A compass needle is not always balanced parallel to the Earth’s surface, bz) f 33*qcpkqlut one end may dip downk qc3*lqz3f )pward. Explain.

Draw the magnetic fieldkx.- s k6yavp* lines around a straight section of wire carrying a current horizontallxpkv 6y-sk. a*y to the left.

In what direction are the magnetic field lines surrounding a straight wirq gsprf:7kdnp l+z4fvm6le-ht3 s.d-/a.ds ,e carrying a cur/n7dl-fft6s . qd-.eg3s dp,p4vz+mk ralsh:rent that is moving directly away from you?

A horseshoe magnet is held vertically u c/ 3utg j* )g+ohdyu+ua*:bqwith the north pole on the left and south pole on the righ+ucbygdhou/ aj *qug: t+) *u3t. A wire 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 metalli aw5 d36eyu,qgc object, or only those made of iron? (Try it and seed3 qy5u,egw 6a.) Why is this so?

Two iron bars attract e3 bjskq-11g llach other no matter which ends are placed close together. Are both magnets? Explain1-jlqls13 kb g.

The magnetic field due to current in wires in your home can affect a compass. /5z*6k faakqa,d.flk Disc k,za5qfa/la. kkd6f* uss the effect in terms of currents, including if they are ac or dc.

If a negatively charged particle enters a region of uniform magnetic xbtb;ge-sh20: x3kk3ly b4bpfield which is perpendicular to the particle’s velocik4hb0s;p3: blt-xx 3kg2ebby ty, will the kinetic energy of the particle increase, decrease, or stay the same? Explain your answer. (Neglect gravity and assume there is no electric field.)

In(Fig. Below), charged part (1ukdajt6zh3icles move in the vicinity of a current-carrying wire. For each charged particle, the arrow indicates the directik u h3zt(6ja1don 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 wire.

Three particles, a, b, and c, enterxy0o 8exbz7:wrl) 6zz a magnetic field as shown in Fig. 20–46. What can you say about the charge on each particle? zzr7 e6z0yl: b8)xxw o

A positively charged particle in a nonuniformu;/ rj pfy2u 3+ne :jb0qgccd8 magnetic field follows the trajectory s:fjp guey3b nc2 /+qj80c; udrhown 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 a magnet attract an iron rod? What must -( o 46bizdv6hkh 2.ckipb(pyyou consider to answer thesi(d-cz (kiy6bpo.v2h64bhpk e questions?

Explain why a strong magnet held ncp0rpilg:v c9*4h k*aear a 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 0 vchki 4lp*c9gp*:ar 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 27-s:ld9 tgsqgtakt )sbk r9 9q2 6etethe third is not. How would you determine which two are the magn29as)7 b:rt - k9dl9k62teettqgssg q ets without using any additional objects?

Can you set a resting electron into motion with a magnetic field? With an electjoa )+6okudm ybh(o azd794 w,ric field? Exdo7j4d+m6a9,o )zb hau( wyokplain.

A charged particle is moving in a circle undkm)i3f6wtfa i jf;w/6er the influence of a uniform magnetic field. If an electric field that points in the same direction as the magnetic field is turned on, desm66k/a wwi f;f3fj)itcribe the path the charged particle will take.

The force on a particle in(oewqk c84ycb: catmit4 ;a a .1rs-u/ a magnetic field is the idea behind electromagnetic pumping. It is used to pump metallic fluids (such as sodium) and to pump blood in artificial heart aa s(cw.:yc 8-u4m;c itbqko4/ret a1 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 wire carrying a rm+ .w*wvs 8cx5q: vxicurrent from les cx8qw :r m5x+i.wv*vft to right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnezgoyl8 6 (9ik*ukv x4mho6 ;chtic fields that surround a moving electric charge. ivk9u m86oy(oghz kl;cxh*46

A charged particle moves in a yep+lz5zmtz-)lxws : u58jd:4m d( ncstraight line through a particular region of space. Could there be a nonzero magn ) 54jdwmn -cylz+:stmu8 l 5xzedpz:(etic field in this region? If so, give two possible situations.

