A compass needle is not always balanced paralleht 2v4ep0uj,nl to the Earth’s surface, but one eu,0ptnv2 j4eh nd may dip downward. Explain.

Draw the magnetic fit5ok/iq gy 0z6jrx a4x 34crd d*jz1fucg8(h ,eld lines around a straight section of wire carrying a currenygit f q1xo5d ck,h*/3j4zar j8(u c4zgr60dxt horizontally to the left.

In what direction are ./g 6a8xq*ax oct(m)wnc9ks- al2h nothe magnetic field lines surrounding a straight wire carrying a current that 892nxacl6sqtxam /akg)woh-*no (. c is moving directly away from you?

A horseshoe magnet is held vertically with the north pole on the lem u)yz., mtjp8m5nu.i zy+ah3ft and south pole on the right. A 5 un. zy3,8.ipmhmm t)j+yu azwire passing between the poles, equidistant from them, carries a current directly away from you. In what direction is the force on the wire?

Will a magnet attract any metallic object, or only those made . ho+dnh0s a-dof iron? (Try it and see.)ho0h-sdd n+.a Why is this so?

Two iron bars attract each other no matter which ends aryn f,;v5yp22k z.cqfne placed close together. Are both magnp ,2n2ynq5. ;y cfkvzfets? Explain.

The magnetic field due to current in wires in your 2hynqx+ opd; *jm:eo7 2j4sj kguyvz5wg8;m*home can affect a compass. Dis:xw*jy+ygp mz8hm* ;jsv dej725 gkno; qu42ocuss the effect in terms of currents, including if they are ac or dc.

If a negatively charged particle enters a region of uniform magnetic fiipgwt h6 y0+-deld which is perpendicular to the particle’s velocity, will the kinetic energy of the particle increwgihdp0 yt+6-ase, decrease, or stay the same? Explain your answer. (Neglect gravity and assume there is no electric field.)

In(Fig. Below), charged particles move in j2 s, w8okn/vqthe vicinity of a current-carrying wire. For each charged particle, the arrow indicates the direction of motion of the particle, and the + or - indicates the sign of the charge. For each of the particles, indicate the direction of the magnetic force due to the magnetic field produced by the wo2/qs , 8kwvnjire.

Three particles, a, b, and c, enter a magnetic field as shown in Fi/zx ,j:q irp. y, n.mn6tnj:vhg. 20–46. What can you say about the cha rjntx:j. m.i,n v/:zy nhpq,6rge on each particle?

A positively charged particle in ad ov7y48zed7b3rviw+zqwm 5g /+ af ;r nonuniform magnetic field follows the trajectory shown in rvz3w5wm/df+b4d 7;z+g78 erioay vq
(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 attract3m;nwork(tid.: a60dwa l +ip an iron rod? What must you0 adwt6(+d amni3 :io;pk l.wr consider to answer these questions?

Explain why a strong magnet helfxq55cu- cy5qd near a CRT television screen (Section 17–10) causes the picture to become distorted. Also, explain why the picture sometimes goes completely b5c cf5yuq5qx -lack where the field is the strongest. [But don’t risk damage to your TV by trying this.][/But don’t risk damage to your TV by trying this.]

Suppose you have three iron rods, two of which are magnetized but the tb olp *mvt*.s;hird is not. How would you determine which two are the magnets without using any addit.vso lpmbt;* *ional objects?

Can you set a resting electron into motion with a magnetic fieldc51smfycq g2 +vg( cq3? With an electric fielms1(fyvcg gq5 +23c cqd? Explain.

A charged particle is moving in a circle under the i1y f0;n-byw98 8sicow k,frknnfluence of a uniform magnetic field. If an electric field that points in the sameocny,0;sk8 1b wr ny9fw-kif 8 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 elecvp9r o-+msq+jo gu4 v1tromagnetic pumping. It is used to pump metallic fluids (such as sodium) and to 1o9vgoqsmrp+vj4 -u+ 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 ions feel a force in the same direction?

