A compass needle is not always balanced parallel to the Earth’s surface,9zywj. wl6)uv (llrxw5;wdv / but one end may dip do6ldwy(vll 9uww. )5xr;v zjw /wnward. Explain.

Draw the magnetic field lines arek/1f5qm cf)a ound a straight section of wire carrying a current hor1 em /kc5qf)afizontally to the left.

In what direction are the magneti7 xo9k sx xsfjoq :*uf3(* (yrik4kqh5c field lines surrounding a straight wire carrying a cu9rk4 so f(35: qj *7xoqf(xkxykhsi u*rrent that is moving directly away from you?

A horseshoe magnet is held vertically with the north pole on the left and soutx9ctkg1isqhay0l4 j3;6.cw2da+o t t h pole on the right. A wire passing betwe2tojck;tl qwta c 396. +h0xisgy4d1aen the poles, equidistant from them, carries a current directly away from you. In what direction is the force on the wire?

Will a magnet attract any metallic obje3ev nnrlv3,a 5ct, or only those made of iron? (Try it and see3nvn5 rea,v l3.) Why is this so?

Two iron bars attract each other no matter which ends are placed close togethertqv (.z;evc 1kvq p*9f. Are e v(*fp 1qck;tv.vz9qboth magnets? Explain.

The magnetic field due to current in wdsc yymlp qh8p p7/5uxgi0/92q s8i ;tires in your home can affect a compass. Discuss the effect in te/x9u0/qidp2 5y y;8ps8 tis h7lcmgpqrms of currents, including if they are ac or dc.

If a negatively charged particle enters a region of uniform magnetic field wf l0jc7g wyh90hich is perpendicular to 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.9 gf0cjlwh7 0y)

In(Fig. Below), charged particles move in the vicinity of a current-carrying wi+vl(6zob -y/ue f,q.b;n nptgre. For each charged particle, the arrow indicates the direction of motion of the particle, and the + or - indicates the sign of the charge. For each of the particles, indicate the direction of the magnetic force due to the magnetic fieldz ebf l,(nuo+y.qvn/g- 6 bt;p produced by the wire.

Three particles, a, b, and c, enter a magnetic field as shown 0* tmo(is,p ewin Fig. 20–46. What, 0esti(*op wm can you say about the charge on each particle?

A positively charged particle in a nonuniform magnetic field follows the rm*(pt0 :wr kdtrajecto0rt(r:*mdwk pry shown in
(Fig. Below). Indicate the direction of the magnetic field everywhere in space, assuming the path is always in the plane of the page, and indicate the relative magnitudes of the field in each region.

Can an iron rod attract a magnet? Can a1*frs0vw 9m ja magnet attract an iron rod? What must you consider to afs0rjm9 w*av 1nswer these questions?

Explain why a strong magnet held near a CRT television s4won( -mfqrlcm4 bm 8qtpd*39creen (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 yourdw( bm-lpc 3*mf4qn9q8 rtmo4 TV by trying this.][/But don’t risk damage to your TV by trying this.]

Suppose you have three iron rods, two of which arh +/56 *p0 vprgxqq 3ob;zbhpue magnetized but the third is not. How would you determine which tqhq0p/u rbgz*6 h+pbx5o 3v; pwo are the magnets without using any additional objects?

Can you set a resting electron into motion with a magnetic field? With an elec,.8 glw3g8cv: yrie)sc kaxr(tric(8c.k:8gcs3,a)glv yeix rw r field? Explain.

A charged particle is moving in a ceh , 15ai-t*nd*o uwgldnu;c1n)n3 dbircle under the influence of a uniform magnetic field. If an- g1d*;b ne3n)w, 1ldaiudntnhc* 5uo electric field that points in the same direction as the magnetic field is turned on, describe the path the charged particle will take.

The force on a particle in a magnetic field is the idea behind electromagnekm)iz*/;x nd7s mfdb (tic pumping. It is used to pump metallic fluids (such as sodium) and to pump blood in artificial heasbmm*d 7z f;d()ixnk/rt 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 ions feel a force in the same direction?

A beam of electrons is directed toward a horizontal w;ac+(ez rws v1ire carrying a current from lefz+awve;r(c 1 st to right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic cji 9)uikdr29tzm23. s*jd:ux( ktvy fields that surround a moving electric charge.ikx)v .z93ir 2yt j:t(uc d*j9d2mkus

A charged particle moves in a stras,/9vgp 7o2ouowsav2uy0 , glight line through a particular region of space. Could there be a nonzero magnetic field in u,/o9 u 2oopayv,sw20s lgg7v this region? If so, give two possible situations.