If a moving charged particle is defl/x8uia);e:bxg:q i 6ww uy*ldected sideways in some region of space, can gy*)wxx w8u;ibl ei:d6a q/: uwe conclude, for certain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of nu 6h-,l7 y6uv/*bgtpcv f6fzspace there 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 in a certain redg2+k4abnfq l1-bl l 3gion of space are being deflected by an electric field or by a malf2 lq14k+da3gbnlb-gnetic field (or by both)?

How can you make a compass without using iron or other ferromagnetic mate/),k bqeb wq1-t ak9ox9ver0urial?

Two long wires carrying equal currents I are at3 dy./)cfzohn( oc6w v right angles to each other, but don’t quite touch. Describe the magnetic force one 6doy3/(v .hzcown f)c exerts on the other.

A horizontal current-carrying wire, free to move in Earth’s grac js7*85okyob zkatgp q.15 .evitational field, is suspended directly above a second yjsb5z*8. ga1kq.c k7top5o e, 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 unmagnetize 6y,+xjruq )8,(6xsdpn2m, ksh lqwtvd piece of iron?

An unmagnetized nail will not attract an unmagnetized paper c r.+;zp4wp9h bu;xjax d i)n5zlip. However, if one end of the nail is in contact with a magnet, the oth94rb p x i.u ;)pdjxna5w;+zhzer end will attract a paper clip. Explain.

Two ions have the same mass, but one is singly ionns/5s r5y,6ty; w 9qgb cf, sz+octv(gized and the other is doubly iong ss,tnbv /t5s+f 9q,6r;yy5w (cocgzized. How will their positions on the film of a mass spectrometer (Fig. Below) differ?

What would be the eff0 j6x8wwdlu.8r9s uec0oxh hkl 7 7jf)ect on B inside 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 relay . A relay is an elzay2zi9;cqydb+4s)eo1+j xrectromagnet (the iron rod inside the coil does not move) which, when activated, attracts a piece of iron on a pivot. Design a relay to clo +cq 9;z+)ebd 41j2ysyx oarizse 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 lent.zsxu1 o osm0n/2qy8 gth on a straight wire carrying an 8.40-A current wheq s8m.2tsuxo /z10yno n 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 forcbi4afx/ah/r w2g0r j.e on a 160-m length of straight wire stretched between two towers carra g0wjx/.bfiah/4 rr2 ying 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 fooz 4b3,4 j pbzr2jbxy-rce on a 160-m length of straight wire stretched between two b4 z3,rxyb 4-j bp2ozjtowers carrying a 150-A current. The Earth’s magnetic field of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  How much current is flowing in a wire 4.80 m long i.xz6yx .ry:q jf the maximum force on it is 0.750 N when placed i.xxq. r6 y:yzjn a uniform 0.0800-T field?    A

  A 1.5-m length of wire carrying 4.5 A of current is 2qyu ds;/b,* mjw0v pooriented horizontally. At that point on the Earth’s surface, the dip02ps, uj bd ;vwoq/ym* 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 maxlg)j8zl5 ,dzl8a r :hqimum of 1.28 N when placed between the pole faces of a magnet. If t:jd,zrg5h8 )l alq8lzhe 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 to be only 35%oh2)yb* 4gh qi of its maximum possible value. Sketch the relationship of the wire and the field if the foh 2)bo4*yi hgqrce 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 maximum mkqq)(yiso )-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 could just “flo1oee,evgxdo v l7y-9.jx 8u3 jat” horizontally in air because of tg9evv87xed .j31ojo, xyule -he 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 charhh5 ;zs lxw33oge $q\,=\,+2e$ 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 +h gse. hbd7d/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 ta9k9 (u2td44gfogvwb he force on a negative charge for each diagram shown in (Fig. Below), uwgob (29a9v 44k fdgtwhere $\vec{v}$ (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 directioncmxi / txcwi/;o69ff ) 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 ls+,bu3/ri1b 4rs 2l 2yeraotwith 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 a plane pzexwgt026)eu6) t hj c7gyrh 4erpendicular to the fieldgyxj4w)h7g )0ht 2ec66 utzr e. What is the radius of its path?    m