A beam of electrons is directed toward okfu43r 5bdap6)2 x .d8 b+ m5srqlqjga horizontal wire carrying a current from left to ra4umg2b5rd86bqx3sfl.o pd + 5kqjr )ight
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields that sur3nfki,xy hw68f/u -cvround a moving electric charge.6-vxwfu/yk,h8 n icf3

A charged particle moccvlq3( 0lgr)ves in a straight line through a particular region of space. Co)rcg3l(v 0lqc uld there be a nonzero magnetic field in this region? If so, give two possible situations.

If a moving charged particle is de 2ep;wwjvixdf vf *g)-x ts:sne2*5b 8flected sideways in some region of space, can we conclude, for certain, ;5wvx** i fv2 efwxd)-:8 pjst nbgse2that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is a uniform jkp:mwcsif7.r f*16.gf2 -j adgigf/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 moh42m2,gbmguafj0:ti c j(wf3ving electrons in a certain region of space are being deflected by an elec ,htfjb0 j2g43agci 2u :mfmw(tric field or by a magnetic field (or by both)?

How can you make a compass withq mi1+a,9wlud out using iron or other ferromagnetic material?

Two long wires carrying equal currents I are at right angles to each other:74hj32 rc gklb/cwxt, but don’t bcjt4lxg 2w 7k/h3r:c quite touch. Describe the magnetic force one exerts on the other.

A horizontal current-carryuk q; + tmgsoulep4sn*1;+)t yr:h;cpct 55h ring wire, free to move in Earth’s gravitational field, is suspended directly above a se1 eh 5; rl+* ctg+ucyrstnou;p5h:q4s)kmt;pcond, 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 w,5jn umfkow9762er4two ,lkipctfj.i.)t7 of a magnet attract an unmagnetized piece of iron?

An unmagnetized nail will not attratx7o/1c2bhu sct an unmagnetized paper clip. However, if one end of the nail is in contact with a m1cu27osxbh/ tagnet, the other end will attract a paper clip. Explain.

Two ions have the same mass, but one ;3/e(jv *jn4fxo54i vh vabd xfvs y++is singly ionized and the other is doubly ionized. How will their positions on the fi5jd+v f4 f3v/evjn+a4iyov ;xs* (hbxlm of a mass spectrometer (Fig. Below) differ?

What would be the effect on B inside a long solenoid if nyre. kl2vl nguj;j)y-(/ ge)
(a) the diameter of all the loops was doubled,
(b) the spacing between loops was doubled,
(c) the solenoid’s length was doubled along with a doubling in the total number of loops?

A type of magnetic switch similar to a solenoid is a relay . -wzl/1ny( i0 oz pf ) bhvaldf2-0gr,mA 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 021lf0)pvi-b alf-zm/gr dh(wz,on yto close an electrical switch. A relay is used when you need to switch on a circuit carrying a very large current but you do not want that large current flowing through the main switch. For example, the starter switch of a car is connected to a relay so that the large current needed for the starter doesn’t pass to the dashboard switch.

  (a) What is the magnitude of the force per meter of length on a straight wirn:jrws.pv 16p vy/pk: e carrying an 8.40-A current when perpendicular tprvv ypjn:p6: k.1w/ so 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 onbmf):t nsk xr.(jw3e9 a 160-m length of straight wire stretched between two towers carrying a 150.(9fs:xt ) knwe m3brj-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 forces9jl)i 0hg (zxpfdz+ezx43prx e7.e . on a 160-m length of straight wire stretched between two towers carrying .(z zgdezli)3 jex07p.xhf4x+ps 9re a 150-A current. The Earth’s magnetic field of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  How much current is flowing in a wire 4.80 m long if the maximum forek4 nislb s )+t;k0yta. 1rn)0ox+ hguce on it is 0.750 N when placed in a uniform 0.0800-h.n btkn) 0o;)kry+sa0 tilu1sg x4+eT field?    A

