A compass needle is not always balanced px4pxcn5x,q i( )vd ap zq5c2:parallel to the Earth’s surface, but one end may dip downward. Expxzc5 (n4dv,:2 i)xpp pqcaxq5 lain.

Draw the magnetic field lines around a straight section of wih b 00g7)kkoblgnn3hxyh 5:5vre carrying a current horizontally to the l ohxgnby5 h7hk5)v0:kgl0b3n eft.

In what direction are the magnetic0o gte48m2,mvv0xraj4b1 akk field lines surrounding a straight wire carrying a current tha00 o,a4j4r8gmbvt 1v ekkx2 amt is moving directly away from you?

A horseshoe magnet is held vertically with the north pole on the le q-w(j0 mavoz2n:: rbkh8 i(ukft and south pole on the right. A wire passing between the poles, equidistant from them, carries a current directly away qzm ik0a:o- hurv8b( 2n:j(kwfrom you. In what direction is the force on the wire?

Will a magnet attract any metallic object, or only ths +b d69dn5i ze*pzv.tose made of iron? (Try it and see+sez*id.6b dv9p5tnz .) Why is this so?

Two iron bars attract each other no matter which ends areb7maj:3ikeib ,apy cg9u+ fyk4f./3 u placed close together. Are both mag ck,3f bbaue439m .pgf+:a u7iyy/k jinets? Explain.

The magnetic field due to current in wires in ejd)pxadqk 2;(z 7 urb wi2,+es/u xp5your home can affect a compass. Discuss the efkr)(2;w s 2+u/d5 apqj, bpiz udxxee7fect in terms of currents, including if they are ac or dc.

If a negatively charged particle enters a region of uniform magnetic field whicqs vgjq/0 wqz i)*v(5rh is perpendicular qrv s j)0 *ivqg5zq/(wto the particle’s velocity, will the kinetic energy of the particle increase, decrease, or stay the same? Explain your answer. (Neglect gravity and assume there is no electric field.)

In(Fig. Below), charged particles move in the vicim h+(h5 te 1so f+zm-1jag r4odyaih0(nity of a current-carrying wire. For each charged particle, the arrow indicates the direction of m0mfeh4dgh sma1tah1j+ (r z i +y5oo-(otion 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 fien veun4b5x1a4hq +wyu.b g+-z,jh 6x vld as shown in Fig. 20–46. What can you say about the charge on each p n5-vh,vyz6naxj+qubx 1ubw+e.g4h 4 article?

A positively charged par:k 2o-hq(atk 6t-e7s gykbvz*nnvl7 .ticle in a nonuniform magnetic field follows the trajectory shown k(ysat6*e-.k :v7 tv k l qngo-7nbz2hin
(Fig. Below). Indicate the direction of the magnetic field everywhere in space, assuming the path is always in the plane of the page, and indicate the relative magnitudes of the field in each region.

Can an iron rod attract a magnet? Can a magnet jj i*yf) sy3v: k-:gwjattract an iron rod? What must you consider to ans3g*)wy:-i: jvfkjyj swer these questions?

Explain why a strong magnet held near a CRT television screen (Secti yyvq)dvi.dvpt jh1.m /.19-m fehv6p on 17–10) causes the picture to become distorted. Also, explain why the picture sometimes goes completely black w 9dy.q6hthvypdm/p-.v)fe .1ji1mv v here the field is the strongest. [But don’t risk damage to your TV by trying this.][/But don’t risk damage to your TV by trying this.]

Suppose you have three iron fm *mxt a-nfl2j79gf8sc68uv rods, two of which are magnetized but the third is not. How would you da*mtsgc8-9j 72fx l86mu vffnetermine which two are the magnets without using any additional objects?

Can you set a resting electron into motiib *coku 5(wile/y8+z on with a magnetic field? With an electric fiel8*wul+kyi/oeib 5cz (d? Explain.

A charged particle is moving in a circle under the influence of a uniform mag xndsg 1jwqr j,48x,h84jes2pnetic field. If an electric field that points in the same directi p8exxjgq nj2d srj1484s,, hwon as the magnetic field is turned on, describe the path the charged particle will take.

The force on a particle nqx.gsn380fr;do3 u u 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 a magnetic field. Explain how ions are caused to move. Do positive and negative un3;f8o3 qunrg x 0.sdions feel a force in the same direction?

