A compass needle is not always balanced parallel to the Earth’s rmzfg5,n b18*gh0bxw surface, but one end may dip downward. Exp0xf* 1 ,rhb b5mnggwz8lain.

Draw the magnetic field lines around a straight section of wire carrying a curre0* 8yxnazzw1 )r-ktpnnt horia- nwykx81rz )n* p0tzzontally to the left.

In what direction are the magnetic field lines surr0p n0u jfqz2i ;vm4/nrounding a straight wire carrying a current that is 0qum/j ;n4 zpivfr n02moving directly away from you?

A horseshoe magnet is held vertically with the north pole on thec zosbu8ddje m6c86:. left and south pole on the right. A wire passing between the poles, equidistant from them, carries a current directly away frou c8: b scjdz6om6d.8em you. In what direction is the force on the wire?

Will a magnet attract any metallic object, or only thosb qfa7 olo8dn,agie9-c b ec--jy-(6we made of iron? (Try it and see.) Why is td7,bc6gwb a -q ao-e8c-y-lf9(ni j oehis so?

Two iron bars attract f- 7 )z*eba-i,swkerheach other no matter which ends are placed close together. kr7*ab, ih)feew z-s-Are both magnets? Explain.

The magnetic field due to current in wires in your home can affect a compass. D4-h2d rvzjs; b/sr i+tiscuss thedr2b -4rhz /vs;+istj effect in terms of currents, including if they are ac or dc.

If a negatively charged particle enrk pt8+q.oe mg(.-caud c.q)pc 1lv+yters a region of uniform magnetic field which is perpendicular to the particle’s velocity, will the kinetic energu+ta( c 8 or dcgq.mp)-ky.q l.cp+ev1y of the particle increase, decrease, or stay the same? Explain your answer. (Neglect gravity and assume there is no electric field.)

In(Fig. Below), charged particles move in the vicinity of a current-carryf)skk( 0yzxu-.q *wf/tc7o z+amg9 rping 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 wfr9/yk7 +o af0uszpmq)cx- .zt(*gk to the magnetic field produced by the wire.

Three particles, a, b, and c, enter a magnetic field as shown in Fig. 20–46. Whaegw/ bwm*4l8x;0ox x;k g;e kzt x b; kw0gezog w*mxk;4l;e8/x can you say about the charge on each particle?

A positively charged particle inbit :q(ywpuo+e )d,q4g wtozi asb249yr(8 ;i a nonuniform magnetic field follows the trajecto(+i ; sid2 :zyq a8oi4wtey, po)wbr4gb9uq(try 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 a mhu1 -;sap3k vbbfe2e +agnet attract an iron rod? What must you cons3+b2ea-f bev1 h;skup ider to answer these questions?

Explain why a strong magnet held near a CRT television screen (Section 17–10) c,o-gyyp a 3:)egq 0kadauses the picture to bec3 p-aqg koad:ey) 0y,gome distorted. Also, explain why the picture sometimes goes completely black where the field is the strongest. [But don’t risk damage to your TV by trying this.][/But don’t risk damage to your TV by trying this.]

Suppose you have three iron rods, two of which are magnetized but the third is 6kxxi(i3b jp*not. How would you determine which two are the magnets without using any additionib(x j*6xp3 kial objects?

Can you set a resting electront;dkfoj td.y(;i: o 6z into motion with a magnetic field? With an electric :.kodzoj ;(yift6td ; field? Explain.

A charged particle is moving in a circle under the influence of a uniform maga vfg0 eu*x;7tnetic field. If an electric field that points in the same direction as the magnetic field is gtx7;0eafv *uturned on, describe the path the charged particle will take.

