A compass needle is not always balanced parallel to the Earth’s surface,vyeiu8 /j.i-p:kz k o: v 637yeymjyk+ but one eeie76-/y:uvk yv+ y 3 y8imjo.zk:pkjnd may dip downward. Explain.

Draw the magnetic field lines around a straight section of wiszox7d49f;u pre carrying a current horiz fuds9ox4; zp7ontally to the left.

In what direction are the magnetic field lines 7)tdux7-1lb w fpz :omsurrounding a straight wire carrying a current7bfzw :tm7)u lxp1d- o that is moving directly away from you?

A horseshoe magnet is held v0pcsvo +o 64al) 8ifgvertically with the north pole on the left and south 6svo08ca4vi)o gp+l fpole 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 metallic object, or onush3ll nh4dk5ys4y6yb 14b ;nly those made of iron? (Try it and see.u 46yynyb4 l5 dksn 41bhsh;l3) Why is this so?

Two iron bars attract each other no matter5l oi s2ukc6z r1n;8nm which ends are placed close together. n21n5c6 m8l ;iruzsko Are both magnets? Explain.

The magnetic field due to current in wires in your4p98 t fvp;nhzvzm 70g home can affect a compass. Discuss the effect in terms of currents, inzvz f;7pv 94m8n0ht gpcluding if they are ac or dc.

If a negatively charged particle enters a region of uniform mvxx:gir m x)u4(i b1r (lbl7f9agnetic field which is perpendicular to the particle’s velocirxbmuxbl i:(x179lgfr i v) (4ty, 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 in the vicinity of a cuh)ij bdvl/c1m1a -tx*rrent-carrying wircltbj) h/1mdvi-xa* 1e. For each charged particle, the arrow indicates the direction of motion of the particle, and the + or - indicates the sign of the charge. For each of the particles, indicate the direction of the magnetic force due to the magnetic field produced by the wire.

Three particles, a, b, and c, enter a magnetic z5b9h2fmhin 8vkd5zc 16f8 p wfield as shown in Fig. 20–46. What can you say about the charge i1289vpn mwhzz65 k f8db5fchon each particle?

A positively charged particle in a nonuniform magnetic field follows the trajeakjm6g5i1f b/ ctory shown16mjkg5 a/ibf 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 mrx znufnjf v,12hyb.u,s2 +w7 agnet? Can a magnet attract an iron rod? What must you consider to answer these,2wuufybs n7+n, 12xf.vzjh r questions?

Explain why a strong magnet held near a CRT tev61s 78 nwdczd39oqx q. cwdl+levision screen (Section 17–10) causes thcwvqd8 6 9cwd 7 n.1lo+sdxq3ze 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 by trying this.]

Suppose you have three ir ko7z;0+d6y hi(qbpf 6ygl+ubon rods, two of which are magnetized but the third is not. How would you determine which two are the magnets witbfpy07l g+ku;+od6yqih6b z (hout using any additional objects?

Can you set a resting electron into motion wituiwxn:) + . 9hh9rlgbvh a magnetic field? With an electric .g hhxin9v:+b )lwr9u field? Explain.

A charged particle is moving in a circle under the influence of a uni f*otdt 8;ujht8.8h 2xpo c-noform magnetic field. If an electric field that points in the same direction as the magnetic field is turned on,t-ntoho88 .*x;hd2t p cuj8of describe the path the charged particle will take.

The force on a particle in a matahlc/fq/i;cju8ryn a3 2+v 5gnetic 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 a magnetic field. Explain how ions are qnv+3lc5i/far jac;/u y th28 caused to move. Do positive and negative ions feel a force in the same direction?

A beam of electrons is directed toward a horizone*g7;ae;v ss7u (tbw ktal wire carrying a current from left to ri;b;w7gskts (e e *v7aught
(Fig. Below). In what direction is the beam deflected?

Describe electric an+( ou7t/3 a1fzfntmmqd/or magnetic fields that surround a moving electric charge.tfqo 317/aum( n +tzfm

A charged particle moves in a straight line through a particular raysp*q kq 9w02q.8dq mg )k.9jv(ecqoegion of space. Could there be a nonzero magnetic field in this region? If so, give tw.q9v.o*2 mk9 8(w ykj0gpcqe )qqa sdqo possible situations.