A beam of electrons is directed toward a horizontal wire carrying jl(6lsie 0. dxa current from sj6ed0 i( x.llleft to right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields that ssbye q2(x-t2gurround a moving electric charge.b-eq 2tsg2 yx(

A charged particle moves in al lhyfamn)w 3pop gi: ,)ipue((.8ms; straight line through a particular region of space. Could there be a nonzero magnetic field in this regmhwnfel a: 8gsm(up() ;l i),3ioy.ppion? If so, give two possible situations.

If a moving charged particle i2il)7pqx:n9*7kwtpoa c nz7m s deflected sideways in some region of space, can we conclude, fo7m qit7pc n2l 97za*p):n kwxor certain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is a uniform mag :jawexljs*ihs3: :e3 netic 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 certaih 6c9uge2 3e0-gajdyy n region of space are being dgc6yea h-gu9 j3 ed02yeflected by an electric field or by a magnetic field (or by both)?

How can you make a compass without using iron or o+*dx 9nrm fm-zther ferromagnetic material?

Two long wires carrying eqg s4m* is1eby*ual currents I are at right angles to each other, but don’t quite touch. Describe the magnetic force one exem4b*y1se gs i*rts on the other.

A horizontal current-carrying wire, free to move in Earth’s gravitational fi2 g.xxawi :8poeld, is suspended directly above a second, parallel, current-carrying wire. o:.2gxx i8 paw
(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 unmaba4kp7h zv kks3f x(,g7 k)a.ggnetized piece of iron?

An unmagnetized nail will not attrac,3kjtdr-2 l ph 8 41tfqjsmu/nt an unmagnetized paper clip. However, if one end of the nail is in contact wit/ sk-th31fp j 28dtu,q4jlrmnh a magnet, the other end will attract a paper clip. Explain.

Two ions have the sam+rm4q8s gs p4re mass, but one is singly ionized and the other is doubly ionized. How will their positions on the film of a mass spep+g rsr8 m44qsctrometer (Fig. Below) differ?

What would be the effect on B inside a1 . ctm5k:3uoychq*pz 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 solene9 se,)cfqj z1oid is a relay . A relay is an electromagnet (the iron rod inside the coil does not move) which, when activated, attracts a piece of iron on a pivot. Design a relay to close an electrical switch. A relay is used when you need to switch on a circuit carrying a very large current but you do not want that large current flowing through the main switch. For example, the starter switch of a car is connected to a relay so that the large current need9 ,1zef) jeqsced for the starter doesn’t pass to the dashboard switch.

  (a) What is the magnitude of the force; 2)j kea5mq8kkvn1ns per meter of length on a straight wire carrying an 8.40-A current when perpendicuka mej)2s 8;n5knqv 1klar 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 magnetici,oxw,9o 4 zq+8tkw4- h yisgr force on a 160-m length of straight wire stretched between two towers carrying a 150-A current. The ot9wqrisg,o4y4 -k whzix8 +,Earth’s magnetic field of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  Calculate the magnitude of-pwh ljtq i06) the magnetic force on a 160-m length of straight wire stretched between two towers carrying a 150-A current. The i 0)w lhjq6pt-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 bzn 6a n-)xi-w7wj2brabk0b+ m long if the maximum force on it is 0.750 N when placed in a uniform n - baw xi-+bbak)rn w70z6jb20.0800-T field?    A

  A 1.5-m length of wire carrying 4.5 A of current is oriez ca,oktu+.xy 9ezv u; r/j/k/nted horizontally. At that point on the Earth’s surface, the d//a.kyek/; +,uzvjuct9xo rz ip 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 maximum of 1.28 N when p aa ,t:6ogarmd:z; wlnq5 x.i-laced between the pole faces of a magnet. If the pole faces are 55.5 cm in diamet,w o5ld:z. :tmi -aqa;nr 6agxer, what is the approximate strength of the magnetic field?    T

  The magnetic force per meter on a wire is measuratov:p(5l qoa 6za2b2ed 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, and sketch the relationship as it actually is, calculating the angle between the wire a:2(aal5p 2o6qbzovt and the magnetic field.    $^{\circ}\,$

  The force on a wire is a q8;1h spmjfh7 a4v e:gmaximum 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-diametekkkkt*)f;p6lh -ls(zr copper wire could just “float” horizontally in airl kz lpk-6*kht(;k)sf because of the force due to the Earth’s magnetic field $\vec{B}$, which is horizontal, perpendicular to the wire, and of magnitude $5.0 \times10^{ -5}\;T$. What current would the wire carry?    A Does the answer seem feasible? Explain briefly.