The force on a particle in a magnetic field is the idea behind electromagne:rp-f9qd*-x jhry7 x 93kt mh(q fxd6etic pumping. It is used to pump metallic fluids (such as sodium) and to pump blood in artificial heq(- :9 d yph xhr6fdej- fx79t3qm*rkxart 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 current froe won6m9b vm+ sz0h9+jm leftov 0 z6m9jnbh+w+me9s to right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields that surround a moving elefz: qe09vrjy6ctric charge.yf:9zre q0vj6

A charged particle moves in a straight line through a pay -7keu)xvw5 qh6z;7stxqo6y rticular region of space. Could there be a nonzero magnetic field in this region? If so, give two possiblek xqtz)s vye y6;-hu65qw7ox7 situations.

If a moving charged particle is deflected sideways in some regio5ai9.vk/tz6bgvkrx*gj , woljzdq -n+;/lo -n of space, can /5xvak rzvznd. bij /, *6-+-gl;l9gtwqjoko we conclude, for certain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is a uniform magnxnmlj6;sq/d9 g7tvc0 etic 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 region of space ar+h8lka w/.izxiee. -+ q0v i f+jwjz6he being deflected by an electric 8x+ +h.zqj.ha6 -iewzkvj eiw0fl+ /ifield or by a magnetic field (or by both)?

How can you make a compass wit rb)ybvo.b)2s idh -kcfv5 o+:hout using iron or other ferromagnetic material?

Two long wires carrying equal currents Igmjemxl +3 1s) are at right angles to each other, but don’t quite t+l eg3ms 1jx)mouch. Describe the magnetic force one exerts on the other.

A horizontal current-carrying wire, free to mohwtht mm578s8ve in Earth’s gravitational field, is suspended directly abov 87h8mws 5mthte 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 at2twnqrq+r ;7wb5l f9q tract an unmagnetized piece of iron?

An unmagnetized nail will not attract an unmagnetized yffmv7 c06ickct(c54 paper clip. However, if one end of t6fcik mc4 y7( vc5c0fthe nail is in contact with a magnet, the other end will attract a paper clip. Explain.

Two ions have the same mass, but one is singly ionized and the other is dous3byb4j*86dos)d a u+ pi ,yhm k98ljcbly ionized. How will theirs8k,o4h*)yu9b b jciy+ddp s63 jlm a8 positions on the film of a mass spectrometer (Fig. Below) differ?

What would be the effect on B inside a long solenoid iite0vg ifff -b73. 5pcf
(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 l r( v11y a (anfp8fs5gwki5u,solenoid is a relay . A relay is an electromagnet (the iron rod inside the coil does not move) which, when activated, attracts a piece of iron on a pivot. Design a relay to close an electrical switch. A relay is used when you w5y1asfni,1gru 85fkla(vp ( 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 5dthlw-;r:9ef;mn+cz nfns4+ x aqi7the force per meter of length on a straight wire carrying an 8.40-A current when perpendicular to a 0.95+amn4r7;9fln-xw+c zfh ; enqitsd:0-T uniform magnetic field?    N/m
(b) What if the angle between the wire and field is 45.0$^{\circ}\,$?    N/m

  Calculate the magnithv3a- zj pso yz.boz**6v(e34v z em fqzt98z4ude of the magnetic force on a 160-m length of straight wire stretched between two towers (qzos.h 4zv-py68b*zo3 avevzte 943zj zf*m carrying a 150-A current. The Earth’s magnetic field of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  Calculate the magnitude of the magnetic force on dg.kexya;.,v 0n f- sta 160-m length of straight wire stretched between two towers carrying a 150-A current. The Earth’s magnetic fien;axv.e-,t gdy f0s. kld 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 force on i h4o,v6 ddx6mft is 0.750 N when placed in a uniform 0.0806o fx4vm 6,hdd0-T field?    A

  A 1.5-m length of wire carry:etf f ban1jm3z) qyd)6 +wr+hing 4.5 A of current is oriented horizontally. At that point on the Earth’s surface, the dip6hjmq) ntf+ z:1wdae r) by3f+ angle of the Earth’s magnetic field makes an angle of 38 $^{\circ}\,$ to the wire. Estimate the magnitude of the magnetic force on the wire due to the Earth’s magnetic field of $ 5.5\times10^{ -5}\;T$ at this point.    $ \times10^{-4 }\;N$