If a moving charged particle it5r02f(::q bn scnyoxs deflected sideways in some region of space, can we conclude, for certain, s trycnnxb20 fo5q:(:that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is a uniformr aj*p qi/m *yx;up:0o 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 electqb a4v 1rav 6,lqis)s(u. qi808cnqftrons in a certain region of space are being d ivuiqsb )q aq .l(,8nc1sft846r 0vqaeflected by an electric field or by a magnetic field (or by both)?

How can you make a compass without using iron or other ferromagnethnjpe-:wz+ phd w*e7eu53mq 7ic material?

Two long wires carrying equal currents I are at righ,wdiqx +y p;wi8z -2a3muser. t angles to each other, but don’t quite touch. Describe the magnetic force one exerts on the othiis rzm.3w uwa pd+xe82y-;,q er.

A horizontal current-cf5:hvbzs0t w)it+2t narrying wire, free to move in Earth’s gravitational field, is suin0 t2t:zf5vwst+h )b spended 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 an unmagnetizedct:4wxhc/ .nu8*, c)uz h oqta piece of iron?

An unmagnetized nail will not attract an unmagnetized paper clip. However, iffm nuyub9v:0z)nr1e 5 one end of the nail is in co n91u: 5 yn0z)burfmventact 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 i)0a;z- l, llmactf ;fte7t eh(s doubly ionized. How will their positions on the fi;7h;lz(c)t0ft -etllf ae,ma lm of a mass spectrometer (Fig. Below) differ?

What would be the effect on B inside a long solenoidx)- 68 kenzmvu n6:ht5d,d hbs 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 relaymek6 :rgsmb; . 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 re sm6:k;mr.be glay 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 pass to the dashboard switch.

  (a) What is the magnitude of the force per meter of e oyy):v/r+cn8c/ dgb length on a straight wire carrying an 8.40-A current when perpendicular to a 0.90-T uniform magneencyc god//) b:rv8y+tic 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 e6m 8ba ;3xqita 160-m length of straight wire stretched between two towers carrying mx ta;b3q6ei8 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 le+ i 4t*o:gmfi7ix,lgbngth of straight wire lii*img:+ tfgo 7b,4x 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 wire to/ hh*d a+lqx) ttz c2 jn.v :09jk-jvu+rhc94.80 m long if the maximum force on it is 0.750 N wx)c0 ldu*t -9:h+2vhckt. h+tozjvqjn 9ra/j 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 horizontally. At+ oiry4p)gusdr x)4foi94c e,sjb9s* that point on the Earth’s surface, the dip angle of the Earth’s s j4x9y*obsgup,4r )io)+9 e 4srifdcmagnetic 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 8.75il049pxa +ly0lgl 8jcq(cd0j A is a maximum of 1.28 N when placed between the pole faces of a magnet. If the pole faces are 55.5 cm i8q0 (4il l0jyjplcxgcd l+90an diameter, what is the approximate strength of the magnetic field?    T

  The magnetic force per meter onz-+) crrmv wx* a wire is measured to be only 35% of its maximum possible value. Sketch the relationship v-z*+rxr wc m)of the wire and the field if the force had been a maximum, and sketch the relationship as it actually is, calculating the angle between the wire and the magnetic field.    $^{\circ}\,$

  The force on a wire iv;t m i(u r3 z,:/o4e udn.;pxbe:fxwvs a maximum of $ 6.50\times10^{-2 }\;N$ when placed between the pole faces of a magnet. The current flows horizontally to the right and the magnetic field is vertical. The wire is observed to “jump” toward the observer when the current is turned on.
(a) What type of magnetic pole is the top pole face?  ----待选择----North PoleSouth pole 
(b) If the pole faces have a diameter of 10.0 cm, estimate the current in the wire if the field is 0.16 T. $\approx$   A(retain one decimal places)
(c) If the wire is tipped so that it makes an angle of 10.0° with the horizontal, what force will it now feel?    N

  Suppose a straight 1.00-mm-diameter copper wire could just “float” horizon l ig:de4a ae4w(1 och58jd8bvtally in air because of the force due to thejh 4c w8dd5oi:le av ageb1(84 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 7 un5qwa ha)4s$q\,=\,+2e$ 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 directim g wdlf(;f7zlp*lzds/h*+5k on of the force on an electron traveling $ 8.75\times10^{5 }\;m/s$ horizontally to the east in a vertically upward magnetic field of strength 0.75 T.    $ \times10^{-13 }\;N$  ----待选择----NorthSouth 

