A compass needle is not always balanced parallel to the En 6yd+5ii ne07zyr kg;arth’s surface, but one end may dip dok0yneiyn76d z+ ;5 irgwnward. Explain.

Draw the magnetic field lines around a str;q3 7y iak4bmqaight section of wire carrying a current horizontall43kb i; aq7mqyy to the left.

In what direction are the magnetic field lines surrounding a stra(xukd 5u d1d7 ch(rj)iight wire carrying a current that is moving directly away fromdi(drju) 17d(u k 5chx you?

A horseshoe magnet is held vertically with the north pole on the left and x(kghr 1ly0;kuys 1p /south pole on the right. A wire passing between the poles, equidistant from them, carries a currh01r ypy guxs1k l(/k;ent directly away from you. In what direction is the force on the wire?

Will a magnet attract any metallic object, or only those madgdeljlg q.caq5*2b3fs2ym0x* ch ; p+e of iron? (Try it and see.)xmy2 fjeqsqca.2 g p l*b 0gc;+l5*h3d Why is this so?

Two iron bars attract ,dmbzdx;6u7mb 53s dbbpi: *yeach other no matter which ends are placed close together. Are both magnets? Explai,zd:; ds 5*ybb7idp mxu6 bb3mn.

The magnetic field due to current in wi25skhq beo6y+ -h r4.ftx bka-res in your home can affect a compass. Discuss the effect in ter6bq5k-s a.- hx rb +fyht2e4koms of currents, including if they are ac or dc.

If a negatively charged particle enters a r )6vmthczy gd4anl;youwe6+0u :k +3legion of uniform magnetic field which is perpendicular to the particle’s velocity, will the kinetic energy of the particle inc uy+3; tokdl+066nhzl)yma:vw 4e cgurease, 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 curren8 oj7cpy dl-o;t-carrying wire. For each charged particle, the arrow indicates the direction of motion of the particle, and the + or - indicates the sign of the charge. For each of the particles, indicate the direction of the magnetic force due to the m ;y 7-pjldo8coagnetic field produced by the wire.

Three particles, a, b, and c, enter a magnetic field as shown in Fig. 20–46.i .cybpw1qc 1,v z:.ih What can you say about the charge oiby .v:,1 c1iwpqh.czn each particle?

A positively charged particle in a nonuniform magnetic field follows the owu2xgh f +)kre(+kc5trajectory shown inrkg2 c+x h( o5weuk)f+
(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 mx ;epaaqbn5 hns 9o8i1.9un-b agnet attract an iron rod? What must you consider to answ-159a x. epuonn9b;banhsq8ier these questions?

Explain why a strong magnet held near w3ydx-p3a+ 6 oyztka *u, y-wba CRT television screen (Section 17–10) causes the picture to become distorted. Also, explain why the picture sometimes goes completely black where the field is the strongest. [But don’t risk damage to your TV by trying this.][/But don’t risk damage to your TV by tryingk -o-aa3+6 yy pdu bzt,y*w3wx this.]

Suppose you have three iron rods, two ofijqsc1f d 3w)ebc18b : which are magnetized but the third is not. Ho:dcw 1ibjeqc)1b38f sw would you determine which two are the magnets without using any additional objects?

Can you set a resting electron into motion with a magnetic field? W (zdxin 8m-1s mx7ccln :dx15qith an electric field? Explain.:qsmcd5x 1-7l z (8cm1x idnxn

A charged particle is moving in a circle under the influem.f s;b v 8/iu7qz,a/ m6twyqy2qwj+cnce of a uniform magnetic field. If an electric field that points in the same direction as the magnetic field is turned on, describe the path the charged pt/+ wqcz7uqv ., 2jswy /q bmf;ai6m8yarticle will take.