  An electron experiences the grw4wtbv mif.*t5c1 xlbj. z0.peatest 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 that go undeflected when pg +6 vzc3ana 7xmc,dn-assing through perpendicular electric 763cvm,-dan naz+x cg and magnetic fields of magnitude $8.8 \times10^{3 }\;V/m$ and $3.5 \times10^{-3 }\;T$, respectively? What is the radius of the electron orbit if the electric field is turned off? $F_E$    $ \times10^{6 }\;m/s$ $F_{max}$   $ \times10^{ -3}\;m$

  A doubly charged helium atom whose maso8y5ym ;f(igh 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-o+v,wstm ++na; z kor a particle of charge q moving with constant speed v to make one circular rewsnk ;,ozo++- rat +vmvolution 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 rairqj5tio8 t5a 2 n7*mkdius r in a uniform magnetic field B. Show that its momentum 7jri*aqmo5i k 2t 5t8nis p = qBr .

A particle of mass m and charge q moves in a circularigjl5l* ba6(f path in a magnetic field B. Show that its kinetic energy i5(fl jblai*6 gs proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momentum of the particle in Problem 21 i0jp4 *n v0men3ue*l dps $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves with a speed of 160 m/s pe0d7s ebh vj9;fi/yx.9bqr3vkrpendicular to the Earth’s magnetic field of sh3di/v.7f xe99 b bv ykjr0;q$5.00\times10^{-5}\mathrm{~T}$, If the bullet possesses a net charge of $13.5\times10^{-9}\mathrm{~C},$ by what distance will it be deflected from its path due to the Earth’s magnetic field after it has traveled 1.00 km?    $ \times10^{-7 }\;m$

  Suppose the Earth’s magnetic field at the equator has magnitu /nms.+jw tte0e- 1i iujohi(yex.t-0de $0.40\times10^{-4}\mathrm{~Т}$ 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 spe,ovnea:4krcs*uu/ ,ntdl; b(ed $\nu=2.0\times10^5\mathrm{~m/s}$ in a field-free region abruptly enters an essentially uniform magnetic field $B=0.850\mathrm{~T~}(\vec{\mathbf{B}}\perp\vec{\mathbf{v}}).$ If the proton enters the magnetic field region at a $45^{\circ}$ angle as shown in (Fig. Below),
(a) at what angle does it leave, $\theta$    $^{\circ}\,$
(b) at what distance x does it exit the field? x    $ \times10^{-3 }\;m$

  A jumper cable used to start a stalled vehicle carries a 65-A c9v)9)tare c*0knnzwd urrent. How strong is the magnetic field 6.0 cm away from it? Compare to the Ea *ze9rn w)c9d0a vn)tkrth’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 allow hy rh5ie((nf-ed to produce a magnetic field no larger than that o(ef -h( rh5niyf the Earth $(0.55\times10^{-4}\mathrm{~Т})$ at a distance of 25 cm, what is the maximum current the wire can carry?    A

In (Fig. Below), a long straight wigglu/c blt:-zohs :4 3re carries current I out of the page toward you. Indicate3s:hzlgb4/ cg lt:- uo, 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 upward 24-j2bi,6d90mcfw / wuviA current exerts an attractive force per uni2,cbd vmjw/6 0iwi9uf t length of $8.8\times10^{-4}\mathrm{~N/m}$ on a second parallel wire 7.0 cm away. What current (magnitude and direction) flows in the second wire?    A  ----待选择----upwarddownward 

  Determine the magnitude and direction of the force between two parallel wire*:suayi2 bs8my ta 0t8s 35 m long and 6.0 cm apart, each carrying 25 utssmya8 y*it0 8ab :2A in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic f 6u m.,t:ytn4pgo.i xuield is being carried out 1.00 m from an electric cable. What is the maximum allowable current in the cai .n46,ouuyp.gt:t xmble if the experiment is to be accurate to $\pm1.0\%?$    A

