A compass needle is not always balanced parallel to the Earth’exhf 2;u.wt o71hd mrc(g(nz0 s surface, but one e( g zc7h mentur0wd; 21.foh(xnd may dip downward. Explain.

Draw the magnetic field lines around a straight secaoodb9c8z u2. tion of wire carrying a current hori 8ad2z9ob. cuozontally to the left.

In what direction are the magnetic field lines surrounding a straight wire ca *;lek-;2bmwi2x qy rj5st0x drrying a current that is mojse 2 b;x2qdt;05 ri-* lymwxkving directly away from you?

A horseshoe magnet is held vertically with the north pole on the left and s t5vl 4zo8-1pingncp4 ;w4ui(qud*zxouth pole on the right. A wire passing between the poles, equidistant from them, carries a current directly away from yq n 4ipz5-zd *u(iot n44g8 pwxv1;cluou. In what direction is the force on the wire?

Will a magnet attract any metall hx fnvwzbkjq77*;w p6:vp 57qic object, or only those made of iron? (Try it and see.)6vj57zkf* v w pbqphx:7qw; 7n Why is this so?

Two iron bars attract ;vbi:wnld69 r 3li yd iv1o8q fir;f91each other no matter which ends are placed close together. Are both mag;nrrd iyvi; f 6 9v1obiwq:dl1li9 3f8nets? Explain.

The magnetic field due to current in wires in your home can affecax.0r 2,xza v8+zv zdvt a compass. Discuss the effect in terms of currents, inc 2+d.vxa0,r vxazz8v zluding if they are ac or dc.

If a negatively charged particle en nldu4rcs-s.g /dd(o 1ters a region of uniform magnetic field which is perpendicular to the particle’s velocity, will the kinetic energy of th 4gsdd(-/d1rcn sl.uo e particle increase, decrease, or stay the same? Explain your answer. (Neglect gravity and assume there is no electric field.)

In(Fig. Below), charged particles mo rxa)ymlpe0-y(-g /n3 qnhv1mve 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 particlnn)yq yxhr3 g0a-p/l e1 vm(-mes, 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 field as e0 lpbu/ez2/y wh 0:7vyi, ycbshown in Fig. 20–46. What can you say about the char0 : ycbb /ip/yy7zvheeul,0 w2ge on each particle?

A positively charged kwcp gst n86 ev)t73s5particle in a nonuniform magnetic field follows the trajectory shown in gps7 kvc3)s5n wt t8e6
(Fig. Below). Indicate the direction of the magnetic field everywhere in space, assuming the path is always in the plane of the page, and indicate the relative magnitudes of the field in each region.

Can an iron rod attract a magnet? Can a magnetjdfa hui9; 53d attract an iron rod? What must you consider to answer these queshfu;5aj3i dd 9tions?

Explain why a strong magnet held near a CRT television screen / zd9tgb1/ds *dh5uc b(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 yo9/duc bs/dh5tb* zd 1gur TV by trying this.][/But don’t risk damage to your TV by trying this.]

Suppose you have three iron rods, two of wo 07.b6agbri az, duc3hich are magnetized but the third is not. How would you determine which two are the magnets without using any add7cz uo,0riabd 3. gba6itional objects?

Can you set a resting electron into motion with a magnetmz45: vxzhv)pj. z9cdic field? With an electric )v 4.d5mjx:pzzhzc9 vfield? Explain.

A charged particle is moving in a circ+jxk ;ii :v1lcle under the influence of a uniform magnetic field. If an electric field that points in thxciv; k ji:+l1e same direction as the magnetic field is turned on, describe the path the charged particle will take.

The force on a particle in a magnetic field iv1jd,s:28 g arocwv3i a.+ vyis 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 perpev+ 2 a r.yc:wvsv8 ,dii1oajg3ndicular 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 direct04smukbi/+ (mc+e. s ki3rslb .;ye yued toward a horizontal wire carrying a current from leftcuy 3ms+b s(0; + .i is4km/breuelky. to right
(Fig. Below). In what direction is the beam deflected?

