9; (d6in 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 alone63r(e l ug,o)-gnzcdk4cy3 ng them, they are at three corners of an equilateral triangle.) The curr46, cey (-zelkdnc) ggn33uro ent in each wire is 8.00 A, but its direction in wire M is opposite to that in wires N and P (Fig. Below). Determine the magnetic force per unit length on each wire due to the other two.
$\frac{F_\text{M net y}}{l_\mathrm{M}}$ =    $ \times10^{ -4}\;N/m$ =    $^{\circ}\,$
$F_{N\,net}$ =    $ \times10^{-4 }\;N/m$ $\theta$ =    $^{\circ}\,$
$F_{P\,net}$ =    $ \times10^{ -4}\;N/m$ $\theta$ =    $^{\circ}\,$

  In (Fig. Below), determine the magnitude and direction of the magnetic fieldfa fxu2 ,1((kxn k7rrvpj5ce6 at the midpoint of the side of the triangle between wir1(, p rx aucn6f5(kevr j7kx2fe M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a distance d apart, carry equal currents I in wi-nr hx4:1p 2ng0e nwjg9 6efthe same direction. e 16i4w: 02h nenjpnwf9 -rgxgOne 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 cz2grd,t4 h0yj)pv j/l-,r sohurrent of 2.0 A. Calculate the field irj4ojpr v h dhl,z2),ygs /-t0nside near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameter is to produce a1wzb0.h 6nodsgj3 lz. field of 0.385 T at swzgl0o . 6h.ndz3bj1its 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 is 33 A. A 3.0-cm-long stra g+h*drnay7 eo5z-7ort+ * xbuight wire cuts td 7 *-x+ehnruaoz*+go t5ybr 7hrough 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 want to make a pract jrqe6 ;-4xpgrk o;lz:ical solenoid that produces the greatest possible magnetic field for a given voltage. Should you make your copper wire long and thin, short and fat, or something else? Consider other variables, such as solenoid diameter, length, a: poe4r;qg 6zk-l;rjxnd so on.

A toroid is a solenoid in the shape o/*ruo+ jag (amf a circle (Fig. Below). Use Ampère’s law along the circular path, shown dashed in (Fig. Below a), to determine that the ou*aj +ar/m g(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 conductors ofdtu+2d 62ykx- tbgvz/ a coaxi-dt ktdbgux+z v62y/2al cable (Fig. Below) is $B=\mu_0I/2\pi r$ if r is greater than the radius of the inner wire and less than the radius of the outer cylindrical braid.
(b) Show that B = 0 outside the coaxial cable.

  A single square loop of wire 22.0 cm on a side is placed with its face para8ppfi* x.oqys7a.ph6 llel to the magnetic field between the pole p*8xh7ayp6 o fipqs.p.ieces 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 deb6qd x1x4e 4edflects full 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 weakens by 25% over the yedwchg m,g(i/hw+h + mzt+9 ae7ars, what current will give full-scale deflag(mw ezc,w 7m9 +h+ h/gdth+iection if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by what factor does the output j0 iu/j+phigf:)xecpy -zb ux u8p7 3:torque chan8gcyppijxf u+0/-): b7:puzjeuhx3 ige?

Show that the magnetic dipole moment M of ad 3bamhw84 ,zxn electron orbiting the proton nucleus of a hydrogen atom is related to the orbital angular momentum L of the electron dh8xb,a m34zw by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 ulir -/sy2+ ejcm in diameter and containing nine loops lies flat on the ground. The Earth’s magnetic field at this location has magnitude2lj+ur i y-es/ $5.50\times10^{-5}\mathrm{~Т}$ 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 cirb9gbid0 t7 r+gcle of radius 5.10 cm in a 0.566-T magnetic field. What value of electric fieligb0g7t 9+db rd could make their paths straight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atoms have radii of curvagcvo + 4u)pj3tture equal to 21.0, 21.6, 21.9, 22.2, and 22.8 cm. The largest u)p4g+ovtcj 3radius 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 the15oqr. i u ei8rrtw;l1 mass spectrometer of (Fig. Btwor 8uq151.err i;i lelow) 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 monit ::xk5p:9*ac5xa,v krwti0 u myjvzq *or air pollutants. It is difficult, however, to separate mox*:vmkavcq5,0 ik5z*9x atyup :jwr :lecules 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( e+8 8+k (ednn nveyxta(nv8x they enter a magnetic field B. The ions are assumed to start from resev+xn(+8d(ety(e nv8xn a8kn t. Show that the mass of an ion is $m=qB^2R^2/2V,$ where R is the radius of the ions’ path in the magnetic field and q is their charge.