The force on a particle in a magnetic field is the idea behind electroms25 cou.t1e;qii,k4m y9 nu jrvqu j2+agnetic pumping. It is used to pump metallic fluids (such as sodium) and to pump blood in artificial heart machines. The basic designy4iv1 trjo; q2,kqu.m25 c u u+jn9sie is shown in(Fig. Below). An electric field is applied perpendicular to a blood vessel and to a magnetic field. Explain how ions are caused to move. Do positive and negative ions feel a force in the same direction?

A beam of electrons is directed toward a horaw; 2 xrd:laf.izontal wire carrying a current from lel af; wa.d2:xrft to right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fie e4;d(qs ub016 lbk donn1r8kk gpj/f5 kt6hd0lds that surround a moving electric charge.ljku b6h0 56 nrn(qk kpf01b4g8 dosd d1te/k;

A charged particle moves in a straight line throuqk zrxpvmj0ko. l u3*s9e+djje0q 9;+gh a particular region of space. Could there be a nonzero magnetic field in this region? Ip+zj3 l. vm0qu *ekr09oxdk ; s9+ejjqf so, give two possible situations.

If a moving charged particle is deflecte1,z.eg( s osztd sideways in some region of space, can we conclude, for certai 1ss(e.t zogz,n, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is a u-dzqa ( x8mfj;niform 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 electroni*y ;jtys;qg4 s in a certain region of space are being deflected by an electric fyyg; jtq;i 4s*ield or by a magnetic field (or by both)?

How can you make a compass without using iron or other ferromagnetic ma ur iqysc/7 -:,ct/idrv1lupis/f8 .7(vfokn terial?

Two long wires carrying equal currents I are at right angles to eac,;n v-bsfmf 3kh other, but don’t quite tou;v fnsf,3 b-mkch. Describe the magnetic force one exerts on the other.

A horizontal current-carrying wire, free te/ i9fde63wki (+ shqoo move in Earth’s gravitational field, is suspended directly above a second, parallel, current-carrying i+ io9qd3eh 6fwes(/k 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 attraeu yg6;-b wi/cct an unmagnetized piece of iron?

An unmagnetized nail will not attract an unmagnetized paper clonu:(qf;/(jin9 r:bx i1jq vrip. However, if one end of the nail is in contact with a magnet, the other end will attract a paper clip. Expo(n::j 9xfjr;vqi1 ir(n/ ubq lain.

Two ions have the same mass, 3hdhpo8lsusj4b* ,2 ebut one is singly ionized and the other is doubly ionized. How will their positions on the film of a mass spectrs3u*4hplh,sbj e od82 ometer (Fig. Below) differ?

What would be the effect on B inside a long solenoid d,6 tgafvk -qm b*rif6za1/ -eif
(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;.d:pw: yuucfw,l 5 gb 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 nec5;,g pywudl bufw::. ed 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 length on ag 9(va25 )ghhu l-5 mp4ukddy:jm/ydd straight wire carrying an 8.40-A current d:)4vh jhd d 259pg5k -dyl(myumug/awhen perpendicular to a 0.90-T uniform magnetic field?    N/m
(b) What if the angle between the wire and field is 45.0$^{\circ}\,$?    N/m

  Calculate the magnitude of the magnetic for2wywe*.5ov)o;a)iv jc b5p ed ce on a 160-m length of straight wire sv)*j;da bc2ie)w 5oe ovyp5.wtretched 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 magnetic force on a 160-m length o u/ (1a -ckcoiecl 9e+:tneaj)f straight wire stretched between two towers carrying a 150-A curr1l /cet 9ice ak+)cj:eua -o(nent. 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 lo2d(zkp :i ik7znfg7r: ng if the maximum force on it is 0.750 N whp z:rik7g7fi2d: z( nken placed in a uniform 0.0800-T field?    A

  A 1.5-m length of wire c(3vun(bvck c)arrying 4.5 A of current is oriented horizontally. At that point on the Earth’s surf((u)nccb3v kvace, the dip angle of the Earth’s magnetic field makes an angle of 38 $^{\circ}\,$ to the wire. Estimate the magnitude of the magnetic force on the wire due to the Earth’s magnetic field of $ 5.5\times10^{ -5}\;T$ at this point.    $ \times10^{-4 }\;N$