If a moving charged particle is deflected sideways in some region of space, can1t drryz6v0-o we conclude, for certain, oz1tr 06r v-dythat $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space theipz/w .4-zx pkre is a uniform magnetic field $\vec{B}$. Outside this region, B = 0 Can you inject an electron from outside into the field perpendicularly so that it will move in a closed circular path in the field? What if the electron is injected near the center?

How could you tell whether moving electrons i;xky z6r4hs1y img.t*v2a0uin a certain region of space are being deflected by an electric field or by a magivamg y4*2.6xykht ;zru i 10snetic field (or by both)?

How can you make a compass wd gv1(4 lr+yljithout using iron or other ferromagnetic material?

Two long wires carrying equal currents I are at right an7 b vray6jjc68gles to each other, but don’t quite touch. Describe the 76 jv6cj r8byamagnetic force one exerts on the other.

A horizontal current-carrying wire, free to move in Earth’s gravitational;7 d.q4c/tnb 5vm ijzn field, is suspb5 ;q.tvncjmn/ d4 iz7ended directly above a second, parallel, current-carrying wire.
(a) In what direction is the current in the lower wire?
(b) Can the upper wire be held in stable equilibrium due to the magnetic force of the lower wire? Explain.

Why will either pole of a magnet attract an unmagnetized pil/lu6*lz; s/z zc.tg bece of iron?

An unmagnetized nail will not attract an unmagnetized paper clip. However, if o1(eu8qu4bx v kd0q.g3 z3rnzfne end of the nail is in contact with a magnet, the other end will attract a paper clip. Explain.v.q3 r(8e3zqfxb1 4 uudkn zg0

Two ions have the same mass, but one is singly ionized and tqibq n8-so,r-he other is doubly ionized. How will their,rq8 -o-nsqi b positions on the film of a mass spectrometer (Fig. Below) differ?

What would be the effect on B inspupbl.lf;aj 0mm3n+g1 ,+9oy lr7q eoide a long solenoid if
(a) the diameter of all the loops was doubled,
(b) the spacing between loops was doubled,
(c) the solenoid’s length was doubled along with a doubling in the total number of loops?

A type of magnetic switch similar to a solenoid is a r1m ok ; l9zh,y2v(zabaww6 e4ielay . 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 tha2oeivz 1,byaw;w4z l9a h(km6 t 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 a straighto)wrufm 1* )fezd d;6m wire carz1m*6owmdeu ;fr f )d)rying an 8.40-A current when 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 force on a 160-m length of straight w:5il2fn3 6cukj4 ae msqsn3+pire stretched between two towers carrying a 150-4efjsc5 ms+2ln uk6 q3nip:3 aA 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 xf8yo7 y(d: sj160-m length of straight wire stretched between two towers carrying a 150-Aoyf8 d7j(xys: 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 flow)5porsahc l7g f*l:4 1luak 1aing in a wire 4.80 m long if the maximum force on it is 0.750 N when placedaha:u lck)75g o4a1sp* 1rfll in a uniform 0.0800-T field?    A

  A 1.5-m length of wire carrying 43tm in*,nde/ h; nw27ysu /dyt.5 A of current is oriented horizontally. At that point on the Earth’//dey;y,t3m7* h un2wdt nsins 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 carryinkq /l x 6h2l.tvboz,u;n:j5aag 8.75 A is a maximum of 1.28 N when placed between the pole faces of a magnet. If th a ov xt6ja5qk2./zlh,l:b;une pole faces are 55.5 cm in diameter, what is the approximate strength of the magnetic field?    T

  The magnetic force per meter on a wire is measured thqte zn0tmt 5s5b 6r 19pot0 6q2ezj4lo 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 t60eoz4 jq02 lzhsq emtbt9 61t nt5p5rhe relationship as it actually is, calculating the angle between the wire and the magnetic field.    $^{\circ}\,$