  A power line carries a current of 95 A along the tops of 8.5-i;wt 0 hk9nnv5m-high poles. What is the magnitude of the magnetic field produced by this wire at the ground? How does this compar 05vtinw9;hnke 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 curreyqpw d.ab5:i2t1/a 1 f6rjzdwh/l c 9hnts in the same direction. Determine the magnetic field at point P, 12.0 cm from one wire and 5.0 cm from t1y/th9l5hbic/aq pj1 f6wr :z .daw2 dhe other(Fig. Below).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18 cm due south from a straights : sx).,rpgv6m-8 2wtgupnt q vertical wire carrying a 35-A current downward. In what direction does the compass needle point at this locwp6gtqun pvxm8- ):.rt2s gs,ation? 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 wi:mz ,/ jouuc16 wyphf8re carries 22.0 A of current due north. What is the net magnetic field 20.0 cm due west,18:/z f jhucpymo w6u of the wire if the Earth’s field there points north but downward, 37$^{\circ}\,$ below the horizontal, and has magnitude $5.0\times10^{-5}\mathrm{~Т}?$
   $ \times10^{-5 }\;T$
$\theta$ =    $^{\circ}\,$ below the horizontal

  A straight stream of protons passes a gave :0k;ey )reiven point in space at a rate of $1.5\times10^9\mathrm{~protons/s~}.$ What magnetic field do they produce 2.0 m from the beam?    $ \times10^{ -17}\;T$

Determine the magnetic field midway between two xp3x0b3 vzn8tlong straight wires 2.0 cm apart in terms of the current I in one when the other carries 15 A. Assup3 t8vz3b xn0xme these currents are
(a) in the same direction,
(b) in opposite directions.

  A long pair of wires conducts),ihvm0m b wi/ 25.0 A of dc current 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 the magneti0w mmhib/i)v, c field of the Earth.
   $ \times10^{-6 }\;T$ The field of the wires is about    % that of the Earth.(retain two decimal places)

  A third wire is placed in the plane of the two wires shown in su p//hwhz(ih03)k fdmup4(* q af(k .rmuk m7(Fig. Below), parallel and just to the right. If it carries 25.0 A upward, what force per m r ) a ffmuikkwp( /dqphu0( 4u.mh/zm*k3h(s7eter 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 23b4 nxk*0yn )qlarkl2/$^{\circ}\,$ E of N outdoors. However, when it is placed 12.0 cm to the east of a vertical wire inside a building, it points 55$^{\circ}\,$ E of N. What are the magnitude and direction of the current in the wire? The Earth’s field there is $0.50\times10^{-4}\mathrm{~T}$ and is horizontal.    A  ----待选择----updown 

  A rectangular loop of wire lies in the satp9oh3 t 9atxz+6:q0 d 1n(jw zkxatw8me plane as a straight wire, as shown in (Fig. Below). There is a current of 2.5 A in both wires. Determine the magnitude and direction of the net force on39a :txn 9j1xhzw poz qwt86tk0 (+adt the loop.    $ \times10^{ -6}\;N$  ----待选择----away from wiretowards wire 

  A long horizontal wire carries a current of 48 A. A s ldd,qxy kqci87z4:,eecond wire, made of 2.5-mm-diameter copper wire and parallel to the first, is kept in suspension magnetically q exl:,qi8dd, 4kyc 7z15 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 m0g; k q/0nmiyeach 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 curr g0;n0mk/ yimqent of 20.0 A and the bottom one carries 5.0 A?    $ \times10^{-5 }\;T$

  Two long straight pa.i s:k mgya3j4rallel wires are 15 cm apart. Wire A carries 2.0 A current. Wire B’s current is 4.0 A in the same directiojsgyi m.a: k34n.
(a) Determine the magnetic field magnitude due to wire A at the position of wire B. $\approx$    $ \times10^{-6 }\;T$(retain one decimal places)
(b) Determine the magnetic field due to wire B at the position of wire A. $\approx$    $ \times10^{-6 }\;T$(retain one decimal places)
(c) Are these two magnetic fields equal and opposite? Why or why not?
(d) Determine the force on wire A due to wire B, and the force on wire B due to wire A. Are these two forces equal and opposite? Why or why not? $\approx$    $ \times10^{-5 }\;N/m$(retain one decimal places)