  A 1.5-m length of wire carrying 4.5 A of curra1.e9fevn h (u/ky rv2ent is oriented horizontally. At that point on the Earth’s surface, the dip angl.fv n/eehkyr 2(1au 9ve 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 carr lvci0e /eg -/ih1j9esying 8.75 A is a maximum of 1.28 N when placed between the pole faces of a magnet. If the pole faces are 55.5 cm in diameter, what i cg/ji1eh 0ev s-i/9les the approximate strength of the magnetic field?    T

  The magnetic force per mp: v7z*m 6d k)d6bosejeter on a wire is measured to be only 35% of its maximum possible vdj)m pv*bzsek 6d6 :o7alue. 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 and the magnetic field.    $^{\circ}\,$

  The force on a wire is a maximul(qi *vbt*) mvm 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 wivg7.jtq9,d kcd ,;m /7g ljlotre could just “float” horizontally in air because of the force due to the Earth’s magnetic c; o d qgm/jvg7k9l. jdlt7,,tfield $\vec{B}$, 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 chargbhdyq9pi / 1ps ;k;7ive $q\,=\,+2e$ 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 direc ceu6n9 p5jp u 6oiv);kk.c*iytion of the force on an electron traveling $ 8.75\times10^{5 }\;m/s$ horizontally to the east in a vertically upward magnetic field of strength 0.75 T.    $ \times10^{-13 }\;N$  ----待选择----NorthSouth 

Find the direction of the force on a negative charge for each diagrapw6 zb8doq q(*m shown in (Fig. Below)z*dpq q( wob86, 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 of :.(xb*nl brcot/pa *d$\vec{B}$ 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 upwardb ,uh .lnu.x5k with a speed of $1.7 \times10^{6 }\;m/s$ into a uniform magnetic field of 0.350 T that is directed horizontally away from the observer. Describe the electron’s path in this field.    $ \times10^{-5 }\;m$

  A 5.0-MeV (kinetic energy) proton enters a 0.20-T field, in 5lmq/k2g9bkmv(t 6 pu a plane perpendicular to the field. What is the radius of itt v5qp6(bk/l km9mug2s path?    m

  An electron experiences the greatest f, 2ank(ge1 ie cu;mx/jorce as it travels $2.9 \times10^{6 }\;m/s$ in a magnetic field when it is moving northward. The force is upward and of magnitude $7.2 \times10^{-13 }\;N$. What are the magnitude and direction of the magnetic field?    T ----待选择----EastWest 

  What is the velocity of a beam of electrons that go undeflected when z++0 h6j wooozpassing through perpendicular electric and mo 0ozjo+w+6h zagnetic 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 mas,t p frm3imb 1d8ax;p b)oa6fj 63d*pro+dj5t s 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 c/jrp/ *jqc-cronstant speed v to make one circular /cj pr-/c*qj rrevolution 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 a35 r /)uo bstu73tr,y *fekeug uniform magnetic field B. Show that its mom/ 7e y*egorutks 5fuu t)3r3b,entum is p = qBr .

A particle of mass m and charxun ho j5o;2n*+ 5dlvege q moves in a circular path in a magnetic field B. Sho n2 nljde+;*xuh5ovo 5w that its 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 Problemouv tcs b(:m8n64 b+ d;einiwjb(z 8c, 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 Earth’s6ymchlq5gx8v 0hvgy cf5f( 9 8 magnety(hyv 6 cx9 fq8g0fv8g5l5chmic 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 mag 7gy:lg8t.s o2scuiuyhs2sjr k p/t5 i45 6qn.netic 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 soc snq ow,uy(/i ;4:xcpeed $\nu=2.0\times10^5\mathrm{~m/s}$ 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 cutqd f.ah8g(+.b olc5vrrent. How strong is the magnetic field 6.0 cm away from it +aq .85vhcld(t fbog.? 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 prod99lrv) :a ra(o.qhjymuce a magnetic field no larger than that of theyaar vr .q)9m:l oh9j( 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 carries current I out of the paged7yxsil m7p /4jn80si toward you. Indicate, with appropriate arrows, the direction of7sj x0i8d mils4np7/y $\vec{\mathbf{B}}$ at each of the points C, D, and E in the plane of the page.