  The force on a wire carrying 8.75 A is a maximu;d1whu y ki*d:6 d3 barsyx6p4m of 1.28 N when placed between the pole faces of a magnet. If the pole faces are 55.5 cm in diameterr4 hup3ds*y1wdx6ki6ay : db ;, what is the approximate strength of the magnetic field?    T

  The magnetic force per meter on v/w4l (alq 0oba wire is measured 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 relationshipo4 w/0( blqalv as it actually is, calculating the angle between the wire and the magnetic field.    $^{\circ}\,$

  The force on a wire is a maxi fr2w vtqf75y/w3t,x fmum 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-diam wq-)scdjdt, 2.ja6uymqc3f.eter copper wire could just “float” horizontally in air because of the force due to the Earth’s magma-dy f jj3d2u.tq,) c.6swc qnetic 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 charplf; b(y,o t,mjfy ;2cge $q\,=\,+2e$ 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 9k*-l h6;uda,o6b idaytq(jkthe 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 negativ r7 +lzq22qkfeb8lapb,qd .;te charge for each diagram shown in (Fig. Below),e8tr +flqklbp7az2 ;b.qqd 2 , 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 u5j( in08 h6mk1;pinfdfm0 beugj f p :je8e9)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 ver0gxbgekl cw358h uxn m (th8/,tically 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) p17zvx h,cq 1wsuca+.u roton enters a 0.20-T field, in a plane perpendicular to the a. s,17uzu1 x+wcqcv hfield. What is the radius of its path?    m

  An electron experiences the greatest force as it t qqbf.74 0n es zumsfd8, 4myg,5okeu3ravels $2.9 \times10^{6 }\;m/s$ in a magnetic field when it is moving northward. The force is upward and of magnitude $7.2 \times10^{-13 }\;N$. What are the magnitude and direction of the magnetic field?    T ----待选择----EastWest 

  What is the velocity of a beam of electrons that go undeflected when pasp 88z- kz)mnwtsing throumz tk-)8p z8nwgh 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 ze d-+q5mi 1kpatom whose mass is $6.6 \times10^{-27 }\;kg$ is accelerated by a voltage of 2100 V.
(a) What will be its radius of curvature if it moves in a plane perpendicular to a uniform 0.340-T field?    m
(b) What is its period of revolution?    $ \times10^{ -7}\;s$

  A proton (mass $m_p$), a deuteron $(m=2m_p,Q=e)$, and an alpha particle $(m=4m_p,Q=2e)$ are accelerated by the same potential difference V and then enter a uniform magnetic field $\vec{B}$, where they move in circular paths perpendicular to $\vec{B}$. Determine the radius of the paths for the deuteron and alpha particle in terms of that for the proton. $r_d$ =    $r_p$ $r_{\alpha}$ =    $r_p$

Show that the time T required for a particle of charge q moving with y- s+b d m0e/ k(zkk h.2c(jqs8sx,jt0ere3h iconstant speed v to make one circuk8t md+.kc 0h-zbre ,hss03e( ekx/jj(iqys2 lar 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 p85rb(kif h1ii kup:vl3za; z/ath of radius r in a uniform magnetic field B. Shbik81pkiru iz:z ; 35 vl/f(ahow that its momentum is p = qBr .

A particle of mass m and charge q moves in a circula8d83wqg6h q 2a-c kxae +b+zl;phjdj:r path in a magnetic field B. Show that itsqcl8g2+3 edzjkdj;a6- qa 8bp hhwx:+ kinetic energy is proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momentum of the particle in Probuo u8pfs/-r(ayg0*b clem 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 Eaka 6g;gxicb6j7 cyf05rth’s magnetic field 06b 7afg6 5y;jicgcx kof $5.00\times10^{-5}\mathrm{~T}$, 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-v ewtn2 +0g,7mw7nbtcgf+ qj at the equator has magnitude $0.40\times10^{-4}\mathrm{~Т}$ and a northerly direction at all points. Estimate the speed a singly ionized uranium ion $(m=238\mathrm{u},q=e)$ would need to circle the Earth 5.0 km above the equator. Can you ignore gravity? $F_B$    $ \times10^{ 8}\;m/s$ $\frac{F_B}{F_g}$    $ \times10^{8 }\;$

