A compass needle is not always irlkbcx,p. 3- balanced parallel to the Earth’s surface, but one enircb- l, 3kp.xd may dip downward. Explain.

Draw the magnetic field lines around a straight section of wire carryingx0ncezz*- f4yq3fb 9/ hpsmj8 a current horizontally to the lefts xjzc0 9 ny-embp*qfz /83hf4.

In what direction are the magnetic fiehwi,tzit k sg w)lt6++:x l(bn1/iqz0ld lines surrounding a straight wire carrying a current that is movxs1iz(k:hi/ 6zgtlni0)lw w ,+t tq+bing directly away from you?

A horseshoe magnet is held vertwn r/+b 8yki8dx/mw8pically with the north pole on the left and south pole on the right. A wire passing between the poles, equidistant from them, carries a current directly away from you. In what direction is the force on the wm wpw/+i8k8bxr/ 8 dynire?

Will a magnet attract any metallic object, odi rve n8y-e.y 59jh 5nzjqw4(r only those made of iron? (Try it and sevyy5ij-(ne r q4 n.de895w jzhe.) Why is this so?

Two iron bars attract each other no matter which ends are uxhz p )z*cn4oqp;n31 placed close together. Are both magnets? Exzpnq1 cn ;h4 uzp*ox)3plain.

The magnetic field due tol7 nf1f2u;urxj50qo g current in wires in your home can affect a compass. Discuss the effect in term1gfq2;f5 7j rx0olnuus of currents, including if they are ac or dc.

If a negatively charged particle enters a region of uniform magnetivi) rlofqdchc36b +y27h ie/) c field which is perpendicular to the particle’s velocity, will the kinetic energy of the particle increase, decrease, or stay the same? Explain yo7/ hbi qccrhvi l))eyod+f326ur answer. (Neglect gravity and assume there is no electric field.)

In(Fig. Below), charged particles move in the vicinity of a current-carryingy0qsp k+8o4as wire. For each charged particle, the arrow indicates the direction of motion of the particle, and the + or - + kqy4o0as8s pindicates 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, enter a magnetic field as shown iltd1 dr4afcq )a5q7w9n Fig. 20–46. What can you say about the charge on each particllqfdaa q1t9d)c7 r 5w4e?

A positively charged particle in a nonuniform magnetic field follows*op t vtjtm0d 8*st.gvz-/4kf the trajectory shownftdogv* kt8mz0 jsv t4 -t/*p. 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? What5olcl+s,1+ dy0vh j wlb,n(l4 .q3nok w;tryk must you consider to answer the 40wdyk5hr c +l+lvtylqs 3.lj,ow 1(onb;n,k se questions?

Explain why a strong magnet held near a CRT televisio q+h5l hpvz(l0n screen (Section 17–10) causes the picture to become distorted. Also, explain why the picture sometimes goes completely black where the field is the strongest. [But don’t risk damage to your TV by trying this.][/But don’t risk damage to ylhhlp5( v0z q+our TV by trying this.]

Suppose you have three iron rods, two of which are magnetized but the third :gtun9; oql 1eis not.;gl:qnt9ue1 o How would you determine which two are the magnets without using any additional objects?

Can you set a resting electron i2n( * j9amc,zggdtrlk a2i:x, nto motion with a magnetic field? With an electric x2gmz *nac r9t (,j:a2,ikldgfield? Explain.

A charged particle is moving in a circle th z55es,+f 4gqygi7ir) uzv, under the influence of a uniform magnetic field. If an electric field i,gq)s7tz 5viur,g h 45e+yzf that points in the same direction as the magnetic field is turned on, describe the path the charged particle will take.

The force on a particle in a magnetic.k3* 5h5:3oe vhx u,tyheytv h field is the idea behind electromagnetic pumping. It is used to pump metallic fluids (such as sodium) and to pump blood in artificial heart machines. The basic design is shown in(Fig. Below). An ee*hyy t53v,u5.h3 hthkexv o:lectric 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 3pd 1ihlzs a*4from left to right iz *ls 3d41aph
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetips5iwz2-pbk/x mmn2)7 wlo x-c fields that surround a moving electric charge.wnim5s-2 k-xml b/p z wo)7p2x

A charged particle moves in a straighvrr498z lq b4vq1lt2ot line through a particular region of spacezv8 2ltr9q4 ovr qb14l. Could there be a nonzero magnetic field in this region? If so, give two possible situations.

If a moving charged particle is deflected s8a8o6pv as i0jideways in some region of space, can we conclude, for certainij a s68ov8ap0, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is4i0qc pr m(et; 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 whkp s(y.egm.42cg+x lt ether moving electrons in a certain region of space are being deflected by an electric field+(x4t kcp.s. g lemgy2 or by a magnetic field (or by both)?

How can you make a comc)7a e:pe35buz/w vl 1+ wjzgopass without using iron or other ferromagnetic material?