  Alpha particles of charge( hr. d pzo*2nsjoxy bj3x8b0ee -oc-6 $q\,=\,+2e$ 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 theng+j7ga guu/y 7-:ugs 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 negativeok z ha7t3lv 00sfc03v charge for each diagram shown in (Fig. Beloak07s3ht fvzoc v3 0l0w), 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 directtit f5q7- yts.ion 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 verticae jhpq;7rsd( +5bp3yslly 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 fi 5xv; jv:tce0tdq 0+xseld, in a plane perpendicular to the field. What is the radius of its petv05+xc;: d sx0jtv qath?    m

  An electron experiences the great jh1t 0fzo nvpq.+0a6iest force as it travels $2.9 \times10^{6 }\;m/s$ in a magnetic field when it is moving northward. The force is upward and of magnitude $7.2 \times10^{-13 }\;N$. What are the magnitude and direction of the magnetic field?    T ----待选择----EastWest 

  What is the velocity of a beamlw,m*0bzr) dy of electrons that go undeflected when passing throu *wym zldr),0bgh perpendicular 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 atom whose r5+65-hf daf 684vxsnnugt scmass 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 w ha7h f8yxe,sm8f stl15kx) y-ith constant speed v s1f,5xkms yh7t)8hay xl-e8f to make one circular revolution 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 un,hz :lja0 ts-niform magnetic field B. Show tj tsn- ,:hz0lahat its momentum is p = qBr .

A particle of mass m andj/ g-vomgqv /0 charge q moves in a circular path in a magnetic field B. Show that its kinetic energy is - /ogqv0 jmgv/proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angulacix-zldm +m-0pyr*+hsqxa+w461 tz r,yrz 2tr momentum of the particle in Problem 21 is $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves with a speed of 160 m/s perpendicular to t 6p+3z9xo6j iyuq/gqkhe Earth’s magnetic field6/ xjqipkg6o9z yuq +3 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 equateau0z- /hz1lsor 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 withio wwa );4gar1 speed $\nu=2.0\times10^5\mathrm{~m/s}$ 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. Hosgivtmz +5 e,5uv 0.wau6 : piewpgv+.w strong is the magnetic field 6.0 cm away from it? Compare to thep : zuat,eu65wv 0vgmpi. eig.5++svw Earth’s magnetic field. $B_{cable}$   $ \times10^{-4 }\;T$ the field of the cable is about    times that of the Earth.

  If an electric wire is allowed to produce a magnetic field no larger than that ilz a0. 3d,ybaid: um7of the Earth i 3 lum,:za0b. iyd7ad$(0.55\times10^{-4}\mathrm{~Т})$ 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 cw0vd/we s6 bf1n aru67dqx56 I out of the page toward you. Indicate, with appropriate arrows, the direction 506r6s6/dbevafx qwc7nu w 1dof $\vec{\mathbf{B}}$ 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 attract9 -u d,ouqsgvv1oqo.-i3q h.hive force per unith-,dqvogio.o .3s 9 qvqu1u- h 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 magnitudw6 x3yci,odlfq;8* twe and direction of the force between two parallel wires 35 m long and 6.0 cm apart, each carrying 25wo3fc 6d *t;i,8x qylw A in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic field is being cykau7o1c 8l7ulo/a/h arried out 1.00 m from an electric cable. What is the maximum allowable current in the cab 17oay7 /lkol/uuach 8le if the experiment is to be accurate to $\pm1.0\%?$    A