  The force on a wire is a max3 z4r --s;: ym4l- ciyfqslyblimum of $ 6.50\times10^{-2 }\;N$ when placed between the pole faces of a magnet. The current flows horizontally to the right and the magnetic field is vertical. The wire is observed to “jump” toward the observer when the current is turned on.
(a) What type of magnetic pole is the top pole face?  ----待选择----North PoleSouth pole 
(b) If the pole faces have a diameter of 10.0 cm, estimate the current in the wire if the field is 0.16 T. $\approx$   A(retain one decimal places)
(c) If the wire is tipped so that it makes an angle of 10.0° with the horizontal, what force will it now feel?    N

  Suppose a straight 1.00-mm-diameter copper wire c)(s 0n7 2fjflkse x2owould just “float” horizontally in air bw )sfko nx0 2f7sl2je(ecause 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 c.-h()jx/h-,) m p g zgnvdyjkm v/xq4iharge $q\,=\,+2e$ and mass m = $ 6.6\times10^{ -27}\;kg$ are emitted from a radioactive source at a speed of $1.6 \times10^{ 7}\;m/s$. What magnetic field strength would be required to bend them into a circular path of radius r = 0.25 m?    T

  Determine the magnitude and direction of the force on an electron j hzn 0o6pv w9,cxs02atraveling $ 8.75\times10^{5 }\;m/s$ horizontally to the east in a vertically upward magnetic field of strength 0.75 T.    $ \times10^{-13 }\;N$  ----待选择----NorthSouth 

Find the direction of the force on a negative cha 9i( .sugztwt;; /ic51zjnr. jmqrw.crge for each diagram shown in (Fig. Below)/zc 1siq.t5tj;nu9w;.( rim w z.cgrj, 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 direct pfuwk; b5ao 4c1i9lr9ion 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 upward with a speedws96*0nig ecf(0 bq kd of $1.7 \times10^{6 }\;m/s$ into a uniform magnetic field of 0.350 T that is directed horizontally away from the observer. Describe the electron’s path in this field.    $ \times10^{-5 }\;m$

  A 5.0-MeV (kinetic energy) proton enters a 0.20-T field, in a plbm2t f h79-mayane perpendicular to the field. What is the radius of itsb-29t7y mmafh path?    m

  An electron experienceo(31w z msyea-s the greatest 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 beam of electrons that9zto rp(71q oe go undeflected when passing through perpendicular electric and magnetic fields of magnitude 9er(7z o 1qpto$8.8 \times10^{3 }\;V/m$ 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 wh t8 6nf ;tseha0macic7(+ovx+ xa qk+*ose 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 covk 8fi-kgd+6harge q moving with constant speed v 8kdik6 + -ofgvto 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 uniformy 4ogv2wh9) 34a mh0e lbua.xk magnetic field B. Show )y4xovkg3 hb42 m9eau.h0wal that its momentum is p = qBr .

A particle of mass m and chau04i:r nf/o vgk(f. afemsq+( rge q moves in a circular path in a magnetic field B. Show that n.f rgkvqmi:(ef s+o au(f4/0its 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 Pro4jd y 0d(ww1;:ogqspu blem 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 rl7b:e3t.i.7qsc jnk to the Earth’s magnett73 :ej7 lis .qn.rcbkic field of $5.00\times10^{-5}\mathrm{~T}$, If the bullet possesses a net charge of $13.5\times10^{-9}\mathrm{~C},$ by what distance will it be deflected from its path due to the Earth’s magnetic field after it has traveled 1.00 km?    $ \times10^{-7 }\;m$

  Suppose the Earth’s magnc7n* aqjt7 u;k i58kxfetic field 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 sc bo6en3(o4wc peed $\nu=2.0\times10^5\mathrm{~m/s}$ 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 -: sbbnm i0 xfu5wxtc0y;)j 3fcurrent. How strong is the magnetic field 6.0 cm away from it? Compar5 s )xnufb 0tmybxciw3j0;f:-e 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 nolne4 4b5zzd4o larger than that of the Earth 4n45o z4lbzed$(0.55\times10^{-4}\mathrm{~Т})$ at a distance of 25 cm, what is the maximum current the wire can carry?    A

In (Fig. Below), a long straight wire carries current I out of t* 5:hgcaoam7ohe page toward you.*hm caoa:57 go Indicate, with 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 u2oc6))phovse be:id pw9-ba +pward 24-A current exerts an attractive force pepsbd2 :p)caw+hv eoi -b9o6 e)r unit length of $8.8\times10^{-4}\mathrm{~N/m}$ on a second parallel wire 7.0 cm away. What current (magnitude and direction) flows in the second wire?    A  ----待选择----upwarddownward 