  The force on a wire carrying 8.75 A is a maximum of 1.28 N when placed betweeni-a4 wl / ,+cnyv8ynbg the pole faces of a magnet. If the pole faces are 55.5 cm in diameter, what is the approximate strength of the magnetic field,8 ag-w n+/vcy4 ibyln?    T

  The magnetic force per meter on a /hx8 fazf+q n(7viy :*wgb0aywire is measured to be only 35% of its maximum possible value. Sketch the relationship of the wire and the field if the force had been a maximum, and sketch the relationship as it actually is, calculating yn7ya +h/(: zfaivq*fgx8b0 wthe angle between the wire and the magnetic field.    $^{\circ}\,$

  The force on a wire is a 0y ;6y+q8too( jqz8pl1aiut g maximum 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 “float” horiz zy9zlrcxh:o24 ccdk793*kd r1tp w. yontally in air because of the force due to the Eayrchzlpx 7k:. 4od 9tc *cyw9d31kzr2rth’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 chargex5/ zt5-n- evqq sh35y:w ncee $q\,=\,+2e$ 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 direox*9h)tk gyn,ction 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 thwgdy 33h0opf (e force on a negative charge for each diagram shown in (Fig. Belogy(f0 3dh3pwow), 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 ir(x(ig+ikck/3krvd7e e z 78of $\vec{B}$ 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 mf:3i*+bdcfl 33 25*iyjqsbdu0vbwpvertically upward with a speed of $1.7 \times10^{6 }\;m/s$ into a uniform magnetic field of 0.350 T that is directed horizontally away from the observer. Describe the electron’s path in this field.    $ \times10^{-5 }\;m$

  A 5.0-MeV (kinetic energy) proton enters a 0.20-T fi6p hc9-bs9pz jeld, in a plane perpendicular to the field. What is the 9 bp9spj-z6ch radius of its path?    m

  An electron experiences the greatest force as i.)3 ild1 -r0gdeoc ik*d(pyw ct 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 undeflec+j l4dn/ayq zy 54. twc3 hqr9-s,ejubted when passing through perpendicular electric and mz3.4 bqhj-tay5qrc 4n,9/lyj eudws+ agnetic 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 ;b,tvy aj2ad:mass is $6.6 \times10^{-27 }\;kg$ is accelerated by a voltage of 2100 V.
(a) What will be its radius of curvature if it moves in a plane perpendicular to a uniform 0.340-T field?    m
(b) What is its period of revolution?    $ \times10^{ -7}\;s$

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

Show that the time T required for a particle of charge q moving with constantcfbqd 1x)enxc v x/4*6 speed v to make one ci)c 6b4fe*q/n1cvxx xdrcular 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 circularq4d:*okz u*f6dzg ,zu path of radius r in a uniform magnetic field B. Show that its momentumf6 u 4zkdgdz*:uo* qz, is p = qBr .

A particle of mass m and charge q movez 8rquuga ur-)u2e,8ss in a circular path in a magnetic field B. Show that its kinetic energy is proportior88)uu2r,g uez aq -usnal to $r^2$, the square of the radius of curvature of its path.

Show that the angular momentum of the particle in Proble;y)rr9 ul :owfm 21 is $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves with a speed of 160 m/s perpendiculn4jvoz24 d- ak;wtmm3 ar to the Earth’s magnetic fiek 2w- v;jm4m tn3a4zodld of $5.00\times10^{-5}\mathrm{~T}$, If the bullet possesses a net charge of $13.5\times10^{-9}\mathrm{~C},$ by what distance will it be deflected from its path due to the Earth’s magnetic field after it has traveled 1.00 km?    $ \times10^{-7 }\;m$

  Suppose the Earth’s magnetic field at theso y2p+toy 4zcpl.,9y 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 speh8+jpby*tmr/e8 )gef )sp.uked $\nu=2.0\times10^5\mathrm{~m/s}$ 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 sta /lit5ti0nev ynh 5(ko7d2+qrrt a stalled vehicle carries a 65-A current. How strong is the magnetic field 6.0 cm away from i v7tl0qne yk +5 rtih2/5o(dint? Compare to the Earth’s magnetic field. $B_{cable}$   $ \times10^{-4 }\;T$ the field of the cable is about    times that of the Earth.