Find the direction of the force on a negative charge9 z 8nboxsjmg58f bjw b045k6m for each diagram shown in (Fig. Below), where wf om5z 0k4s889jgbbmb 5j6 xn$\vec{v}$ (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 directioncdg ff-5v,l)ea ,-9 jwi p1lbx 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 vegngf:k47 5 ujrrtically upward with a speed of $1.7 \times10^{6 }\;m/s$ into a uniform magnetic field of 0.350 T that is directed horizontally away from the observer. Describe the electron’s path in this field.    $ \times10^{-5 }\;m$

  A 5.0-MeV (kinetic energy) proton enters a 0.20-T field, in a plane peb 7znety* op: eo74o1orpendicular to the field. What is the radius pez7en4oo o7:yb*1 t oof its path?    m

  An electron experiences the greatest force as z( .jtoxor0p)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 electrooo r,3zlru4oo6bxie9n 8/k 6nns that go undeflected when passing through perpendicular en6, l3roo94 86n xizu/r boeoklectric 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 whosm88 /b)nmg(ct zzk ei;e 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 a particle of charge q moving wit c1 6 dbzqp/w/he;luy3h constant speed v to make one circular revolution 3/; wey zuqcd/ph6bl1in a uniform magnetic field $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge q moveanh uj9v65r*9o b,qn as in a circular path of radius r in a uniform magnetic field B. Show that its mome* a9nhqv,5abr jun6 9ontum is p = qBr .

A particle of mass m and charge q moves in a circular path in a4tp0m vepi+ m;b4zf4a/wgw l2 magnetic field B. Show that its kinetic energy is proportional to 4;vf/bepwplw 0am2+g4mzi t4 $r^2$, the square of the radius of curvature of its path.

Show that the angular mom ;to yngamm86p;3w08b fres 8jentum 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 lyb:6r p2q5ix m/s perpendicular to the Earth’s magnelq56ib :2yxp rtic field of $5.00\times10^{-5}\mathrm{~T}$, If the bullet possesses a net charge of $13.5\times10^{-9}\mathrm{~C},$ by what distance will it be deflected from its path due to the Earth’s magnetic field after it has traveled 1.00 km?    $ \times10^{-7 }\;m$

  Suppose the Earth’s magnetic field at apl5hf jc. okmtp0-u5aiv/3: 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 sn,yck6bjy . 6npeed $\nu=2.0\times10^5\mathrm{~m/s}$ 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 vehipko qtang8 i zw38k1:r6. 8 0scgiii0acle carries a 65-A current. How strong is the magnetic field 6.0 cm away from it? Compare to the Earth’s magnetic field.0n p0zg ogkk :1 iras6qai.it8 8i83wc $B_{cable}$   $ \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 larger tha3nwyxmq w b e,8j3hzc52 ;6b6hxp cj.cn that of the Eq,e6h3bb w j58 xy2xn6j czmw3.;chpcarth $(0.55\times10^{-4}\mathrm{~Т})$ at a distance of 25 cm, what is the maximum current the wire can carry?    A

In (Fig. Below), a long straight *q7pey 5ibw4u ywym :*kz7-hiwire carries current I out of the page toward you. Indicate, with appropriate arrows, the dip5w yh*i:y-7emqbi y7w4z u*krection of $\vec{\mathbf{B}}$ at each of the points C, D, and E in the plane of the page.

  A vertical straight wire carrying an upward 24-A current exerts an atc 0jt1a- ; y*; ryn;wbkttju0ftractive force per unit lja;fr; ;tb0 kt-tuc jy0*w yn1ength 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 yzgx6je*72gvc4wz *hly ;w/aof the force between two parallel wires 35 m long and 6.0 cm apart, each care7*yx /2;y4 av 6hjzwlgg*cwz rying 25 A in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magneti (eqd qo oz;*0f.txc2,e(ns pkc field is being carried out 1.00 m from an electric cable. What is the maximum allowable current in the cable if the exps0 f,tqe(qeopcnx. ;zkd 2*o(eriment is to be accurate to $\pm1.0\%?$    A