  Determine the magnitude and dirynch8+ jt)-u;xrsy x/ fdjqojc,9 08dection of the force between two parallel wires 35 m long and 6.0 cm apart, each carrying 25 A in the same directi xy/0)yjcod+f8,jjh trqusn9dc;8 x - on.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic field is being carried oes)bn :0 pbf qciz/r hr84puo2a7m ceu8/u/)kut 1.00 m from an electric cable. What is the maximum allowable mo2qbp74/8h s 0eurp8r):i/c uacub z e)nfk/current in the cable if the experiment is to be accurate to $\pm1.0\%?$    A

  A power line carries a current o:pi8;owxp. pd f 95 A along the tops of 8.5-m-high poles. What is the magnitude of the magnetic field produced by this wire at the ground? How does this compare witxwodp ;p8p i.:h 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 wire 161 jco-1yneb 9decuzs 13.0 cm apart carry 25-A currents in the same direction. Determine the magnetic field at point P, 12.0 cm from69d1n11eecyu zj boc- one wire and 5.0 cm from the other(Fig. Below).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is plag vh 0r67mmb60kgb7oyo :ig ,mced 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 horizont670 bm7g ,hmy0ig 6vo omrbgk:al 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 due north. What is the net59hmf nkvs/p9 magnetic field 20.0 cm due west of the wire if the Earth’s sfk99 hv/pm5n field there points north but downward, 37$^{\circ}\,$ below the horizontal, and has magnitude $5.0\times10^{-5}\mathrm{~Т}?$
   $ \times10^{-5 }\;T$
$\theta$ =    $^{\circ}\,$ below the horizontal

  A straight stream of protons passes a given po/tycb5tk ..zw0t / y i o5i8dxv)wfkm3int in space at a rate of $1.5\times10^9\mathrm{~protons/s~}.$ What magnetic field do they produce 2.0 m from the beam?    $ \times10^{ -17}\;T$

Determine the magnetic field midway betweeyk qgsap .hw629 l.*8k cjd9ivn two long straight wires 2.0 cm apart in terms of the current I in one whd g.yl.*wkq8p6v9 9s ahik2cjen the other carries 15 A. Assume these 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, anh 5j +0sc-x(l)ld dtmy 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 the magnetic field of t tjx- )ycd0m5 ls+dlh(he 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.lxmh mceegf1e:2caxql+x29)*dt vdv/o )+ m the plane of the two wires shown in (Fig. Below), parallel and just to the right. If it carries 25.0 A upward, what forc2ch+192 d:o*vmxexc) edm vqxfat/+ lmgl) .ee 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 poik8ion; t7fn5u nts 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 wi.uq;*ad:i+ue9nslvg oaw/ )a;n;ry n d n+c9qre lies in the same plane as a straight wire, as shown in (Fig. Below). There is a currennno.ws ;:9dandc/i +l;qgq+ay )u;v*enr9 aut 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 carrimdh k;h7mzwvfz5/(aodh/ v30g5 1a q5k(dpmwes a current of 48 A. A second wire, made of 2.5-mm-diameter copper wire and parallel to the first, is kept in suspmvaoh( ;gpd5701 d5hd hkzmf(ma/5 qvwk/w z3ension 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 eac x6vs w.at4lk 7h6+ldvh 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 carries a current ov 6 s6htk lv4+7awdl.xf 20.0 A and the bottom one carries 5.0 A?    $ \times10^{-5 }\;T$

  Two long straight parallel wires are 15 cm apart. Wire A carries c0cakc fob83feo )9eo/ e7hi*2.0 A current. Wire B’se8 0/oc9b chaefco3)okif e*7 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 ds9rxzh1e*;7 k 4n3zodww10thf(aa8kw8mil from one another. (Looking along them, they are at threes3kd07i(1onawxz ;*8tzwhf1l8aer 4 dkmh9w corners of an equilateral triangle.) The current in each wire is 8.00 A, but its direction in wire M is opposite to that in wires N and P (Fig. Below). Determine the magnetic force per unit length on each wire due to the other two.
$\frac{F_\text{M net y}}{l_\mathrm{M}}$ =    $ \times10^{ -4}\;N/m$ =    $^{\circ}\,$
$F_{N\,net}$ =    $ \times10^{-4 }\;N/m$ $\theta$ =    $^{\circ}\,$
$F_{P\,net}$ =    $ \times10^{ -4}\;N/m$ $\theta$ =    $^{\circ}\,$

  In (Fig. Below), determine the magnitude and directioa ikf , vcs;uyx*29ielr.7- nin of the magnetic field at the midpoi.u f;xiskv,a*i c 7i9nr-y2lent of the side of the triangle between wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a distance d apart, carry 7/*s pny3a ,wre+gyfb equal currents I in the same direction. One wire is at x = 0, the other is at x = d, (Fig. Below) pfgbray7/3+w y ns*e,. Determine $\vec{B}$ along the x axis between the wires as a function of x.