Describe electric an3uf+;)yura-cv lcd x/ d/or magnetic fields that surround a moving electric charge. uc df/vacu+ )x3l;yr-

A charged particle moves in a straight line through a 6ed3jwun j4-hptf-m1 ygd,l+particular region of space. Could there be a nonzero magnetic -,ddwjhy fe+ujt4- 63 pg1nl mfield in this region? If so, give two possible situations.

If a moving charged particle is deflected sideways in some regio eh/hjucas5.0s)8 oyd lag ;l8n of space, can we conclude, for /dh )58;a.0aoel 8sc jsylhgucertain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is a,d2p vs*aio)02leeu f0azs; k 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 electrons in a certain region of space arbs ;t3zp.q;xee being deflected by an electric field or by a magnetic field (or by;tqb ;zp3es .x both)?

How can you make a compass without using iron or other ferromagnetic muyw j9+6u2e tv5)i kusm+xw* zaterial?

Two long wires carryingbm y /j-s *iwxnf,ka4+ equal currents I are at right angles to each other, but don’t quite touc/4baxyn+ mf k*jw,i -sh. Describe the magnetic force one exerts on the other.

A horizontal current-carrying wire, frep) s0+pdazna t,r4ky+e to move in Earth’s gravitational field, is suspended ++r4pzksa, )nyp0 tad 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 pj1gx/-9a f xsa magnet attract an unmagnetized piece of iron?

An unmagnetized nail will not attract an unmagnetized paper clip. However, ifleqmxi2w 329x3r9 8t 5 ys6 ap3cmyopnkqk:r9 one end of the nail is in contact with a magnet, the other end nqr:r9 pmk39ks2a9 5pot l3c28qiy 36xwemxy will attract a paper clip. Explain.

Two ions have the same mass, but one is singly ion rp4wulm0xkd/o *8vagwpp ))/w:,z kxized and the other is doubly ionized. How will their pwu w kol8 4*pmxp)a0pz gr:kdwv/ /,)xositions on the film of a mass spectrometer (Fig. Below) differ?

What would be the effect on B inside a long solenoid if )p; ug2sh m t,9r+ )h5sslrtih
(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 4 bp62xtr6 :dqed +ygoa relay . A relay is an electromagnet (the iron rod inside the coil does not move) which, when activated, attracts a piece of iron on adoy6q4b d:+ r6p 2etxg pivot. Design a relay to close an electrical switch. A relay is used when you need to switch on a circuit carrying a very large current but you do not want that large current flowing through the main switch. For example, the starter switch of a car is connected to a relay so that the large current needed for the starter doesn’t pass to the dashboard switch.

  (a) What is the magnitude of th:qiy.t x4t8kxe force per meter of length on a straight wire carrying an 8.40-A current when perpendicular to a 0.90-T unifk:x tx8tq y.4iorm 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 lzk o8fnf) 2hnti+co -7 6tfuaw d(h*7aength of straight wire std 8wf n(znc*7k6)fuh 2t+of 7aoh-ia tretched between two towers carrying a 150-A current. The Earth’s magnetic field of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  Calculate the magnitude of the 1 6nk 6cwow4q up(8iaa3;imay magnetic force on a 160-m length of straight wire stretched betweeq;wu64np6c 1ia (my8okaa3i w n 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 if the maximum forc1pqhj u;g -nh-+ k4nbwd)6vi qe on it is 0.750 N when placed in a uniform 0.0800-T fielun h;1+kdn6vh-4qp iw-bjq) gd?    A

  A 1.5-m length of wire carrying 4.55jzc l7p5n y 3e7v7r5ebvbgj - A of current is oriented horizontally. At that point on the egynz vrvb5b-c5p75 7e73jl jEarth’s surface, 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 i7xdksdv 71n*h8gq-2 vwl4*qcgffli )s a maximum of 1.28 N when placed between the pole faces of a magnet. If the pole faces are 55.5 cm -hw) q *di* 1ff2xkv7sc l7gv4gdqnl8in 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 mwng+cwz 17*te aximum possible value. Sketch thew+1 * 7wtzgnec relationship 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 is a maximku +vu. (hi8mwum 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 1o3/c.d bes rjt92 bvtcopper wire could just “float” horizontally in air because of the force due to tov cbjt3.19s/redbt 2he 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 charg /qmw)od05*qgx2v y ice $q\,=\,+2e$ 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 anr+ ),zlwgtqwo. q5xlh.n x;6nd direction 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 negatiqiiz qx-j1qu-qc t* 6 .12mtkpve charge for each diagram shown in (Fig. Below),mqq6qkt-j* tzx1. qc1-iu2ip 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 rfd(u*quv kek2r b-8+1a thn/of $\vec{B}$ for each case in(Fig. Below), where $\vec{F}$ represents the maximum magnetic force on a positively charged particle moving with velocity $\vec{v}$.