  A long thin solenoid has 430 loops of wire 9jaa e; :*o+xoc qrzq)per meter, and a 25-A current flows through the wire. If the permeabilio;ax+)q:ez o9 aj*rqcty 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 cmnhi*npp7/* d/w iwsp,x 4ej/a in diameter, and has 640 turns of wire. The magnetic field ini/ i4*wh*ne s,wx7nap d/ ppj/side the solenoid is 2.2 T when 48 A flows in the wire. What is the permeability $\mu$ at this high field strength?    $\times10^{-5}\mathrm{T}\bullet\mathrm{m/A}$

  Protons with momentum 4nvrat mos*z6mw663m$4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 entering a regiazte:s9go/v9jmgq;/u ; .tdz on of constant magnetic field. What is the ratio of the radii of their /q/9tj:d ozt;.g; me sug az9vcircular paths?   

  The power cable for an electric trolley (Fig. Below) carrieswf ;ixu1e(azg 62(s48q kdl:m pm+jtt a horizontal current of 330 A toward the east. The Earth’s mxa fp kg:lis u+w2jt(48 mz mq;16e(tdagnetic 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 acquir8m;7)cqb;l bjaq l15-ogmlkted 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 horizo,gk+ 8s:dd 3-amxw eakntally to the nortg+kdam3-x: ks8e,wd ah and has magnitude $B=0.50\times10^{-4}\mathrm{~T.}$ What should be the magnitude and direction for the velocity of an electron if its weight is to be exactly balanced by the magnetic force?    $ \times10^{-6 }\;m/s$  ----待选择----eastwest 

  A doubly charged helium ,mo) fu-0yfvm 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 showx,nz q.ob-vn3b3rcz z1m8s3/q+gqz c n in (Fig. Below). A large current moves in a closed loop composed of fixed rails, a power supply, and a verz,/c b.1xz cbzs+r 3nqzn8gqq -3vom3y 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 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 rdhnrw ,1-ds1q77yd7c 3myus 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 therw,sh1yud7d qsd1cmry773 n- two bottom wires is 95 A in each. Calculate the required current flow in the suspended wire.    A

Two stiff parallel wires a distance l aparmyjqnneak z6/6 +x,(rt in a horizontal plane act as rails to support a light metal rod of mass m (perpendicula6(,+y6 jz nanxqerkm/r to each rail), (Fig. Below). A magnetic field $\vec{B}$, directed vertically upward (outward in the diagram), acts throughout. At t = 0, wires connected to the rails are connected to a constant current source and a current I begins to flow through the system. Determine the speed of the rod, which starts from rest at t = 0, as a function of time
(a) assuming no friction between the rod and the rails,
(b) if the coefficient of friction is $\mu_k$.
(c) Does the rod move east or west if the current through it heads north?

  Estimate the approximate maximum deflection of the electron beam near the centhiux,v);ueu( yv,et ec, +t u2er of a TV screen due to t(,2) +uie vtcte,v yuhue,x ;uhe 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 eleme/ 9vx85a4wmww.w su/dxfc3ep ntary particles such as protons to high speeds. Particles starting at point A with some initial velocity travel in circular orbits in the magnetic field B. The particles are accel3f4/x ux8sde wwmpa9w.c 5vw/erated 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 parallef4 l.r za)8rpqs3/t5ki /nunwl wires, located at the corners of a square of sidn )wr.k5itf34a8qs/zpu nr l/ e l, carry equal 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 ffz yzjo:r9:0mm rehv;m m9 f2/or “beam steering”; that is, the magnetic fields can be used to change the beam’s direction without altering its o:r 9zzm:fmj m0ev9yhm r2f ;/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 centere;28dx iyrh5hnxt ;q 3 of a circular coil of wire carrying a current I (as in Fi eh;3y2hdrx n;58 tqxig. Below) 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 magnzqn /0n6zg3ft etic 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 e,s/8misvo9 qof the magnitude of magnetic fields produced by overhead power lines. You estimate that the two wi,s8sie mqo/v9 res 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 of electr7sie0 qrh:*xc rf 0nl1ons, traveling to the right at a : r 1eq0c70xishfn*lrspeed 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 *( jl:lkp2r4sibop7q 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. Calculate th qkipl4bp srl*7:o 2(je 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)m tetpa,)zh xld/2u1s78e 5 su az2vc sn.cs3 cm in diameter, is to produce a 0.30-T magnetic field at its center. If the maximum current is 5.7 A, how mals zu cpt/t2zs5suxm 3 ) ,7ne)1a82.echv asdny turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, each of diameter 0.50 k *a, wzx)nk,vmm, carry the same current but in opposite directions. They are suspended by 0.50-m-long strings as z*wxa)k vnk,, 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 fielc jja-pb5ft+; d 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$