  A thin 12-cm-long solenoid has a total of 420 turns of wire and ca)8v 08n *mqokdt(o4ixv6cp l brries a current of 2.0 A. Calculate the field insidplkb xt4i )(n 80d mo6qvcv8*oe near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameter is to produce a field +x)df+r0at y+b v vz)vf2-0ucuvj8buof 0.385 T at its center. How much current should the solen+t0v+u )b-zu8yb2cf) 0 fvvujx a+vdroid 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-c/smf(x,gzd8kz5 pb r 4b4,sb fm-long straight wire cuts through the center of the solenoid, alon8bzbf5s4x( ,gz, 4rfm bs/kpdg 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 ))balwdtv,4p to make a practical solenoid that produces the g4pl)) aw dbt,vreatest possible magnetic field for a given voltage. Should you make your copper wire long and thin, short and fat, or something else? Consider other variables, such as solenoid diameter, length, and so on.

A toroid is a solenoid in the shape of a circle (Fig. xk+ ilx:u ;f4vBelow). Use Ampère’s law along the circular f kiu+lx;vx4:path, 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 thatnlk;s/ 0eoshuk5g n5- wv: )st the magnetic field between the conductors of a coaxial ca ssn5sn ltv:w0;oh/ k)5 u-kgeble (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 fa q3 xcw.x85vvjce parallel to the magnetic field between the pole pieces of a large mavxcq w8 5jxv3.gnet. 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 deflectc4 dfddt. l5oew2jzl v: t08;vs full scale for a $53.0 -\mu A$ current. What current will give full-scale deflection if the magnetic field weakens to 0.860 of its original value?    $\mu A$

  If the restoring spring of a galvanometer weakgrci 9bxvtmc /3r)6v 3ens by 25% over the years, what current will give fu9vc/bc3g tix rv63r) mll-scale deflection if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by what fact jj )7 gcdz.4ubqq,duto n2p);hf +/azor does the output torque change?7 tauh,4 /dp)o)2n+qczjuz gbjd f;.q

Show that the magnetic dipole g6f(p hxq7 ypbbk;/vn vtufy:9s)+2 emoment M of an electron orbiting the proton nucleus of a hydrogen atom is related to the orbital angular momentum L of the electron by bu tesvfyg ; /n kv72hy()xfqp:p+9b6
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter and containing nine loops lies it vh2xc , -u7r jm q)qm:wurj0xr25k3flat on the ground. The Earth’s magnetic field at this location hasr-7mm25ujuch)3 xxrq w tik 20: rvjq, 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 ras ff,bec db5hu m)0g25z:bf t3dius 5.10 cm in a 0.566-T magnetic field. What value of electric field could make their paths straight? In what direction mustf 5 bez c3f0b :hf,gub25sm)dt it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atoms have radii of curvatu i 1n/ucz8rovkb1 5*6wcrxq4 sre equal to 21.0, 21.6, 21.9, 22.2, and 22.8 cm. The largest radius cwvx iuc ro15kc1q8/zr* 64 nbsorresponds to an atomic mass of 76 u. What are the atomic masses of the other isotopes?