  Three long parallel wires are 3.8 cm from one another. (Looking along them, they, kiazaln1 d1 ruuv)9( 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 that in wires N and P (Fig. Below). Determine the magnetic force per unit length on each wire due to the othu )1ai(rk,l1an9zuvder 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 magslcnam ( o9p*oz e71*vnetic field at the midpoint of the side oe1 lac97m* vn*(oszpof the triangle between wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires,u9np o41gscjg8 :-s5hjjn: j u a distance d apart, carry equal currents I in the same direction. One wire is at x = 0, the other54:ngcuusj :9sj jhp- o1 jgn8 is at x = d, (Fig. Below). Determine $\vec{B}$ along the x axis between the wires as a function of x.

  A thin 12-cm-long solenoid has a total, /j9w0q g vr/5n);gjpzm0 nkhr vz0hr of 420 turns of wire and carries a current of 2.0 A. Calculate / rvg9nkz0 n)5 j;zg0rvhj0h/wpmq, rthe field inside near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameter is to produce a field of 0. ,men p*09qj35 egio)dwhyxa 0385 T at its center. How much current should the solenoid carry if it has 975 *we)ny dm,he0qa50ij x9go3p turns of the wire?    A

  A 550-turn solenoid is 15 cm long. The cud,+u2zlff3d 7 q.qzbyrrent in it is 33 A. A 3.0-cm-long straight wiredfz7,3 yd+2lq .uzqbf cuts through the center of the solenoid, along a diameter. This wire carries a 22-A current downward (and is connected by other wires that don’t concern us). What is the force on this wire assuming the solenoid’s field points due east?    N

You have 1.0 kg of copper andh;rh(0 5by xkd want to make a practical solenoid that produces the greatest possible magnetic fieldhykbr dh;0 5x( 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. )-cra k2de;dc3, yu i6 u6iqalBelow). Use Ampère’s law along the circular path, shown dashed ik 6eqi-ia;)c6r u3udlca ,yd 2n (Fig. Below a), to determine that the magnetic field
(a) inside the toroid is $B=\mu_0NI/2\pi r$ where N is the total number of turns, and
(b) outside the toroid is B = 0 .
(c) Is the field inside a toroid uniform like a solenoid’s? If not, how does it vary?

(a) Use Ampère’s law to show that the magnetic fielb 9wa ic6(+1avx8gxelq r0 al8d between the conductors of a coaxial cable (Fig(cwxe+ qar6 x1 aig8 8alb9l0v. 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 gssfxg4p(cgijt:i d9r +5(a9side is placed with its face parallel to the magnetic field between the pole pieces of a large magnet. When 6.30 A flows in the coil, the i5x rjpi (a9d s(9cg:g4t+fsgtorque on it is $0.325\cdot N$. What is the magnetic field strength?    T

  A galvanometer needle deflects febhee2g))4 qt 8:fx p/6gwlb wull 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 25% over the years, whatsi9j1g e d4)qp current will give full-scale deflection if it or g je94s1)iqdpiginally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by wh wuzqf9gk3)z +qtz qav p11bh::/f,uvat factor does the output torque chqpfzbf:9 zqvga+1tkvw31 u:/z uh q,)ange?

Show that the magnetic dipoleo y ou((5ihfn a4p-:ml moment M of an electron orbiting the proton nucleus of a hydrogen atom is related to the orbital angular momentum L oi mn uoh5(fyo-ap l:(4f the electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter abipib9j l 0/u ;jnd ,;hevsv ;a2k5i;jnd containing nine loops lies flat on the ground. The Earth’s magnetic field at vsv5l;n ;9j; /pje,iak bbi 02di u;hjthis location has magnitude $5.50\times10^{-5}\mathrm{~Т}$ and points into the Earth at an angle of 56.0$^{\circ}\,$ below a line pointing due north. If a 7.20-A clockwise current passes through the coil,
(a) determine the torque on the coil,   $\times10^{-5}\mathrm{m}•\mathrm{N}$
(b) which edge of the coil rises up: north, east, south, or west?