  A proton moving with syi-liz 93ugc x6 ;g/8*zi v5s uh7mrlfpeed $\nu=2.0\times10^5\mathrm{~m/s}$ 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 svkvc0 kqlp( +.talled vehicle carries a 65-A current. How strong is the magnetic field 6.0 cm awayvqv l 0c+.k(kp from it? Compare to the Earth’s magnetic field. $B_{cable}$   $ \times10^{-4 }\;T$ the field of the cable is about    times that of the Earth.

  If an electric wire is allowed to produce a magnetic field no largerp k j06n)hvzltl2;i-rbj* /vd than that of ti6p/d2 ;nk0r-zlj *tbl )jvhvhe Earth $(0.55\times10^{-4}\mathrm{~Т})$ at a distance of 25 cm, what is the maximum current the wire can carry?    A

In (Fig. Below), a long straight wire ci:j9lz 0bppel8w9h0 rx u5m x,arries current I out of the page toward you. Indicate, wit zj5w9e00l lx imx9b uhrpp,:8h appropriate arrows, the direction of $\vec{\mathbf{B}}$ at each of the points C, D, and E in the plane of the page.

  A vertical straight wire carrying an upward 24-A 07 s;rj*al z9dbo9/gqgc6 acb3 b1bbf current exerts an attractive force per unit lq r17 dfszc/b3 a;g09agcbb6o*9bb ljength of $8.8\times10^{-4}\mathrm{~N/m}$ on a second parallel wire 7.0 cm away. What current (magnitude and direction) flows in the second wire?    A  ----待选择----upwarddownward 

  Determine the magnitude and direction of the fo*b b3 7)cq52wdqdrb/skb:d djrce between two parallel wires 35 m long and 6.0 cm apart, each carrying3: rd dw)bcbq/2*jbs d57d qkb 25 A in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic field is beingzz/e87pdk zi b8 z5*ft carried out 1.00 m from an electric cable. What is the maximum allowable current in the cable if the z zz/k 5b 7dtpef88*izexperiment is to be accurate to $\pm1.0\%?$    A

  A power line carries a current of 95 A along the tops of 8.5-m-high polej3 f le o4f*e1rwfrb6)bi+wap:h*.qos. What is the magnitude of the magnetic field produced by this wire at the ground? How does this com wp*f4r e3ai *ojw+f .)lh:ebo f6qr1bpare 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 carry 25-A currents ince :qjxzsc8,o;k*+ wl the same direction. Determine the magnetic field at point P, 12 8,lkw* qjzsexc;co:+ .0 cm from one wire and 5.0 cm from the other(Fig. Below).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18 cm due souk2 *5usvpprv4 u-v smoujw8-.th from a straight vertical wire carrying a 35-A current downward. In what direction does the compass needle point at this location? Assume the horizontal component of the Earth’s fieldks-p8.v-umv2r ou w4*j 5 usvp 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 curren+zk7ksch148 /aoj p btt due north. What is the net magnetic field 20.0 cm due west of the wire if the Earth’s field there points northoka4 78hs 1 tkp+cbzj/ 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 q6ck/*hl hla wk/4ayx -b;fd0 space at a rate of $1.5\times10^9\mathrm{~protons/s~}.$ What magnetic field do they produce 2.0 m from the beam?    $ \times10^{ -17}\;T$

Determine the magnetic field midway between two long strg2 m;c w4y(kog8a8n,nw rabu0aight wires 2.0 cm apart in terms of the current I in one when the other carries 15 bkncgyg2an8a0um ,o( ww;r48A. Assume these currents are
(a) in the same direction,
(b) in opposite directions.