  A power line carries a current of 95 A along the tops of 8.5s0mc/ n(;/y xo pahp)swr(lf y42;gdd -m-high poles. What is the magnitude of the magnetic field produced by this wire at the ground? How does this compare with lsd(yr4 ghsm2fop) 0/ ;wn p axc(yd/;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 carry 25-A currek uhee3t6izg ae-i(20nts in the same direction (ehga6i i k-te2z3u0e. Determine the magnetic field at point P, 12.0 cm from one wire and 5.0 cm from the other(Fig. Below).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is (lfi-jfsbu)+o0j8 fo placed 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 location? Assume the h fiosjl+-f objf )u80(orizontal 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 ldpw)6 lp2uf7ge-**y. zl:1xeuj ws m carries 22.0 A of current due north. What is the net magnetic field 20.0 cm due west of the wire if the Earth’s field there poiu em g*u wpyjl1lzse)7*x6lw- :f.2dpnts 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 a-(3d3h kwrp omt 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 w8nojyh ;(8gl,z zp)y jx z:nt1ires 2.0 cm apart in terms of the current I in one when the other carries 15 A. Assume thespylyh ,zx8 ot8: ;znjz1n) (gje 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 from, an instrumenhzi 7 )cy-)bjnz2v ua nvn5.6it. If the insulated wires are of negligible diameter but are 2.8 z)i6znnj yc .b5nvvh ui27a) -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 shgy rk ex-,47-gbsq l:4g wb;hmown in (Fig. Below), parallel and just to the right. If it carries 25.0 A upward, what force per meter of leng-7-gbxq;sg: e,k44mhlryw bgth 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 poin(ishc pm261gwq9ysq xtni:(4 ts 23$^{\circ}\,$ E of N outdoors. However, when it is placed 12.0 cm to the east of a vertical wire inside a building, it points 55$^{\circ}\,$ E of N. What are the magnitude and direction of the current in the wire? The Earth’s field there is $0.50\times10^{-4}\mathrm{~T}$ and is horizontal.    A  ----待选择----updown 

  A rectangular loop ol)acj80sjygqd5i//0tvt+rw f0sk n ,4,mzph f wire lies in the same plane as a straight wire, as shown in (Fig. Below). Therji sz4, d jp0)+c/vqayfr,t h8wngt/0 slk5m0e 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 48e /g nl9.opi45 rmd854:edssnl;b rpd A. A second wire, made of 2.5-mm-diameter copper wire and parallel to the first, is kept in suspension magsl /5o4p:gbp9l .4edmrseird8n ; 5n dnetically 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 perpn, u(f38kxet ,eeu gg;tn xd.usg(r,+endicular to each other. At their closest, they are 20.0 cus3gkunege+ .(ux,r 8n(;dx,tft , ge m apart (Fig. Below). What is the magnitude of the magnetic field at a point midway between them if the top one carries a current of 20.0 A and the bottom one carries 5.0 A?    $ \times10^{-5 }\;T$

  Two long straight parallel wires are 15 cm apart. Wir ,1avlhvq 0doi0rh,4ie A carries 2.0 A current. Wire B’s current is 4.0 A in the same direction. dv vhiairo4, 1 ,qhl00
(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. (Lo+ s vf8aa, yekr67zgy9 b- tfc+pg-vj+ no;e5aoking along them, they are at three corners of an equilateral triangle.) The current in eache6vbzv ;ae7g+ gsp+k8- 95 jco-n ,yyafrf+at 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 magnitude7,w1 snzkrsl1g q vp6* and direction of the magnetic field at the midpoin zv6 kql1,*7g psrws1nt of the side of the triangle between wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wi5wwgh6ffs(l l /y9d:y1 i axc7res, a distance d apart, carry equal currents I in the same direction. One wire is at x = 0, the other is at x = d, (Fig. Below). Determine /9:ily5(7yfs6ahww gfclx d 1 $\vec{B}$ along the x axis between the wires as a function of x.

  A thin 12-cm-long solen4ol2kue. h)jdw bvxuzf;. c3/oid has a total of 420 turns of wire and carries a current of 2.0 A. Calculate the fiel) .jxb;oh4z fud2w.eck3 vu/ld inside near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diam41qgnt0ge gny2rkq 6; eter is to produce a field of 0.385 T at its center. How much current should the solenoid carq6k rgyg 02;4ng1q tnery if it has 975 turns of the wire?    A

  A 550-turn solenoid is 15 cdjo1e mke:e xbc* :g83m 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 current downward (and is connected by other wires that don’t concern us). What is the force on this wire assuming the solenoidxme:3o*ek e:jd81gb c ’s field points due east?    N

You have 1.0 kg of copper and want to make a practical solenoid that producj /wkto.cf/1q es 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 vt/ qfk/j.oc1w ariables, such as solenoid diameter, length, and so on.