  If an electric wire is allowed to produce a magnetic field 44y+;cqk za )0u6 kfeh4hfoqrno larger than that of thkkfqh6u)z4foha + 4;e 0rcyq 4e 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 s1mga i.5f /tu6eh;gl hywl0u 7traight wire carries current I out of the page toward you. Ihymuh6u 7l .g g51;efl0/tai wndicate, 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 carryg( j/ v6yyy pz4my.x4ting an upward 24-A current exerts an attractive force per unit /4xy4ypy(mg .vtz6y j 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 bf 1:ybq52zltsb j6 am3etween two parallel wires 35 m long and 6.0 cm apart, each carrying 25 A in the same di:z3lybjft am6 2sq5 b1rection.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magneuqfjn s7 *2 inj*k,3u 53nfpugtic field is being carried out 1.00 m from an electric cable. What is the maximum allowable current in the cable if the experim3,ffn3u*nn*jjsqup5 k72gu i ent is to be accurate to $\pm1.0\%?$    A

  A power line carries a current of 95 h 8,yskhp7c0-f-h o udA along the tops of 8.5-m-high poles. What is the magnitu kf7-8o0hhs-cu, pyhdde of the magnetic field produced by this wire at the ground? How does 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 cm apart carry 25-A currents in the same direci7:zj7tv.:d pjskr.j*y xe*mig0 , lytion. v.i m:y7*js:grtez.*ki pjd,0jy x7l Determine the magnetic field at point P, 12.0 cm from one wire and 5.0 cm from the other(Fig. Below).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18 cm due (n/hlfm7 g;oksouth from a straight vertical wire carrying a 35-A current downward. In what directl/m7 (o;ghf nkion 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 carriesqy,,ks * 927me ckwazo, mg8qo 22.0 A of current due north. What is the net magnetic field 20.0 cm due west of the wire if the Earth’s field there points north but downwq2c* ,sog ,o9meakmzwk7 8y,qard, 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 passe58 z1: jvmdqujz a z6dn4,t8lqs a given 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 long straight wires 2.8ufzg7f26es x0 cm apart in terms of the current I in one when tu2gs8xzf 7e6fhe 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 ycc4rlf,r: 2z, 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 magnetic field of the Ear yl2 ,fcczr4:rth.
   $ \times10^{-6 }\;T$ The field of the wires is about    % that of the Earth.(retain two decimal places)

  A third wire is plac3:6fpi.x/ frvvf p8hbed in the plane of the two wires shown in (Fig. Below), parallel and just to the right. If it carries 25.0 A upward, what force per meter of length does it exertb6v3v8r f i fp:/x.fph 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 poi pu8u*hh)1wvwva +i( knts 23$^{\circ}\,$ E of N outdoors. However, when it is placed 12.0 cm to the east of a vertical wire inside a building, it points 55$^{\circ}\,$ E of N. What are the magnitude and direction of the current in the wire? The Earth’s field there is $0.50\times10^{-4}\mathrm{~T}$ and is horizontal.    A  ----待选择----updown 

  A rectangular loop of wire lies in the uqzm k*3g.v3lyv y6/v same 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 forc/u*z lky3.m3yqv6v gve on the loop.    $ \times10^{ -6}\;N$  ----待选择----away from wiretowards wire 