  An electron is projected vertically upwardye(p1shgwtzeg5/ +uq y.za +: 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, t kuvl1f4m55f+mm*s dypsi y0 ,ww4e.20-T field, in a plane perpendicular to th55,stymfufmvpw +w,k4is 4*md l0y e1e field. What is the radius of its path?    m

  An electron experiences the greatest /y.1fpkgm / itforce 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 undeflec3k+av0 )rbz)s vroisab/qj -.ted when passing through perpendicular electric and magvsb) )+a 3js r.ar 0b/ovzki-qnetic 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 , cs6d poi5t up1-2rfdis $6.6 \times10^{-27 }\;kg$ 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 requi6.drc pf. zxa1red for a particle of charge q moving with constant speed v to make one circular redfz 6a..cx1p rvolution in a uniform magnetic field $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge q moves in a circular path of radius r in a 2*eha c8f;du 1 zu*wtvuniform magnetic field B. Show that its momentum wa*uc 8fh dt; 12vue*zis p = qBr .

A particle of mass m and charge q moves in a 9u+(v i3wmr37s a,jpmcv:h bs circular path in a magnetic field B. Show that its kinetic energy p+ (b,:j3u s9w3hm is7mrvacvis proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momentu.*na1gs)br uqm 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 E 0y/u;,dwrc ;imsvyj*arth’s magnetic mi;*r w/, uys0jvcy ;dfield 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 magnitm9;rn)cl v zwj ie46q/ude $0.40\times10^{-4}\mathrm{~Т}$ 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 speq/wepf* kj)+gp 4b1 0n1 eoxz h6sweq.ed $\nu=2.0\times10^5\mathrm{~m/s}$ in a field-free region abruptly enters an essentially uniform magnetic field $B=0.850\mathrm{~T~}(\vec{\mathbf{B}}\perp\vec{\mathbf{v}}).$ If the proton enters the magnetic field region at a $45^{\circ}$ angle as shown in (Fig. Below),
(a) at what angle does it leave, $\theta$    $^{\circ}\,$
(b) at what distance x does it exit the field? x    $ \times10^{-3 }\;m$

  A jumper cable used to start a stalled vehicle carries a 65-A current. Htk7z9oug p:0vow strong is the magnetic field 6.0 cm away from it? Compare to the Ez09ogvkt7up :arth’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 ly**1xsf;lv rmagnetic field no larger than that of 1l;flv* xs*yr 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 wi*x+wi9kw .x fire carries current I out of the page toward you. Indicate, with appropriate arrowsxk i.+wfw 9xi*, the direction of $\vec{\mathbf{B}}$ at each of the points C, D, and E in the plane of the page.

  A vertical straight wire carrying an upward 24-A current exerts an a0k -zg w; *fvaffg*1tkttractive force per ungk 1-t*zwf*ff a ;gk0vit 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 os990fnk t7.0wpgrm.r5doav c f the force between two parallel wires 35 m long and 6.0 cm apart, each carrying 25 A i s75 r0.k9t9d0 p vno.cawgfrmn the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic field is being carried out 1.00 m fro,s*z,egp +lzt7a z 1zom an electric cable. What is as7z1+zz,p tz,*leg othe maximum allowable current in the cable if the experiment is to be accurate to $\pm1.0\%?$    A

  A power line carries a x ae192qdkp3jcurrent 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 g p32jed1ak9x qround? 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 cm apart iqkaz b1sh552 carry 25-A currents in the same direction. Determine the magnetic field at point P,kq5b2 is1ha5z 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 ps-6bnqumari;/:wk:8wgsi k(d1ym0bp k61 molaced 18 cm due south from a straight vertical wire carrying a 35-A cuy:p8w: i16gq am0sds ;kk/b -mn(k61boriwm urrent downward. In what direction does the compass needle point at this location? Assume the horizontal component of the Earth’s field at this point is $0.45\times10^{-4}\mathrm{~T}$ and the magnetic declination is 0$^{\circ}\,$.    $^{\circ}\,$ N of W