  A power line carries a cur ( rypj f fr5x+v5.1k.zhbjr3 zr,g6gcrent of 95 A along the tops of 8.5-m-high poles. What is the magnitude of the magnetic field produced by this wire at the ground? How does this compr+.g(k5j1ghy5vz6 frz b,.r3 cp jfx rare with the Earth’s field of about $\frac{1}{2}G$?    $ \times10^{-6 }\;T$ The field of the cable is about    % that of the Earth.(retain two decimal places)

  Two long thin parallel wires 13.0 cm apar+clvkn7a00oc.wb wd; t 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(Fb7v0l0c; c+an wdok.wig. Below).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is pl,c5r,m9 ez (us dyzj5:4hffr n,lh9-j )zbguwaced 18 cm due south from a straight vertical wire carrying a 35-A current downward. In what direction does the compass needle point at this locaw5j, -s h,dugzf,4ej99:f rnu l(z bh5myr)cztion? 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 22.0+cup0 ;p./ lzt,jrzcidp*4 ro A of current due north. What is the net magnetic field 20.0 cm due west of tpz, *+/.r;cr jzou 0ptdp4 liche 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 passes a given point in space at,. n2i0neqhfnzk(h1/ n7l mio 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 2.0dsajq(/p4(qod js6f(k ) awu( cm apart in terms ouwd (f jka64/qjp qd)os(sa ((f the current I in one when the other carries 15 A. Assume these currents are
(a) in the same direction,
(b) in opposite directions.

  A long pair of wires conduc7 w yt6ur *x/6nkr6hspts 25.0 A of dc current to, and from, an instrument. If the insulated wires are of negligible diameter but are 2.srr6kht p7x u 6n/6*yw8 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 (Figrfw 9wyms7p6wfss0 tv2g0k1 (. Below), parallel and just to the riww1p s fyk7mvs2s09 (wr60tgf ght. If it carries 25.0 A upward, what force per meter of length does it exert on each of the other two wires? Assume it is 2.8 mm from the nearest wire, center to 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 3oh7 fazpy6a ysb6 r.zjdybf 9/4 5*.v.thwpo23$^{\circ}\,$ 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 wire, huc8*g: j nj(das shown in (Fig. Below). There is a current of 2.5 A in both wires. Determine the magnitude and direction of the nec(8j dhjgu*n :t 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 secoqed /j yckb8+d 6mz92unpomjhd*m:5 0w*vd w 0nd wire, made of 2.5-mm-diameter copper wire and parallel to the first, is kept in suspension magnetically 15v0q96dd8pdj*ymb+ 2o*wnd 5e u:/wck0 m jmzh 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 perpw jobb40hl-m +endicular to each other. At their closest, they are 20.0 cm apart (Fig. Below). What is the magnitude of the magnetic field at a point midway ob+0-4mbwjh l 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 2.0 A current.f ywnz)w*4hv 7 Wire B’s current is 4.0 A in tvnh7f4w) zw *yhe 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 them, thec31 fr lk wca-vcf52*9vo vki.y are at three corners oc 3vw2v5*vc9c1fk- a.f korli f an equilateral triangle.) The current in each wire is 8.00 A, but its direction in wire M is opposite to that in wires N and P (Fig. Below). Determine the magnetic force per unit length on each wire due to the other two.
$\frac{F_\text{M net y}}{l_\mathrm{M}}$ =    $ \times10^{ -4}\;N/m$ =    $^{\circ}\,$
$F_{N\,net}$ =    $ \times10^{-4 }\;N/m$ $\theta$ =    $^{\circ}\,$
$F_{P\,net}$ =    $ \times10^{ -4}\;N/m$ $\theta$ =    $^{\circ}\,$

  In (Fig. Below), determine the magnitude and dxb*9ozwe/zr m,ds )5eirection of the magnetic field at the m ,mer5zw)eodz 9b/s x*idpoint of the side of the triangle between wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a distance d apart, carry equ :e*oh38 h wh8o:+2rjk)pfqabclw 8skal currents I in the same direction. pb h:qe:*w8asfhj)ch +r83 ol28kkwoOne 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 wiremxf 0n gk8ay4svf)1m2f, qi /m and carries a current of 2.0 A. Calculate the field inside near the ce4m,mqf /m fna)fv ik8gs2x1y0 nter.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameter is to produce zp9ol,iimy7h5n82sg (h g5gr a field of 0.385 T at its center. How much current should the solenoid carry if it has 975 turns of the wire? n2i( gg,olmyh hi8 p57 5zsrg9   A

  A 550-turn solenoid is 15 cmut sh9 /3vyfb1 long. The current in it is 33 A. A 3.0-cm-long straight wire cuts through the center of the solenoid, along a diameter. This wire carries a 22-A c syf3bhv1t/9uurrent 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 practical solenoid that pro:tbue)o2dhh6dj f (6rduces 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, suc eot6) h2rjh:b uf(dd6h as solenoid diameter, length, and so on.