  A long pair of wires conducts 25.0 A of dc cu 8bi zohpxjm12wb*8 n9rrent to, and from, an instrument. If the insulated wires are of negligible diameter but are 2.8 mm apart, what is the magnetic field 10.00 cm from their midpoint, in their plane (Fig. Below)? Compare to th8*xh8 im 2n wbp19zobje 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 twr3b(f ne gkya/m +9(0z,m l9eclmjbs4 o wires shown in (Fig. Below), parallel and just to the right. If it cm0(sy(43kbzar99ebm l c,j g +lmnf /earries 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 je9 2 hqmlio)/ji5wqqtg*59h 23$^{\circ}\,$ E of N outdoors. However, when it is placed 12.0 cm to the east of a vertical wire inside a building, it points 55$^{\circ}\,$ E of N. What are the magnitude and direction of the current in the wire? The Earth’s field there is $0.50\times10^{-4}\mathrm{~T}$ and is horizontal.    A  ----待选择----updown 

  A rectangular loop of wire li ioyi+h g4i 39zjr;st;es in the same plane as a straight wire, as shown in (Fig. Below). There is a zoh9t+i;yg ;s 3rii4 jcurrent 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 wire, ma0tybdex+ o8o o/yx e/(de of 2.5-mm-diameter copper wire and parallel to the first, is kept in suspension magnetically +xty0 ydxbo(/ee8/o o15 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 l;m hvafnmtn;;vuz;x*sq 7zrw- :, e ,they are perpendicular to each other. At their closest, they are 20.0 cm apart (Fig. Below). What is the magnitude of the magnetic field at a point midway between them if the top one chn* nfs -auqztvwz ;:,,m7l ;e;vm;xrarries a current of 20.0 A and the bottom one carries 5.0 A?    $ \times10^{-5 }\;T$

  Two long straight pa a9sa62p8lcg 23en qahrallel wires are 15 cm apart. Wire A carries 2.0 A current. Wire B’s current is 4.0 A in the same direct63pe8g shaca2na9q2 lion.
(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. (Loodo3h;r9oq+owej(h 01ix, lb mking along them, they are at three corners of an equilateral triangle.) The current in each wire is 8.00 A, but its direction in wire M is opposio(x1j0l, 9howqh +mdbe 3ro ;ite 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 fiel5d rdh,eg87jj d at the midpoint re5jh, 8d dg7jof 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 equn( 6, e4dc;r5g/ sb, qpcpgb e+wxz58lcsnpw2al currents I in the same direction. One wire is at x = 0, the other is at x = xc pw6pb bn q,rz4scwgd5,e +2;c58es( gpn/ ld, (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 4 +ighlmqfe ta:(6; z6n20 turns of wire and carries a current of 2.0 A. Calculate the f:nh+litgm (6af6 zq;eield inside near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameter is to produce a fjo6 m:5 nt5s crze. (qjuus/y-ield of 0.385 T at its center. How much current should the solenoid carr/uo 5-t5yjj su (6:zqrn ce.msy 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- zpg e3:f311kzhr,fppcm-long straight wire cuts t3hkzrpgfzf1p1:e ,3phrough the center of the solenoid, along a diameter. This wire carries a 22-A current downward (and is connected by other wires that don’t concern us). What is the force on this wire assuming the solenoid’s field points due east?    N

You have 1.0 kg of copper and want to make a practs456 9snwji+ gvm wol7(s-ywc ical solenoid that produces the greatest possible magnetic fielg67wn+wlmcs -4j sv(w 9ysio5d for a given voltage. Should you make your copper wire long and thin, short and fat, or something else? Consider other variables, such as solenoid diameter, length, and so on.