  A long horizontal wire carries 22.0 A of current dugmb0kk m,5x :wwao:-je north. What is the net magnetic field 20.0oa:mwjk w 0-5kx bm:g, cm due west of the 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 ayvls 037*w aqcnc f50* o6rzqi 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 m br7i9la2teo.1qqbw( ,0nje iidway between two long straight wires 2.0 cm apart in terms of the current I in one when the other carries 15 A. Assume these currl,ajt9eb0 . e(nr2 1qiob w7qients are
(a) in the same direction,
(b) in opposite directions.

  A long pair of wires conducts 2qeong h82:g; hm3t x5y5.0 A of dc current to, and from, an instrument. If the insulated wires are of negligible diameter but ar 8g3hqmn:5yto;ge2x he 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), parxq s2v6 c)e4g-tj6 l5s mqi9*5gbk r9yrk, tgxallel and just ktq9e,xm9 - b4sgy xqr56t 5)grkiglc2*6 svjto 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, 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 03;f p pnhp iz; vh(svmnt,*zs2p*8nx23$^{\circ}\,$ 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,;(0qs6ht(iom (6gue/n ta mfq as shown in (Fig. Below). There i0ai( sqehu6/tm( n6g fq(m;to s 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 second wire0e oq.bk +cq-k,xsl:x6s0 6krvn*i gs, made of 2.5-mm-diameter copper wire and pa0knogl cbi+q6v-sk0 ek, xqs: x*r6s.rallel 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 perpendicular to each o)(aq) *6r zk*b gjudbqther. At their closest, they are 20.0 cm apart (Fig. Below). What is the magnitude of the magnetic field at a p gbqr*q u) (jdk)6zb*aoint 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 i (sf m)0ui:tsare 15 cm apart. Wire A carries 2.0 A current. Wire Bs (ifmu):is t0’s current is 4.0 A in the same direction.
(a) Determine the magnetic field magnitude due to wire A at the position of wire B. $\approx$    $ \times10^{-6 }\;T$(retain one decimal places)
(b) Determine the magnetic field due to wire B at the position of wire A. $\approx$    $ \times10^{-6 }\;T$(retain one decimal places)
(c) Are these two magnetic fields equal and opposite? Why or why not?
(d) Determine the force on wire A due to wire B, and the force on wire B due to wire A. Are these two forces equal and opposite? Why or why not? $\approx$    $ \times10^{-5 }\;N/m$(retain one decimal places)

  Three long parallel wires are 3.8 cm from one another. (Looking along themp7d hn nbj 7nk5*(2imp, they are at three corners of an equilateral triangle.) The current in each2 pkpi7*5(hbmd jnnn7 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 field::xtan ve ps uf-x4sh-h+t3 et+-1uun at the midpoint of te s- +uht-t-:nvexu phatuxs1f: 4 n3+he 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 equal currents I eelgb74c t+gdfr :u4l+iky-u45;b fiin the same direction. One wire is at x = 0, the other eb4l+yti ru:u- +d74 k f;5lggb4ecif 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 solesod if x8nj)6(hd6ol:xo,rhe ;o;6ctnoid has a total of 420 turns of wire and carries a current of 2.0 A. Cal:x sno6,fh; 8ir)6x6 ;ldeoo hjt oc(dculate the field inside near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1xm0x/w-6 jfaa .25 cm in diameter is to produce a field of 0.385 T at its center. How much currfxm waax/6-0 jent 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 str9j;ro4jzmox eh3 s/5gl. v x,uaight 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 concer jxvhg ./45uz39olsrjox em,;n 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 ako87:(0wfbdl 6fy:v dkti2:d k9ffrical 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, lenydk :8(d0rwif7 dkfa: 9ff:lvk bot 26gth, and so on.