  A vertical straight wire carcjqfhbrw 3 9e+nb-./h qtd4 ;;6fchplrying an upward 24-A current exerts an attractive force per unit l39j /ld.pqt6hfc; bwh-e + ;cqnf4bhrength 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 force between twxj hl6 y/ow-ong7e6t) o parallel wires 35 m long and 6.0 cm apart, each carrying 25 A in the same directiont)gown/ elxjy76 h-6o .    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic field is being carried out 1.00 m f ttvw;fq: qgp mlug.j6kd+txvp 3( :.1rom an electric cable. What is the maximum allowable current in the cable if the experiment is to be accur .tvm (+gkd:t.q3jqv tlx pg6f1u;:wpate to $\pm1.0\%?$    A

  A power line carries a cuftyn .tv s jued7l/ 47zj7n*(arrent of 95 A along the tops of 8.5-m-high poles. What is the magnitude of the magnetic field produced by this wire at the ground? How d7dt/ .us njj(yvza7e 7f4*ltnoes this compare with the Earth’s field of about $\frac{1}{2}G$?    $ \times10^{-6 }\;T$ The field of the cable is about    % that of the Earth.(retain two decimal places)

  Two long thin parallel wires 13.0 c*b 5(7gjazcu6n tl c1(y4h4g dtl rva(m apart carry 25-A currents in the same direction. Determine the magnetic field at point P, 12.0 cm from one wire and 5.0 cm from the other(Fig1 g t vnc6llyd*4ghazcb(rj47a5(t(u. Below).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18 cm due south from a straight o/y e4rig ,*cevertical wire carrying a 35-A current downward/igocry4* ,e e. In what direction does the compass needle point at this location? Assume the horizontal component of the Earth’s field at this point is $0.45\times10^{-4}\mathrm{~T}$ and the magnetic declination is 0$^{\circ}\,$.    $^{\circ}\,$ N of W

  A long horizontal wire carries 22.0 A of current due north. What isu eint6kr7zdq:j++9 c the net magnetic field 20.0 cm due west of the wire if the Earth’s field there points n6e+:r 7uji9dn+k tzcqorth 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 xt;m+fmml ,a n- -1idpat a rate of $1.5\times10^9\mathrm{~protons/s~}.$ What magnetic field do they produce 2.0 m from the beam?    $ \times10^{ -17}\;T$

Determine the magnetic field midway between two long straight wires ,yfemhumv+-j71i :ixk 5 rf 3;+4cg qobm+srh2.0 cm apart in terms of the current I in one when the other carries 15 A. Assume these+7j+o5feg i-u y:risqbh,xkr3+ cfmm4 1; vmh 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 instrufo*lz 3uu;s9n1 r-: cx; mrrttment. If the insulated wires are of negligible diameter but are 2.8 mm apart, what is u:n;l; *msruo x3cf91ztr- rtthe 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 itywc6d j gx*4g;5ci 2shown in (Fig. Below), parallel and just to the right. If it carries 25.0 A upward, what force per meter of length does it exert on each of the other two wires? Assume it is 2.8 mm from c6t4;id*cijxgg w5y 2 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 poixa o5grhd,9fcqah62 )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(73e ; eokl4c7 ywd:uwcph q.wre lies in the same plane as a straight wire, as shown in (Fig. Below). There is a current of 2.5 A in both wire4cq3p(u;7oc .eh :e7k l wywwds. 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, mineo*;7 bw+9gy4dz oj ade of 2.5-mm-diameter copper wire and parallel to zdi*g +jbw47n9o; eoy the first, is kept in suspension magnetically 15 cm below (Fig. Below).
(a) Determine the magnitude and direction of the current in the lower wire.    A the current is to the  ----待选择----leftright 
(b) Is the lower wire in stable equilibrium?  ----待选择----not in stable equilibrium in stable equilibrium 
(c) Repeat parts (a) and (b) if the second wire is suspended 15 cm above the first due to the latter’s field.