  A long horizontal wire carries a current of)rs axy msg9(-0)yx vr 48 A. A second wire, made of 2.5-mm-diameter copper wire and parallel to the fir -s)yxmsvya r)90gr (xst, 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 are perpendicular to each o fl0py1udbc6:mpq2w a,,xqu1ther. 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 of 20.0 A and the bottom one carries 5.0 Alwm61 bad uu: xp, 0cq1yfq2,p?    $ \times10^{-5 }\;T$

  Two long straight pabqldt;0br,5 rrt /rw )rallel wires are 15 cm apart. Wire A carries 2.0 A current. Wire B’s curren tbrqdr/0rt) brw,l;5 t 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 from one anot3hsze/w; k1adp gz+c3y 2b 4jaher. (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 that in wires N and P (Fig. Below). Determine the magnetic for+gak z3 ysdpjb;23e4/z1w hcace per unit length on each wire due to the other two.
$\frac{F_\text{M net y}}{l_\mathrm{M}}$ =    $ \times10^{ -4}\;N/m$ =    $^{\circ}\,$
$F_{N\,net}$ =    $ \times10^{-4 }\;N/m$ $\theta$ =    $^{\circ}\,$
$F_{P\,net}$ =    $ \times10^{ -4}\;N/m$ $\theta$ =    $^{\circ}\,$

  In (Fig. Below), determine the magnitude and direction o -u:l 2kw2kcgl +ytyo2 .3n* ipz)ivxzf the magnetic field at the midpoint of the side of the triangle betw +kiit:kulzczxl g .owy3 v) 2np22-*yeen wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a distance d apart, carry equal currents I iw) ehg: p;wtzqh qqzru 6;9v:8n the same direction. One wire is at x = 0, the other is at x = uq;p9vhreh68zw :gqw;: tz q)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 of 420 turns of wire andosua ws uzc1p;1(,te1 carries a current of 2.0 A. Calculate the field inside near the centerswcsz u1; o,1 pua1te(.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid q xx il1wb,3z8azk0 ;ak2rvu(1.25 cm in diameter is to produce a field of 0.385 T at its center. How much current should the solenoid carry if it has 975 turns of the wik2zlx8u; ri vaa 01,3z(wbkxqre?    A

  A 550-turn solenoid is 15 cm long. The aqddj)/. oz;i current in it is 33 A. A 3.0-cm-long straight wire cuts through the center of the solenoid, along a diameter. This wire carrioj a ;)z/diq.des 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 so+t 1u1vd6t gczlenoid that produces the greatest possible magnetic field for a given voltage. Should you make your copper u+6 1dzc tvtg1wire 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 thm.c+i8 p7r6q:bz lvaj e shape of a circle (Fig. Below). Use Ampère’s law along the circular path, shown dashed in (Fig. Below a), to determine thatb:zlac.6ij8v pr +7mq 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 showmg*g4ixd g.qh 9,kn1hkrx(ir sep 5.e, p7j5y that the magnetic field between the conductors of a coaxiay5,5krk.h n iee*x17pq 4ggd . s(9rixgjpm,hl 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 placed withgy+ inb p7w8c.zp.1w:k ikui/ its face parallel to the magnetic field between the pole pieces of a large magnet. When 6.30 A flows in the 1pwiwi7+.:z n pyck 8gk/u.bi coil, the torque on it is $0.325\cdot N$. What is the magnetic field strength?    T

  A galvanometer needlezso 7 x3p-(tsevq5gh(yd0h b* deflects 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 weakens by 25% over thew v 8,agn1b5gy-y,bbu years, what current will give full-scale d-8,yn,bubg y5gw1va beflection if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by what factor does the outputj xk z+d,2xpr1 torque change?x+ djzp k,21rx