A toroid is a solenoid in thg goir+e15f(a e shape of a circle (Fig. Below). Use Ampère’s law along the circular path, shown dashed in (Fig. Below a), to determine i5f+gregao1 (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 tvd+rsj 3z3j4conductors of a coaxial cabjj34 szrtd3+vle (Fig. Below) is $B=\mu_0I/2\pi r$ if r is greater than the radius of the inner wire and less than the radius of the outer cylindrical braid.
(b) Show that B = 0 outside the coaxial cable.

  A single square loop of wire 22.0 cm on a side is placed with its face p/kxu yzy13 rcmh0fyr+c/8 7qzarallel to the magnetic field between the pole pieces of a large magnet. When 6.30 A flowc yyfq7ky cz3u8 /xr/m +zr1h0s in the coil, the torque on it is $0.325\cdot N$. What is the magnetic field strength?    T

  A galvanometer needle deflects f- r c 5g1f1::kpesixqeull scale for a $53.0 -\mu A$ current. What current will give full-scale deflection if the magnetic field weakens to 0.860 of its original value?    $\mu A$

  If the restoring spring of a galvanometer weakens by : vi1(nrux0 9suj :yfm25% over the years, what current will give full-scaf :vyixs( 9umnru: j01le deflection if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by what factor does the output torque ch7k*qv4vz e, vnang,vnz*7vv4k e qe?

Show that the magnetic dipole moe3)(njoosdj teq8 tonea s:q2w+ d(27ment M of an electron orbiting the proton nucleus of a hydrogen atom is related to the orbital angular m7tj2q(swe)eenqo s:joo8 d+( n3at2domentum L of the electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter and containing nine loops lies fb z2mr 2qmxu8)lat on the ground. The Earth’s magnetic field at this location has magnitude bxu)m z m82q2r$5.50\times10^{-5}\mathrm{~Т}$ 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 9;z3ptzb dq.o radius 5.10 cm in a 0.566-T magnetic field. What value of electric field could make their paths strq bztp.o 3d;9zaight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atoms have radiiz b1 c ,cz+ ---gedtdgn0aqi5/hypm )l of curvature equal to 21.0, 21.6, 21.9, 22.2, and 22.8 cm. The largeg5zel ia cn)y1-hzd /p-cg -q+ ,mt0bdst 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 gjyy 4-/q5:jrf lcu0e(lpp 7bnrm /-cthe mass spectrometer of (Fig. Below/ jf/(j7:yup-pm crc 4ybl0r- 5le ngq) 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. r7j;xz -hr *x mllwx bh2;;w+h2rd.f gIt is difficult, however, to separate molecules with nearly equal mass such as CO (lgw.zh* lh;rhwrj d;x-72rm2bf +x; x28.0106 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 befor76wa 0mf 4bnmy donk*6e they enter a magnetic field B. The ions afwn 0dao4bmn6m*6k7 yre 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 wiuw.hiaxe+s+n x3vvl6fi.2 pl3c,q j9 re per meter, and a 25-A current flows through the wire. If the permeability o 9s2qll.jev3 3 . acvi6+,ipxnwxfu+hf 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 640 turns 5wz6)x2cjs .nkgqi bosg o )09of wire. The magnetic field inside the solenoid is 2.2 T when 48 A flows in the wire. What is thejzs 9 5x)csn06qow) .ib k2gog permeability $\mu$ at this high field strength?    $\times10^{-5}\mathrm{T}\bullet\mathrm{m/A}$

  Protons with momentueye: -c-i7yfeeuex h2w:o74u p8u*wgm $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 ki(3i b x7trys9ypo( hx1netic energy upon entering a region of constant magnetic field. What is the ratio of the radii of thei (yoy(pt7six 91rx b3hr circular paths?   