A toroid is a solenoid in the shape of a circr b0fq;0oirl. v4o k6bfe6q*ble (Fig. Below). Use Ampère’s law along the circular path, shown dashed in qi4;6 lbqk* 6o0bv.borfe 0rf(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 thansw5 z*bh2v6(fivl zn/-n + yyt the magnetic field between the conductors of a coaxifn5vbi* vnzs+2-hzyy6(w n l/ al 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 a4v,l2rb t5mzo side is placed with its face parallel t4 5zv2ob rm,lto the magnetic 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 deflects full scale foc:z; qo6kbez,,m k2 jcu fif)5r 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 galvanome+ cbzi96mrea: ter weakens by 25% over the years, what current will give full-scalea ecz9:ri 6mb+ deflection if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor dropsi*/mub0d0h:cu a . co*qsmb()h6bne b by 12%, by what factor does the output torque channbo sdc h)m*(mheb 0ib60/ab. uqc*u:ge?

Show that the magnetic dmmiy5)aoer p3a l90 y9ipole moment M of an electron orbiting the proton nucleus of a hydrogen atom is related to tyo3my eama5r 90lip9)he orbital angular momentum L of the electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter a oi-h mp:x9a6:q6rq(r h s9lndnd containing nine loops lies flat on the ground. The Earth’s magnetic field at this location has magnitun: s6 h9 lad9r-p6 xo:qhrimq(de $5.50\times10^{-5}\mathrm{~Т}$ 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 magm96g s20vhnhnd hc3w*jtc .tx xj:0h3netic field. What value of electric field could make their paths straight? In what direction munv9m0hhtg: csw33n j x6*j0 h2h t.xcdst it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atoms have ,vk;qz;v x,vdradii of curvature equal to 21.0, 21.6, 21.9, 22.2, and 22.8 cm. The largest radius corresponds to an atomic mass of 76 u. What are the atomic massqx,vd,k;z v; ves of the other isotopes?

  Suppose the electric field between the electric plates 5qy1 x+zu o okc2:ljq 1z3m,sbin the mass spectrometer of (Fig. Belooc:zsu13myl 2k 1q+ ,zq5bxojw) 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 monitoy-.2:vgdhwd0 y ;q ksm (ffj88s+aog sr air pollutants. It is difficult, however, to separate moleq8g2;j ha 0s sf(8 wdyfsvgyk. :m-d+ocules 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 accelerat2sowvtrw5v h1/cy 08 mu *iyl2es ions by a voltage V before they enter a magnetic field B. The ions are assumed to start from rest. Show that the *ov5m/ 0il 22cuyw1y whvrts8mass 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, j;t ;.r5ud nkdand a 25-A current flows through the wire. If the permeabiukrn jd .dt;;5lity of the iron is $3000\mu_0$ what is the total field B inside the solenoid?    T

  An iron-core solenoid is 38 cm long and 1.8 cm in diameter, anq9 u:ir8h)rcsd has 640 turns of wire. The magnetic field inside the solenoid is 2.2 T when 48 A flows in the wire. What is sqhc 9ri8u: )rthe permeability $\mu$ at this high field strength?    $\times10^{-5}\mathrm{T}\bullet\mathrm{m/A}$

  Protons with momentu,bluy, 7 /3 o5kcikf:t ,pv iexpu)m6bm $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 ee/j+ ljf 9h r/0d d;bc.t41usi.r dhybnergy upon entering a region of constant magnetib /id. th; jl4y/bscdfr9h.1er+ dju0c field. What is the ratio of the radii of their circular paths?   

  The power cable for an electric trolleyaqmk. ei)rfc 7x3alog02sq38uh7 ) s k (Fig. Below) carries a horizontal current of 330 A toward the ea rqme2o3qh uk aig)873ks.)lfs0a 7 cxst. The Earth’s magnetic field has a strength $5.0\times10^{-5}\mathrm{~T}$ and makes an angle of dip of 22$^{\circ}\,$ at this location. Calculate the magnitude and direction of the magnetic force on a 15-m length of this cable.    N the force on the wire is  ----待选择----southerlynortherly  and   $^{\circ}\,$ above the horizontal .