  Two long wires are oriented so that they ar/ di ue*wsz1glgs)+7ie perpendicular to each other. At their closest, they are 20.0 cm iz 1/*)i7wes g+dgs luapart (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. Wire A carries 2.0 A u()/u4 9xu rco ;kovft/v:vg ccurrent. Wire B’s current is 4.0 A in the same (vv;c : ouguxu crv9k)tof4// direction.
(a) Determine the magnetic field magnitude due to wire A at the position of wire B. $\approx$    $ \times10^{-6 }\;T$(retain one decimal places)
(b) Determine the magnetic field due to wire B at the position of wire A. $\approx$    $ \times10^{-6 }\;T$(retain one decimal places)
(c) Are these two magnetic fields equal and opposite? Why or why not?
(d) Determine the force on wire A due to wire B, and the force on wire B due to wire A. Are these two forces equal and opposite? Why or why not? $\approx$    $ \times10^{-5 }\;N/m$(retain one decimal places)

  Three long parallel wires are 3.8 cm from one anothe ;uxa+o n5zeza*o0(bcr. (Looking 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 opposite to t(*xau+;eoba5zo cz0n hat 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), determi-itlo tax9-:en2avl:ne the magnitude and direction of the magnetic field at the midpoint of the side of the triangle bee: onaxa9-lv2l t-:ti tween wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wkixsmigw1 6/.:-z u haires, 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). De/ xas16m:kiu.ihwgz- termine $\vec{B}$ along the x axis between the wires as a function of x.

  A thin 12-cm-long solenoid has a totx1h zlox9/) pyal of 420 turns of wire and carries a current of 2.0 A. Calculate the p/x9xzlh)y1 ofield inside near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameter is to pewk9ua7ls.k0wwjypf4:y. difc7 0s,roduce a field of 0.385 T at its center. How much current should the solenoid carry if it has 975 0lcwf4 f sj dpw07y k,9.uesya.w7 ki:turns of the wire?    A

  A 550-turn solenoid is 15 cm long. The c5 5mfqt*mju ; 00*.nhghwgc kzurrent in it is 33 A. A 3.0-cm-long straight wire cuts through the center of the solenoid, along a w ;g qhzn0gcuj*.k0fm5t*5mh 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 practical solenoid that prk;ofsf4l- ld mz/3 sh-oduces the greatest poz -ls/f 34 mf;ldk-shossible 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. Below). Use Am wh ez.pu7(6mp 7)hjkqpère’s law along the circular path, shown dashed in (Fig. Below a), to deterwujk(7qh7 p6phmz.e) mine 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 magnetimnfdif 2vyf *.2emj qx -s823gc field between the conductors of a cf 8g3-fnmm 2x2sqe j.f*y2vi doaxial cable (Fig. Below) is $B=\mu_0I/2\pi r$ if r is greater than the radius of the inner wire and less than the radius of the outer cylindrical braid.
(b) Show that B = 0 outside the coaxial cable.

  A single square loop of wire 22.0 cm on a side is lnkx f:6(l1pug7*crb- ;q cnzplaced with its face parallel to the magnetic field between g7 cpqb k:cn nfrx6;(1l-zu* lthe pole pieces of a large magnet. When 6.30 A flows in the coil, the torque on it is $0.325\cdot N$. What is the magnetic field strength?    T

  A galvanometer needle deflefuf2d:*mh rs*he w3q2m.5tepq d+uw4 cts 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 galv:;kqioseus xi h.-f, 9anometer weakens by 25% over the years, what current will gf-k ieuhss. q o9,ix;:ive full-scale deflection if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops b (+g :*aupfp/eaes,kn y 12%, by what factor does the output torque change?g+ne(ek,u:p*a p sfa/