Show that the magnetic dipole moment M of an electron orbiting the ph nng2 4lfgcy2q4 w4e/roton nucleus of a hydro22c/q gyehw4 lgfn 4n4gen atom is related to the orbital angular momentum L of the electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter and containing nine loops+uh,e1 5rmc2pdf- 1et 4 w9rycksal3r lies flat on the ground. The Earth’s magnetic field +51yru42tf1 ca3-eld wpr, s9c ermhkat this location has magnitude $5.50\times10^{-5}\mathrm{~Т}$ and points into the Earth at an angle of 56.0$^{\circ}\,$ below a line pointing due north. If a 7.20-A clockwise current passes through the coil,
(a) determine the torque on the coil,   $\times10^{-5}\mathrm{m}•\mathrm{N}$
(b) which edge of the coil rises up: north, east, south, or west?

  Protons move in a circle of radius 5.10 cm in a 0.566-T magneti x :-xa-zn 2z7c(gohkic field. What value of electric fielk( xcnhgi2xzz-7 -:oad could make their paths straight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium a-5k:0lqbf p;o4u jd :ic4og wotoms have radii of curvature equal to 21.0, 21.6, 21.9, 22.2, a 0gwk :5bqoof;c4j i4oud-p:lnd 22.8 cm. The largest radius corresponds to an atomic mass of 76 u. What are the atomic masses of the other isotopes?

  Suppose the electric field between the electric plates in the mass spectromet 7r0tbhi:1pzt *wpar lfgdbp281;j7 per of (ip*7h zgp p;0 btlrr11wa7pt:jbd2 8f 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 iux1fg9zo:em 0 () ywqjs being used to monitor air pollutants. It is difficult, however, to separate molecules with nearly equal mass such as CO (281)ye9gowuj:f ( qz0mx .0106 u) and $N_2(28.0134u)$. How large a radius of curvature must a spectrometer have if these two molecules are to be separated on the film by 0.50 mm?

One form of mass spectrometer accelerates ions b s(/3g4grcnj5)nu 0 n wh fni0e);pdpky a voltage V before they enter a magnetic field B. The ions are assumed to start fr5wjeku;gn3 rg)) dhnn(fn/40isp0p c om 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 meter, lt).s p ni89 lt)gbr9sand a 25-A current flows through the wire. If the permeability of tls r gp ))bsi9nt89lt.he 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, ar3pcfvdoxqkb (dr:(+zv wdr23 n4 5z 0nd has 640 turns of wire. The magnetic field inside the solenoid is 2.2 T when 48 A fo30:zdnk q+vxv(53wzrdfr p(d4 r bc 2lows in the wire. What is the permeability $\mu$ at this high field strength?    $\times10^{-5}\mathrm{T}\bullet\mathrm{m/A}$

  Protons with momentummlja. xhal lm2s4w wd)pfdr,-/0s1n 42lq w+i $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 th p(xl y:w:vyy r)p gwd9a+y:5he same kinetic energy upon entering a region of constant magnetic field. What isp:ya yhrywg:v:(5l9pxyw +d) the ratio of the radii of their circular paths?   

  The power cable for an electric trolley (Fig. Below) carries a horizontal curre0kn ++gk5 9lprcmvc--cbin6 fnt of 330 A toward the eak0-mfcl+ck 9-n6 +pc5b nvrig st. The Earth’s magnetic field has a strength $5.0\times10^{-5}\mathrm{~T}$ and makes an angle of dip of 22$^{\circ}\,$ at this location. Calculate the magnitude and direction of the magnetic force on a 15-m length of this cable.    N the force on the wire is  ----待选择----southerlynortherly  and   $^{\circ}\,$ above the horizontal .