  Suppose the electric field between the electric plates in the mass spectromz n* 9d9a3o(zug3:qn eia-wks eter ou ( dz n93 zk*e3:qianao9g-swf (Fig. 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 monitor air poll74d9ambkmaj8 +q jjj:utants. It is difficult, however, j j7ama4bd + m8q:9jjkto separate molecules 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 ac0.92x:xm2vjwa n vndfcelerates ions by a voltage V before they enter a magnetic field B. The ions a:2xjfvnv dm. 9xw2n0a re 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 m9twz v3mnnb /9eter, and a 25-A current flows t v9tz93 bnwn/mhrough the wire. If the permeability of the iron is $3000\mu_0$ what is the total field B inside the solenoid?    T

  An iron-core solenoid is b8* abmh4cibs3 9rz( .lhooe2 38 cm long and 1.8 cm in diameter, and has 640 turns of wire. The magnetic field inside the solenoid is 2.2 T when 4b28co .s(b9rim4 le3z aob *hh8 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 momentum7u e6d c9my;jl $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 v:-8npk rxc6d1tmmt7 svfg3 j v 8bu38kinetic energy upon entering a region of cvstvpctk 1bg 83uxm-m8 87r3j 6ndvf: onstant magnetic field. What is the ratio of the radii of their circular paths?   

  The power cable for an electric trolley (Fig. Below) carries a horizon toav:e5* 8phjbekk ;dh7tte/y2 4fn.tal current of 330 A toward the east. The Earth’sh72fyjp .hbv45d:/ak*;e n keott 8et 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 ch hrnjkr -i,em9s 9,ze4 i5j3sharge 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 horizoy4 ** pvk dhp-*jx6hzmntally to the north and has magnitup-**kpm4hdy *h6xvz jde $B=0.50\times10^{-4}\mathrm{~T.}$ 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 kxd6k*3 vi 4rdtzv27c ;jn6llmass 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” iqcw6zx5 6 f*aes 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 perpendic6 efazw c*x6q5ular 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 copper44wd)l;/d cs ga (cfrh wire and is suspended in air due to the two magnetic forces from the bottom two wires.(4ghr c ;dsdl4 f)caw/ 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 in a horizontal plane act as rails x8aj (fgh q:k5)jwh 9,j+zmjmto support a light metal rod of mass m (perpendicular jhjx mwa+j ,qg5(h km9 jf):8zto each rail), (Fig. Below). A magnetic field $\vec{B}$, directed vertically upward (outward in the diagram), acts throughout. At t = 0, wires connected to the rails are connected to a constant current source and a current I begins to flow through the system. Determine the speed of the rod, which starts from rest at t = 0, as a function of time
(a) assuming no friction between the rod and the rails,
(b) if the coefficient of friction is $\mu_k$.
(c) Does the rod move east or west if the current through it heads north?

  Estimate the approximate maximum deflection of the electron beam near the rq88n* lcqpc6 center of a TV screen due to 8 qr*8cq lnc6pthe 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) /h+a2o8ocmk pis a device used 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 B. The particles are om8co/p+ak2h 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, locat+pvgqa y i5w8pk;qd mz8 ,k)n5ed at the corners of a square of siv+k pw)p88yg n mi;zqk5da q,5de l, carry equal currents $I_0$ perpendicular to the page as shown in (Fig. Below). Determine the magnitude and direction of $\vec{B}$ at the center C of the square.

  Magnetic fields are very useful in particle acc5vohn*xxo1u+bq,,fw :o zp 9helerators for “beam steering”; that is, the magnetic fields can be used to change the beam’s direction without altering its speednb *,:q xzx h,v uhw19p+o5ofo (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 Btd/co6ke o:0b at the center of a circular coil of wire carrying a current I6/bo: edtko 0c (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 polessp vg;aw j5 )e-9g;qxcwzuqp ryf821/ 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 od7acupvkk3y c3:e;3bf the magnitude of magnetic fields produced by overhead power lines. You est;vd 33 ykk7a:e bcu3pcimate 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 field will be changing.] $B_{net}$ $\approx$    $ \times10^{ -5}\;T$(Round to the nearest integer)

  (a) What value of magnetic field woue1ze( n1dmu9; jwk )zold make a beam of electrons, traveling to the right at a speed of ;emon)w(j 1d 1z keu9z$4.8 \times10^{ 6}\;m/s$ 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. hpulk:ya-1im u*d6f)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 pr-6:ia)p u mf*hyud 1lkoton as it travels from P to Q.    $ \times10^{-20 }\;J$

  A 32-cm-long solenoid, 1.8 cm in diamt*t, , mrjph4geter, is to produce a 0.30-T magnetic field at its center. If the maximum current jmhrg tt p4,,*is 5.7 A, how many turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, each ow c67)3auqwqp f diameter 0.50 mm, carry the same current but in opposite directionq )a w7cpuqw63s. 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 magnetigs m1;kv(vdtsc *nh4r )xwjo ch7+i38c 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$