  The power cable for afv w;d7pluc 8.n electric trolley (Fig. Below) carries a horizontal current of 330 A toward the east. The Earth’s magneti7c8; vpwf. ludc 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 airw d/f( wp 5zr ib.:vtf/v0l:jhplane 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 Earth’s magnetic field points almost horizontally to theyr(pf ;8mxb9s1 a:fh fqal 8p7 north and has magnitudl9y8p h7;1: faa rpbsxf m8(qfe $B=0.50\times10^{-4}\mathrm{~T.}$ What should be the magnitude and direction for the velocity of an electron if its weight is to be exactly balanced by the magnetic force?    $ \times10^{-6 }\;m/s$  ----待选择----eastwest 

  A doubly charged helium atom, whose m9w:nam: 92 i hxg+vzktass 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 “projectilba95 gw,f8) /344aujz,yuqhvy b uwzse launcher” is shown in (Fig. Below). A large current moves in a closed loop composed of fixed rails, a power supply, and a very light, almost fricb 9au4vfu8bya 4,3whyz,)/5jqzw sug tionless 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.b/(o wf8 qp32l a2d9 oik+t/axk+ir rq00-mm-diameter copper wire and is suspended in air due to the two magnetic forces from the bottom two wires. The current flow through theb f9aa 2oqi3/r / (t+rplowi8x2qdk+ k 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 in a horizontal plane jzorlw* :4g j,act as rails to support a light metal rod of mass m (perpendicular to each rail), (Fig. Below). A magnoj zjr* g,w:l4etic field $\vec{B}$, directed vertically upward (outward in the diagram), acts throughout. At t = 0, wires connected to the rails are connected to a constant current source and a current I begins to flow through the system. Determine the speed of the rod, which starts from rest at t = 0, as a function of time
(a) assuming no friction between the rod and the rails,
(b) if the coefficient of friction is $\mu_k$.
(c) Does the rod move east or west if the current through it heads north?

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

The cyclotron (Fig. Below) is a device usedp( 5oam(*p 4a;m i2ylmv7inac to accelerate 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 m2m n ;oci*(p 7yvap(ia45malB. 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 thdu60t(s3e fnn c zgtlt,.o0nc1e v92ce corners of a square of side n( et0e30z1vd t.o2tscgu cnnc, 6lf9l, carry equal currents $I_0$ perpendicular to the page as shown in (Fig. Below). Determine the magnitude and direction of $\vec{B}$ at the center C of the square.

  Magnetic fields are very useful in particle accelerators for “beam st2r008 br7f8up,xa3ndrn yzrseering”; 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 protond,rasb8np7xrry0f0 u23 z8rn s that are not moving with the speed that the magnetic field is designed for? If the field extends over a region 5.0 cm wide and has a magnitude of 0.33 T, by approximately what angle will a beam of protons traveling at $ 1.0\times10^{7 }\,m/s;$ be bent?    $^{\circ}\,$

  The magnetic field B at the center ouidbqp7rkfa( ; ,r u(hdo:(b (f a circular coil of wire carrying a current I (as in Fig. Below) bb7hdo( (dr(( iu uaprq:f;,k 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 th7 4lb3 gimfc2cgrnycfco,670 e 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 by*+ qrc su lial+xh-/+h 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 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 q r+hxu a+c+*- llhsi/field will be changing.] $B_{net}$ $\approx$    $ \times10^{ -5}\;T$(Round to the nearest integer)

  (a) What value of magne pt0o5/cf9w7 1esg/3;yowbj7cf ayi gtic field would make a beam of electrons, traveling to thc7 p9 a5 /t b3ogs0yw/oiw7e;cfg yj1fe right at 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 path through a gas in a magnetic field of 0.010 T,rcoou3 . ay6m; 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 thm ourao y;36.ce proton as it travels from P to Q.    $ \times10^{-20 }\;J$

  A 32-cm-long solenoid, 1.8 cm in diameter, is to produce av7dphy m9 d 2yjxz)3;m 0.30-T magnetic field at its center. If the maximum current is 5.7 A, how many turns muyhpdmx39 7ydz2vj ;m)st the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, each of dia v 6w7nml1xv6ayiyg . yq(o)s1v4ox+fmeter 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 suspe6 (s wxy4m11v. fv y7onlx6q g)ya+voinsion 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 = 0.23 T a5r.rocb5(zty t 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$