  Calculate the force on an airplane which has acquired a net charge of/;d dv+vw zvjuh8.,ki $1550\mu C$ 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 poinm+xf:sw ;qq6)pej 5 vpts almost horizontally to the north5 6;pp+ev)x:qsqjf mw 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 xbbi5gh; vu75 atom, 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 (Fig. Below)*dr0 qj ezu*e hie09*d. 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*iuhqd*r 9* dee0ez0j 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-diamf:x 7pk zxzd3)eter copper wire and is suspended in air due to the two magnetic 3zd:pxfk) 7xzforces from the bottom two wires. The current flow through the two bottom wires is 95 A in each. Calculate the required current flow in the suspended wire.    A

Two stiff parallel wires a distance l apart in a horizontal pllc0cb ,w k1mh 2:6h.b2fzr.kienzw2h ane act as rails to support a light metal rod of mass m (perpendicuhh.inb mzc21lbr w,w06: ekc2h.k 2fzlar to each rail), (Fig. Below). A magnetic field $\vec{B}$, directed vertically upward (outward in the diagram), acts throughout. At t = 0, wires connected to the rails are connected to a constant current source and a current I begins to flow through the system. Determine the speed of the rod, which starts from rest at t = 0, as a function of time
(a) assuming no friction between the rod and the rails,
(b) if the coefficient of friction is $\mu_k$.
(c) Does the rod move east or west if the current through it heads north?

  Estimate the approximate maximum deflection of the elecwwr 4v r;nner 4d:8zw;lo(9s wtron beam near the center ofrz4vwd89 w(ls4r;: n w w;rneo a TV screen due to the Earth’s $5.0\times10^{-5}\mathrm{~T}$ field. Assume the CRT screen is 22 cm from the electron gun, where the electrons are accelerated
(a) by 2.0 kV,    mm(Round to the nearest integer)
(b) by 30 kV. Note that in color TV sets, the CRT beam must be directed accurately to within less than 1 mm in order to strike the correct phosphor. Because the Earth’s field is significant here, mu-metal shields are used to reduce the Earth’s field in the CRT.    mm(Round to the nearest integer)

The cyclotron (Fig. Below) is a device used to accel; tzy9gslc;1xerate 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 parti lsg; yx9t1cz;cles 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, locatedpul f uf7)5wa,ng3i a4 at the corners of a square of side l, carry eq4wag53n 7)fu , lauifpual 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 “bk q zp+-ma)g(6jpwv)x tydr:c6a dw:8eam steering”; that is, the magnetic fields can be used to change the beam’s direction without r ) w(8jd-) qda+ptz:mxw 66akpcgvy: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 obn(2j 2:jy)n/:ixcth8 tsw sg f a circular coil of wire carrying a current I (as in Fib:xtjcnh8/ :s)y(g i2tsn2j w g. 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 pole anl27ke uxz6zfn.v7q vd9)kvn1y;o 4 s the magnetic field is about 1G($ 1\times10^{ 4}\;T$) Imagine a simple model in which the Earth’s field is produced by a single current loop around the equator. Roughly estimate the current this loop would carry. [Hint: Use the formula given in Problem 80.]    $ \times10^{ 9}\;A$

  You want to get an idea of the malkzxs i/6b ;eei, ql+uh25n d.t0c s+pgnitude of 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 field you might experience walking under these power lines, and compare to the Earth’s field. [For an ac currebz ic+6 / kixnl;s+ eqted02spu, 5.hlnt, 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 magnety1g :adqu9:yin;r,kzmb 0n8mic field would make a beam of electrons, traveling to the right at a speed ofm;:9 gymu:dnz0q aibynrk,8 1 $4.8 \times10^{ 6}\;m/s$ 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 0.00 fw e;,zjbq5z10 T, perpendicular to the plane of the spiral, as shown in (Fig. Below). In two successive loops, at points jw50bqz,efz; 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 producy mrb7 cpky 39;es)d)pe a 0.30-T magnetic field at its center. If the maximum current is 5.7 Am s7dr9 by3p;)kcype) , how many turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, each of diameter 0.50 mm, carry the same /u, y w65eexdwcurrent but in opposite directions. They are suspended by 0.50-m-l ex6yd, 5eww/uong 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 magneticvc.j01 mv , ,hdc9wwjt/o adhfa;8+gf 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$