A toroid is a solenoid in the sz -1lmbkb0a9wlbo/ ,ujhx- +eh q/3 uvhape of a circle (Fig. Below). Use Ampère’s law along the circular pathl 0/+- bbkquz1e9 -hlom,/aubw jhx v3, shown dashed in (Fig. Below a), to determine that the magnetic field
(a) inside the toroid is $B=\mu_0NI/2\pi r$ where N is the total number of turns, and
(b) outside the toroid is B = 0 .
(c) Is the field inside a toroid uniform like a solenoid’s? If not, how does it vary?

(a) Use Ampère’s law to show that the magnetic field between 3urax9 p4dh/xxj ld;2the conductors of a coaxial cable (Fig. Below) i4lx;3ra 9d xux /dphj2s $B=\mu_0I/2\pi r$ 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 ply kvk nkfn ai9j*1dg ;)gf9+*daced with its face parallel to the magnetic field between the pole pieces of a large magnet. When 6.30d9gd;g 1j i+ knyk*v*f9f)kna 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 hqk/m)houvte9 vyy3; c +ku,wnk u3:+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 galvanometef):.kvrlk,n pk3 j nt-h y:f4yr weakens by 25% over the years, what current will give full-scale deflection if:klyk )yfpk h t:.nj n3r-v,f4 it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops yk /u5xc9zp-u/yowjo3a 6kksq;:tn 7 by 12%, by what factor does the output torque chanyo kn swyzu /:oa7jk9up 6/ck3-q;5t xge?

Show that the magnetic dipole moment M of an elee25wh kl a zr4g8)+csectron orbiting the proton nucleus of a hydrogen atom is related to the orbital angular momenl5zg2ahc8s e4 e+)rkw tum L of the electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter and contaewj5 /g rcgw je)n)()wining nine loops lies flat on the ground. The Eartj(j )w5)ww gr)e ncg/eh’s magnetic field at this location has magnitude $5.50\times10^{-5}\mathrm{~Т}$ and points into the Earth at an angle of 56.0$^{\circ}\,$ below a line pointing due north. If a 7.20-A clockwise current passes through the coil,
(a) determine the torque on the coil,   $\times10^{-5}\mathrm{m}•\mathrm{N}$
(b) which edge of the coil rises up: north, east, south, or west?

  Protons move in a circle of radius 5.9)0ysqsbb)qlxnwt 8. qo6+fpf- clv, 10 cm in a 0.566-T magnetic field. What value of electric field coul6p-fbq )lnv lbq.)9x8+ ostf,ys0qc wd make their paths straight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium ab+omv- fb2v3 bfx *05ovx4enftoms have radii of curvature equal to 21.0, 21.6, 21.9vf-fb 3 0mfbn*b4exx52v o+vo, 22.2, 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 mam0u. b oo/un.sod8jk7mc - kn4ss spectrometer of (Fig /o.uunkc87 o nk 4mmos-b.dj0. Below) 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 mogyy m4:p9 t1eu6lm/cvnitor air pollutants. It is difficult, however, to separate molecules with nearly equalcvpy9 :l6 m14m yeu/tg 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 voltaggjdnw 44-*tkg e V before they enter a magnetic field B. The ionsgtdjng4w-k4* are assumed to start from rest. Show that the mass of an ion is $m=qB^2R^2/2V,$ where R is the radius of the ions’ path in the magnetic field and q is their charge.

  A long thin solenoid has 430 loops of wire per mghaljv2x)3le2a .r s2eter, and a 25-A current flows through the w3.ja) e2rahsg lv2l x2ire. 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 cm long and 1.8 cm in diameter, and has /hutd3hd55uz8 c+ukz 640 turns of wire. The magnetic field inside the solhu5u5hc3kd 8zd+ zt /uenoid 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 mjwr x+j0pt8 ($4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 a67m + q-jhadyw region of con6m +d-jy a7qwhstant magnetic field. What is the ratio of the radii of their circular paths?   