  Protons move in a circle of radius 5.10 cm in a 0.566-T magnetic fiel)t()se8m y.kw.wp3ei0l m nd dd. What value of electric field could make their paths straight? In what directionwse)it3(epld.mnd) 0 8wk y .m must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, /rwf: 4wb cf,bo +zxs.eh w*dvu/)mz-germanium atoms have radii of curvature equal to 21.0, 21.6, 21.9, 22.2, and 22.8 cm. The largest radius corresponds to an atomic mass of 76 u. What are the atomic ma)ufm*4:bxz zcf .,+rs ww d/eh-o wv/bsses of the other isotopes?

  Suppose the electric field between the electric w -4igim,07m w: wfsyuplates in the mass spectrometer of (Fig 47iyw:mm s,wfiw-0ug. 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 monito:(ynrzjr5hyrj7avsf8 . 4:znr air pollutants. It is difficult, however, to separate molecuanrjrjzs.7 fn5vhy :r8y (4z:les 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 spectr9g(n w e0lyj2aometer accelerates ions by a voltage V before they enter a mal2w0(eagj9y ngnetic field B. The ions are assumed to start from rest. Show that the mass of an ion is $m=qB^2R^2/2V,$ where R is the radius of the ions’ path in the magnetic field and q is their charge.

  A long thin solenoid has 430 loops of wire 7c 03axi7rz0ajx/vhqper meter, and a 25-A current flows through the wire. If the permeabi ch07a/v0zjq3rxxia7lity 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 1.8y 7+dd:y;h ws94e xh0uqw*znol0 5rkk cm in diameter, and has 640 turns of wire. The ma09no;wr kh4xd +*yly5e k hquw:07zs dgnetic field 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 momentumc9/aze 0;.cci amjk/ l+q 0tsh cd6x-m $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ are magnetically steered clockwise in a circular path 2.0 km in diameter at Fermi National Accelerator Laboratory in Illinois. Determine the magnitude and direction of the field in the magnets surrounding the beam pipe.    T

  A proton and an electron have the same kinetic energy upon entering a region of pv1zqlwm) 2 e+constant magnetic field. What is tlv 12qw) +mezphe ratio of the radii of their circular paths?   

  The power cable for an electric trolley (Fig. Below) carries a horizontaliuw80 xu).shg+w 1e cu5f6*i cuku7br current of 330 A toward the east.) .re i78 50chus*+bwuuw6kxfug1iu c The Earth’s magnetic field has a strength $5.0\times10^{-5}\mathrm{~T}$ and makes an angle of dip of 22$^{\circ}\,$ at this location. Calculate the magnitude and direction of the magnetic force on a 15-m length of this cable.    N the force on the wire is  ----待选择----southerlynortherly  and   $^{\circ}\,$ above the horizontal .

  Calculate the force on an airplane whay)2tk+8k6fo bz anq, ich 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 tfy*82 xeycar ;ruu7.Earth’s magnetic field points almost horizontally to the nort . yrtr7;2 yfcu*ae8uxh and has magnitude $B=0.50\times10^{-4}\mathrm{~T.}$ What should be the magnitude and direction for the velocity of an electron if its weight is to be exactly balanced by the magnetic force?    $ \times10^{-6 }\;m/s$  ----待选择----eastwest 

  A doubly charged helium atom, whose mzp5w/h/1 tqvp ass 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 (Fig. Below). A large curre* gmoyf l/4bw 7t2.3hcyxp n)pnt moves in a c h2p/y3*xln m. )c yf7bogtwp4losed loop composed of fixed rails, a power supply, and a very light, almost frictionless bar touching the rails. A magnetic field is perpendicular to the plane of the circuit. If the bar has a length L = 22cm, a mass of 1.5 g, and is placed in a field of 1.7 T, what constant current flow is needed to accelerate the bar from rest to 28m/s in a distance of 1.0 m? In what direction must the magnetic field point?
   A
the magnetic field must be ----待选择----updown 