A toroid is a solenoid in the shape of a circle (Fig. /bg91j6/ot55srwe r tt b u,ksBelow). Use Ampère’s law along the circular path, shown dashed ss1/rbttbj gok,e9/ 55ur w 6tin (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 conductors of :a gfx4rslo /cza:+- ja coaxial cable (Fig. Be:lf4g+r-s/ o :zxj acalow) 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 q9 t v.f)ds mt d9;dykir*o42uvbf6;t 22.0 cm on a side is placed with its face parallel to the magneti.4 d9vri*m d2qt9 ub;kov6f tts;)yfd c field between 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 deflect wrym/ofigfs7:.2r74: encu1bg (n dis 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 wear,eqe2uz0 y.gkens by 25% over the years, what current will give full-scale deflection if it originally0ygr2u ., ezeq required $36-\mu A$ ?    $\mu A$

If the current to a motoh (daj 28rj (yb/v:qfhr drops by 12%, by what factor does the output torque chanry/jqhj fbd(a v28(h :ge?

Show that the magnetic dipole moment M c( 1gf )qgm:piof an electron orbiting the proton nucleus o:f pcmiq)g1 (gf 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 lies flat on thn1d x4o+ hm k7m-uxy;ue ground. The Earth’s magnetic field at this locatioknx7udm-+ ohumxy4; 1n 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 magbch0no3c ey qzt*0v p79+48xi fqp /dznetic field. What value of electr4v p8q zfz3 cyxbicnht/epq*+90od 7 0ic field could make their paths straight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium ato3 gv x6fvsy:uw x 6g*.qscu,.zms have radii of curvature equal to 21.0, 21.6, 21.9, 26gs yq.u3v*w :,c u.fxzxg6 vs2.2, and 22.8 cm. The largest radius 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 spectrqataxe c *w o *oao28xtu9y-f1ls6 e;0ometer of (Fig. Belo; wl e* q92atf-8y*0 uaaxotooxe6s1cw) 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.*jp zrkk. 6wwec+ 1y0i It is difficult, however, to separate molecules with nearly equal mass such as C j wcikp*6+r1zky e.w0O (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 befot,: fn;qlsra.6prf 5u re they enter a magnetic field B. The ions are assumed to start from ren ;tl ,rfrsa6f:.5 puqst. Show that the mass of an ion is $m=qB^2R^2/2V,$ where R is the radius of the ions’ path in the magnetic field and q is their charge.

  A long thin solenoid has 430 loops of wire per meter, and a 25-A current flbrhb t:8 c4 k.dqn*ov7ows through 4d: o t8kvhbbnq*r7 .cthe wire. If 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 ,h gpa gva45d3e,1 zaacm long 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.g3pv1aa hzea,5gd a,4 What is the permeability $\mu$ at this high field strength?    $\times10^{-5}\mathrm{T}\bullet\mathrm{m/A}$

  Protons with momentum q o*)caukq 5s3$4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 electrow q7qzk8ofgwrah8) +(n have the same kinetic energy upon entering a region of constant magnetic field. What is the ratio of the radii of their co kqg7h8r)fw+ z(a q8wircular paths?   

  The power cable for an up1u xv*f -y5- k*qofqelectric trolley (Fig. Below) carries a horizontal current of 330 A toward the e--*vuy1 p fquqkx*5foast. The Earth’s magnetic field has a strength $5.0\times10^{-5}\mathrm{~T}$ and makes an angle of dip of 22$^{\circ}\,$ at this location. Calculate the magnitude and direction of the magnetic force on a 15-m length of this cable.    N the force on the wire is  ----待选择----southerlynortherly  and   $^{\circ}\,$ above the horizontal .