  Calculate the force on an airplane which has acquired a net c)v vpkk+yf ;5ce z zvp s7vc;:1d7tz1vharge 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, th+ypq5+19-smuobaa t ee Earth’s magnetic field points almost horizontally to the north +yp-+qe5as 9bt1m aouand 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 heliumhf;onqsm:*ez xxe2 -: 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” isttzi (jcr (q+. m. 4vit0hdfm; shown in (Fig. Below). A large current moves in a closed loop composed of fixed rails, a power supply, and a very light, almost frictionless bar touching the rails. A magnetic field is perpendicular to the plane of the circuit. If the bar has a length L = 22cm, a mass of 1.5 g, and is placed in a field of 1.7 T, what constant current flow is needed to accelerate the bar from rest to 28m/s in a distance of 1.0 m? In what direction must the magnetm.cm(t.(vjtq4 0+ti rhdfz;iic field point?
   A
the magnetic field must be ----待选择----updown 

  In (Fig. Below) the top wire is 1.00-mm-diametu ic )00an9qimer 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 )iu0ci0n9 amqA in each. Calculate the required current flow in the suspended wire.    A

Two stiff parallel wires a di )p/f -dnkg ;8dfvjkr6stance l apart in a horizontal plane act as rails to support a light metal v)jdp;-8d/g6fnrkf krod of mass m (perpendicular to each rail), (Fig. Below). A magnetic field $\vec{B}$, directed vertically upward (outward in the diagram), acts throughout. At t = 0, wires connected to the rails are connected to a constant current source and a current I begins to flow through the system. Determine the speed of the rod, which starts from rest at t = 0, as a function of time
(a) assuming no friction between the rod and the rails,
(b) if the coefficient of friction is $\mu_k$.
(c) Does the rod move east or west if the current through it heads north?

  Estimate the approximate maximum de3te1bcw yhut+1*5(xhhus )ujp 7tn w :flection of the electron beam near the center of a TV screen due to the Earthsbwhnw5ux11p tu cj3)e*(: 7 thuy+h t’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 accelerak)k d, r6bdlzn9(iszc c;x(pb);*v o vte elementary particles such as protons to high speeds. Particles starting a* );rkdlznb,i6(;cs( c op 9vzkd )vxbt 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, 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 squar p0-t86deme,m/* llyygn,mwxe of side l, carrym*wl68/edm t,exmp - ,ynl 0yg 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 sxm 7*1cjrw7dum6q,q 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 fieldqw77 xqu1s6m,jrm* dc 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 )cai,w(kd m)y(riy) vof a circular coil of wire carrying a current I (as in (kv)aiw (imy)),yrd c Fig. 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 thsxgfb) 9crj 0)l)l7vqe magnetic field is about 1G($ 1\times10^{ 4}\;T$) Imagine a simple model in which the Earth’s field is produced by a single current loop around the equator. Roughly estimate the current this loop would carry. [Hint: Use the formula given in Problem 80.]    $ \times10^{ 9}\;A$

  You want to get an idea of the magnitude of magnetic fields produced byure: s(/wdbbj3a )v6d overhead power lines. You estimate that the two wiresr6bbw3jsua /d :e)vd( 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 electrons, t3t c;,inpc. qzuai 2una;o11m raveling to the right at a sp an,3uz1 q i.oc n;tmu1ci;pa2eed 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 patm ;p c8e +8uxmthz:ey9xu4jw8h 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 energy of the w+e8:4p88 juhec;m mx xt9yuz proton as it travels from P to Q.    $ \times10^{-20 }\;J$

  A 32-cm-long solenoid, 1.8 cm in diameter, is to produce a 0.30-T magnetic field2ca7ua)jt- /+ hlleax at its center. If the maximum current is 5.7 A, hoatal 72u lj+axehc) /-w many turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, each of diameter 0.50 mm, carry the so/uwmcda.ejq ),1nz b6w0p o:ame curreca6nb .0u: mdp, qjzow e1o)w/nt but in opposite directions. They are suspended by 0.50-m-long strings as shown in (Fig. Below). If the suspension strings make an angle of 3.0$^{\circ}\,$ with the vertical, what is the current in the wires?    A

  An electron enters a uniform d/bn,gbo* i xr93z1 ktv7-6s8 jm*gpul;x lrzmagnetic 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$