  In (Fig. Below) the top wire is 1.00-mm-diameter e:n dx15vao8 wcopper wire and is suspended in air due to the two magnetic forces from the 81nax e :wd5ovbottom two wires. The current flow through the two bottom wires is 95 A in each. Calculate the required current flow in the suspended wire.    A

Two stiff parallel wires a distance l apart in a horizontal plane act wj7-kv) yde;s7eyrb) as rails to support a light metal rod of mass m (perpendicular to each rail), (Fisr);d yvybe7 wk) je-7g. 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 erz px/5wo.6xq l tv)bo. k6i9w0;cnpflectron beam near the center of a TV screen d.f x6itpkqz;oc/nvx0pw 9 .)6 olwrb 5ue 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 used to a6b g;g nqaxq /ini)dpu(s+( k8ccelerate elementary particles suca6uq+n )g;( 8ipqidxbk/ s(n gh as protons to high speeds. Particles starting at point A with some initial velocity travel in circular orbits in the magnetic field B. The particles are accelerated to higher speeds each time 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 s3c/ / a(cxzdzsquare of side l, car/a/zcd cz(x s3ry 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 steg/23 fvhil zx(ering”; that is, the magnetic fields can be used to change the beam’s directio2l3g fhv(zx /in without altering its speed (Fig. Below). Show how this works with a beam of protons. What happens to protons that are not moving with the speed that the magnetic field is designed for? If the field extends over a region 5.0 cm wide and has a magnitude of 0.33 T, by approximately what angle will a beam of protons traveling at $ 1.0\times10^{7 }\,m/s;$ be bent?    $^{\circ}\,$

  The magnetic field B at the center of a circular coil of wire carrying0 cw1dior clpgt/t66- a current I (as ingoli6 t0w6dt-c1/rp c Fig. Below) is
$B=\frac{\mu_{0} N I}{2 r},$
where N is the number of loops in the coil and r is its radius. Suppose that an electromagnet uses a coil 1.2 m in diameter made from square copper wire 1.6 mm on a side. The power supply produces 120 V at a maximum power output of 4.0 kW.
(a) How many turns are needed to run the power supply at maximum power?    turns
(b) What is the magnetic field strength at the center of the coil?    $ \times10^{-4 }\;T$
(c) If you use a greater number of turns and this same power supply (so the voltage remains at 120 V), will a greater magnetic field strength result? Explain

  Near the Earth’s poles the magnetic fie:;/* ogpxf zqdld 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 field;6r4dtjhwg 6/iaxd;d s 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 that6g d;/4jh6 xi;tr addw the lines operate at 10 kV and provide a maximum of 40 MW to the local area. Estimate the maximum magnetic field you might experience walking under these power lines, and compare to the Earth’s field. [For an ac current, values are rms, and the magnetic field will be changing.] $B_{net}$ $\approx$    $ \times10^{ -5}\;T$(Round to the nearest integer)

  (a) What value of magnetic field would manh2)2/ pu.nk em e6wsxke a beam of electrons, traveling to the right at uem wsxp ./2e2 n6k)hna 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 gajl nhs) rn,b6/s in a magnetic field of 0.010 T, perpendicular to the plane of lh rb/)js,n6nthe 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 dpx 3e4g(x5jg1:s1 c *ewbpwxs iameter, is to produce a 0.30-T magnetic field at its center. If the maximum current x4ej*3pbxc 1(gs se 1:wg5wpxis 5.7 A, how many turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, each of diameter 0.50 mm, carryi0 14k0flv.q 8sxmsf x the same current but in opposite direls.sxfx 0i81 0vqfkm4ctions. 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 magne:-e2bdo: ug3bjss8l ctic 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$