Show that the magnetic dipole moment M of an electrozkzh -v)shyd.39bna . n orbiting the proton nucleus of a hydrogen atom is related to the orbital a9.sk-dha 3bnz)y z.hvngular momentum L of the electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter and containing nine loops lies flat o9mf7 qoxtk; ohl.a*muaw0 . n0n the ground. The Earth’s magnetic field at this locati ;0m0q*m.af7l ato .hk9 uowxnon has magnitude $5.50\times10^{-5}\mathrm{~Т}$ and points into the Earth at an angle of 56.0$^{\circ}\,$ below a line pointing due north. If a 7.20-A clockwise current passes through the coil,
(a) determine the torque on the coil,   $\times10^{-5}\mathrm{m}•\mathrm{N}$
(b) which edge of the coil rises up: north, east, south, or west?

  Protons move in a circle of radius 5.10 cm in a 0.566-T 5f0 1f8i 4 9atvsomatimagnetic field. What value of electric field could make their pata oiaf4 501ftvm8 i9sths straight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atoms have radii of curvature equal t d-shm4 j1abtt4c;lmc9s(5 mj 3z7f gpo 21.0, 21.6, 21.9, 22.2, and 22.8 cm. The largest radius corresponds to an atomic mass of 76 u. What are thm-59 4b tsm4czc a3pfjgmh ; 1l(jsd7te atomic masses of the other isotopes?

  Suppose the electric field between the electric plj bfa hc 5:rx,(62xeexates in the mass spectrometer of (Fig. Below)xx:fecrb(5j2h ,a6ex 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 fqx4l,,d,*.cotfj to is being used to monitor air pollutants. It is difficult, however, to separate molecules with nearlj*x4.t q,fc,o l todf,y 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 accun f0dg) lfb- *u6 lsu)72oaemelerates ions by a voltage V before they enter a magnetic field B. The ions are assumed to start from rest. Show that the mass of a0lu-*ea g o7n)d)b2 ufful6smn ion is $m=qB^2R^2/2V,$ where R is the radius of the ions’ path in the magnetic field and q is their charge.

  A long thin solenoid has 430 loops of wire per meter, and a z3; 6b;bzd8khesp(wf 25-A current flows through the wire. Ifsp3f;( kbwbh6z8 e zd; 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 640 turpr/lb0x dsc .v-i42l3b do1yt ns of wire. The magnetic fiely4p/sb t1bl-30r li 2o.cvxddd inside the solenoid 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 momentumgqc8 jfp ,n8c rjw v04c49dgul,e3dl*ryn+-h $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 q 9u. eol 0uh/9zrj)iiupon entering a region of constant magnetic field. What is tqui u hzel0o./9rj9)ihe ratio of the radii of their circular paths?   

  The power cable for an electric trolley (Fig. Below)0kwksu7b 2w 8f carries a horizontal current of 330 A toward the east. k87b sf kww0u2The 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 jm* kys 0f;n*wacquired 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 horizontallr3 8y9my z ::g tsgy:k:fscz(5rb3zmo y to the north and has magnitude tyzrf3yso:: z8mggc:95z (s : bry3k m$B=0.50\times10^{-4}\mathrm{~T.}$ 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,u l5cfi69,o rz 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 in (Figm ( *5ukysq1sz. Below). A large current moves in a closed loop composed of fixed rails, a power supply, and a very light, almost frictionless bar touching the rails. A magnetic field is perpendicular to the plane of the circuit. If the bar has a length L = 22cm, a mass of 1.5 g, and is placed in a field of 1.7 T, what constant current flow is needed to accelerate the bar fro5y(* 1mskq uzsm 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 0qztyp t*cx2; is 1.00-mm-diameter copper wire and is suspended in air due to the two magnetic forces from the bottom two wires. The current flow through the two bottom wires is 95 A in each. Calculate the required current flow in the * 20qcztyp; xtsuspended wire.    A