  Calculate the force ozs:: b. tu:jedn an airplane which 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 )4 p4faoay5rmapzh18+ndw a3 h39 pzsEarth’s magnetic field points almost horizontally to the north and has m )fpawphasz5p +9mh3azd any r814 34oagnitude $B=0.50\times10^{-4}\mathrm{~T.}$ 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 hele ;r*j jl(gh11 qba8vtium 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 aw-8gn) bbm/wyymg) 7shown in (Fig. Below). A large current moves in a closed loop composed of fixed rails, a power supply, and a very light, almost frict)) m 8anbwgwm/b- y7ygionless 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 1.00-mm-diameter copper wire az y8 * ;y 1au5eewql6(aamah6znd is suspended in air due to the two magnetic forces from the bottom two wiresu (5y* ea6; zezaam6lah18wq y. 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 apez6xu5 ; /qksw ;o1*gwag5vres a distance l apart in a horizontal plane act as rails to support a light metal rod of mass m (perpendicular to each rail), (Fig. Bel*;ww au5z g;s1/ e6avqxkgp 5oow). 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 maximumdpt3q)+ 0q uz(7x1;mt.qb)bxrui szj deflection of the electron beam near the center of a TV screen due to the Ez d bjqp3t1);m7)t+ix.zus 0q(buqxrarth’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 acceleratah,-ff/a9m eoe elementary 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 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 electricfm/ fa-hoea,9 field inside the hollow metal dees.) The electric field changes direction each half-cycle, owing to an ac voltage $V=V_0\sin2\pi ft,$ so that the particles are increased in speed at each passage through the gap.
(a) Show that the frequency f of the voltage must be $f\,=\,Bq/2/pi m,$ where q is the charge on the particles and m their mass.
(b) Show that the kinetic energy of the particles increases by $2qV_0$ each revolution, assuming that the gap is small.
(c) If the radius of the cyclotron is 2.0 m and the magnetic field strength is 0.50 T, what will be the maximum kinetic energy of accelerated protons in MeV?

Four very long straight parallel wires, located at the corners of a square oljg 6ua ics(14f side l, carry equu64(ls a1 jgcial 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 acceleraxm9ueo; 6b 9hntors for “beam steering”; that is, the magnetic fields can be used to change the beam’s direction without altering its speed (Fig. Below). Show how this works with a beam of protons. What happens to protons that are not moving with the speed that the magnetic field is designed for? If the field extends over a region 5.0 cm wide and has a magnitude of 0.33 T, by approximately what angle9;9mhu b6nx eo will a beam of protons traveling at $ 1.0\times10^{7 }\,m/s;$ be bent?    $^{\circ}\,$

  The magnetic field B at te tbtd cfs2/ j:8zcrf02hi5n*he center of a circular coil of wire carrying a current I (as in Fig. Belo/8 2dcb: i*2thzjcfnt 5r0 fsew) 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 abo2v 5s8z08u qdlmlrb65q0 kmpo ut 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 produ0f +fz8qs gy9qip/ vp-ced by overhead power lines. You estimate that the two wires are each about 30 m above the ground and are about 3vf+s09p 8g p/ziyfq q- 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 electrons, traveline +xhu7ssi r46 vj/f*zg to the right atrzs6 vufj 7e +/sh4x*i 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 ulzne 8dgt/ppa.zfai3 pxc 3 vva.:yi40; k12path through a gas in a magnetic field of 0.010 T, perpendicular to the plane of the spiral, as shown in (Fig. Below). In two successive loops, at points P and Q, the radii are 10.0 mm and 8.5 mm, respectively. Calculate the change in the kinetic enerek4a nzpxc3d ;t :faa3v/2.u 8 ii pg.ypl1vz0gy of the proton as it travels from P to Q.    $ \times10^{-20 }\;J$

  A 32-cm-long solenoid, 1.8 cm in diameter, i sp8x57g 4fequs to produce a 0.30-T magnetic field at its center. If the maximum current is 5.7 A, how many turns must the solenoidqus efp7x48g5 have?   $ \times10^{4 }\;turns$

  Two long straight alu6.j aeck .cb;m ;:i 0mjzhnpe/minum wires, each of diameter 0.50 mm, carry the same current but in opposite directions. They are suspended by 0.50-m-.je:na; .;0 pbh/6imecm jzcklong 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 = 0.k9ka0p0 m, z/q1 uius vp+8ert23 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$