  The power cable for an electriccxzj3 ,npm*t - trolley (Fig. Below) carries a horizontal current of 330 A tc ztx*,-n3 jpmoward the east. 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 charge ofmvljqd4 6b(ejc+c *nn0 x00f a $1550\mu C$ 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 p iw br0t,cv5d 2expm3b*fl ,k:oints almost horizontally to the north and he :*b03fim rxc lbkv2,tw, p5das 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 at /hpz3.xp. ydmom, whose mass is $6.6\times10^{-27}\mathrm{~kg},$ is accelerated by a voltage of 2400 V.
(a) What will be its radius of curvature in a uniform 0.240-T field? $\approx$    m (retain three decimal places)
(b) What is its period of revolution?    $ \times10^{-7 }\;s$

  A sort of “projectile launcher” is shown i2e;b6o+7:rs j-:d5bf r z6uv; rcio txsvx3mvn (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 px2u 7vsvj: crt z3vb;bd6f5r;x: r-o+ mos6ieerpendicular 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 wvzi9a gkd j6xjbwl)8m6) *,ecire and is suspended in air due to the two magnetic forck ,8bj6ld x9)gmw) vi6z*jeaces from the bottom two wires. The current flow through the two bottom wires is 95 A in each. Calculate the required current flow in the suspended wire.    A

Two stiff parallel wires a distance l apart ii *9whd5leklg2 j; 5;hj8p dxdn a horizontal plane act as rails to suppoi5ej 8l 9dp2 h*d h;5;xkwlgdjrt a light metal rod 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 deflection of tb2,o x dw7czlo7z7hm-he electron beam near the center of a TV screen due to the Earth2w ocld x7hz7m,b7-oz’s $5.0\times10^{-5}\mathrm{~T}$ field. Assume the CRT screen is 22 cm from the electron gun, where the electrons are accelerated
(a) by 2.0 kV,    mm(Round to the nearest integer)
(b) by 30 kV. Note that in color TV sets, the CRT beam must be directed accurately to within less than 1 mm in order to strike the correct phosphor. Because the Earth’s field is significant here, mu-metal shields are used to reduce the Earth’s field in the CRT.    mm(Round to the nearest integer)

The cyclotron (Fig. Below) is a device used to accelerate elementary pmnhp gbf9)2 +zyi)t2iarticles 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 th2gy2bm)inz9 h+f ip)tey 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, locqa: ur3pndpzh39 e10 fated at the corners of a square of side l, carry equnp3 rap0d3:eh9f1q zual 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 ibl(*pm1hnu n1n particle accelerators for “beam steering”; that is, the magnetic fields can be used to changbhun*lm 1(p1ne 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 angle will a beam of protons traveling at $ 1.0\times10^{7 }\,m/s;$ be bent?    $^{\circ}\,$

  The magnetic field B atbi4cnwyigr-u 5r+ 3hufk7 --p the center of a circular coil of wire carrying a current I pinyc -w-+ 3k5urg7 r4i-ufhb (as in 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 poles8j5tntoppm .4o fqvvzd6u46 9 the 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 fe r7;pz;d;fy e) yr/+ih wl:pproduced by overhead power lines. You estimate that the two wires are each about 30 m above the ground and are about 3 m apart. The local power company tells you that the lines operate at 10 k rzee)frd wh:yl fyppi; /7;+;V 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 ykoe.. tj3 4cq6 ml8wwbeam of electrons, traveling to the right at a speed 8.w twl kq.j 4oyec3m6of $4.8 \times10^{ 6}\;m/s$ 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 shv smx(c1)j m7piral path through a gas in a magnetic field of 0.010 T, perpendicular to the planmcj7 sxv)mh(1 e of the spiral, as shown in (Fig. Below). In two successive loops, at points P and Q, the radii are 10.0 mm and 8.5 mm, respectively. Calculate the change in the kinetic energy of the proton as it travels from P to Q.    $ \times10^{-20 }\;J$

  A 32-cm-long solenoid, 1.b2mng iyuu3( .0hre(t8 cm in diameter, is to produce a 0.30-T magnetic field at its center. If the maximum(u0gne 3h.tu 2bmr i(y current is 5.7 A, how many turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires,+ aspqaajq3:2 each of diameter 0.50 mm, carry the same current but in opposite directions. They are suspended by 0.50-m-long strings as shown in (Fig. Below). If the suspension strings make2 p3 s:+aajaqq 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 =.fq*q:/y3wmy lje2t e 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$