Two stiff parallel wires a distance l apart in a horizontal plane act a c+xy.p86fjj)t2 vx bq uh*c1ks rails to support a light metal rod of mass m (perpendicular to each rail), (Fig. Below). A magnetic x* 6j.u8fq 2pc cbx+vt)1 hjkyfield $\vec{B}$, 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 the4gtefip:i.9i tq8cebc2)4oa center of a TV screen due to the Earthe a)44et9f qcitcpb.i28 gi :o’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 accwjl,i2s0 :lmjvm zc ,4elerate elementary particles such as protons to high speeds. Particles starting at point A with some initial velz:l,ijmv jc04l mws, 2ocity travel in circular orbits in the magnetic field B. The particles are accelerated to higher speeds each time they pass through the gap between the metal “dees,” where there is an electric field E. (There is no electric field inside the hollow metal dees.) The electric field changes direction each half-cycle, owing to an ac voltage $V=V_0\sin2\pi ft,$ so that the particles are increased in speed at each passage through the gap.
(a) Show that the frequency f of the voltage must be $f\,=\,Bq/2/pi m,$ where q is the charge on the particles and m their mass.
(b) Show that the kinetic energy of the particles increases by $2qV_0$ each revolution, assuming that the gap is small.
(c) If the radius of the cyclotron is 2.0 m and the magnetic field strength is 0.50 T, what will be the maximum kinetic energy of accelerated protons in MeV?

Four very long straight parallel wires, located at the corners of a square of g t08h)a0mtzbq+v 3e xsitbg3zatmh08e+ vxq0) de 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 accelerators for “ahmsv ;bux ., 1:3zl z0cweh9cbeam steering”; that is, the magnetic fields can be used to change the beam’s direction without altering its speed (Fig. Below). Show how this works with a beam of protons. What happens to protons that are not moving with the speed that the magnetic field is designed for? If the field extends over a region 5.0 cm wide andhbv13ulc saz;,x 9ezwh :c0m . 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 twa ey4: 0xa:uohe center of a circular coil of wire carrying a current I (as in Fig. Below) i0uy4 aw: xoae:s
$B=\frac{\mu_{0} N I}{2 r},$
where N is the number of loops in the coil and r is its radius. Suppose that an electromagnet uses a coil 1.2 m in diameter made from square copper wire 1.6 mm on a side. The power supply produces 120 V at a maximum power output of 4.0 kW.
(a) How many turns are needed to run the power supply at maximum power?    turns
(b) What is the magnetic field strength at the center of the coil?    $ \times10^{-4 }\;T$
(c) If you use a greater number of turns and this same power supply (so the voltage remains at 120 V), will a greater magnetic field strength result? Explain

  Near the Earth’s poles the magnetic field is abopn : :ohi.y+lhut 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 lejrm74qk346.p ss ugof magnetic fields produced 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 kV and provide a maximum of 40 MW to the local area. Estimate the maximum magnetic f44g7 uj spemlk3rsq. 6ield 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 wokr5k1 kf3 e/cnolh-4yuld make a beam of electrons, traveling to the right at a speedl f-e/k3 5ych 4n1rkok 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 8 :iu w6z(dv rx*:afcuT, peru wfc 6r8dzu (aivx*::pendicular 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 proton as it travels from P to Q.    $ \times10^{-20 }\;J$

  A 32-cm-long solenoid, 1.8 cm in diameter, is to p h:xal,2 gk-myroduce a 0.30-T magnetic field at its center. If the maximum culmx2 h-,:yg akrrent is 5.7 A, how many turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum og2j/j vd:mq e9de;e/wires, 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 stringjeqe: eo9/dg/ ;jv2m ds make an angle of 3.0$^{\circ}\,$ with the vertical, what is the current in the wires?    A

  An electron enters a unqb .+ )rhnojn d68z y/t9ddp-eiform magnetic 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$