Two long wires carrying equal currents I are at right angles to each o 5:t+ra lv06-f euzawqther, but d:r+fw-tu0 ql5e6 zvaaon’t quite touch. Describe the magnetic force one exerts on the other.

A horizontal current-carrying wire, freelcz74:ghraifw ; .*oi to move in Earth’s gravitational field, is suspended directly above a secr4;a *l: whi.7f zgoicond, 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 unmagnevsbyjha7:jl6 xa5/ v302ylj t tized piece of iron?

An unmagnetized nail will not attract an unmagnetized paper clip.hf,sr y* ycetzld1l*m 1b9 :ksj7- hr9 However, if one end of the nail is in contact with a magnet, the other end will attract a paper clip. Expymdhys krl*9 szlbtc,1 7fjh1r9* -e:lain.

Two ions have the same mass,a+zjlhohexw ;y)/q g h(qe37+ but one is singly ionized and the other is doubly ionized. How will their positions on the film of a mass spectrometer (Fig. Below) differ? j(7wyheqz;xhe/ 3q)ag+h+ l o

What would be the effect on B inside a lon2y*6b .ns+bkedwb y-zg 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 sigxdo y*6xhc65l v u5 (k:xup0fc *b+yqmilar to a 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 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 cargxxck+dp6x( huv*b uyo5lf 5*06q yc: 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 pe jity:i*zue- 2 i/oir/iap,*tnl ork(:rt+)or meter of length on a straight wire carrying an 8.40-A current when perpendicular to a 0.90-T uniform magi :*ry*le rkoatrjz :ip +i)/-tt u 2nooi/,i(netic field?    N/m
(b) What if the angle between the wire and field is 45.0$^{\circ}\,$?    N/m

  Calculate the magnitude of the magnetic force on a 160-m length o8j/mfr h+i ;lof straight wire stretched between two towers cal+jh/mf ro 8;irrying 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 magnituxv6 z 38h9-ubf zg8kdvde of the magnetic force on a 160-m length of straight wire stretched between two towers carrying a 150-A 3ku 8vgdf8z xbv9-6hz 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 long6-w s2hfk,edcg74a0 okuaj(r if the maximum force on it is 0.750 N when placed iow,ed7r 2(hf0-gu s6 ckakj4a n a uniform 0.0800-T field?    A

  A 1.5-m length of wire carrying 4.5 A of current is n3 u/+g kx+ownoc.b2qbx( ch8 oriented horizontally. At that+2xxo gbnqw ouk(83/c.b +hnc point on the Earth’s surface, the dip angle of the Earth’s magnetic field makes an angle of 38 $^{\circ}\,$ to the wire. Estimate the magnitude of the magnetic force on the wire due to the Earth’s magnetic field of $ 5.5\times10^{ -5}\;T$ at this point.    $ \times10^{-4 }\;N$

  The force on a wire carrying 8.75 A is a maximum of 1.28 N when placed bex ,- 5mcaf i x3tzs)rmu(awee.o+ 6be4tween the pole4oc bxwamxe e i .asre-+5,6tm3z)(uf faces of a magnet. If the pole faces are 55.5 cm in diameter, what is the approximate strength of the magnetic field?    T

  The magnetic force per met8yk oxlll9yxgb9p .)w/ g g17ser on a wire is measured to be only 35% of its maximum possible value. Sketch thb/lys.9 pk79ygg8 x)lxwgol 1e 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 maximu6 x3.zjz:hjnk kn)3;7le c lovm 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 juj)vsb .8vhj.dgs /56lgrdp *,n/ hrolst “float” horizontally in air because of the force due to the Earth’s magnetic fielbv hns/.gjdg/jr s.hp86)l5 ld r,o*v d $\vec{B}$, 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 chari(.sbs5febk3c.jj u-, fjkx x, ta e.0ge $q\,=\,+2e$ 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 dire7r.u++cd:zk s(j hljnf s8e:iction 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 each4bog0 qubn:k4wf+0kg*q w 4dhg y86a n diagram shown in (Fig. Belo0 g nfouw486y a:kbng4*gk q0+h4qdbw w), 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 directio 7a.v 0gmk9qyogroi1i7 1i.s nn 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 proje9.eyd 5xsjs5 q(w5 xtzcted vertically 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 field, in a plane pkl oyr.:jt uv;( )hpe)erpendicular to the field. Wj.;v)u:hp ( )ekrotlyhat is the radius of its path?    m

  An electron experiences the greg7 -zwi gl92ceatest 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 uwp kauy 0 *,d+qrbwnyk-t5: 7fndeflected when passing through perpefbq: yuy tk+kd-w0a5*wrn ,7pndicular electric and magnetic fields of magnitude $8.8 \times10^{3 }\;V/m$ and $3.5 \times10^{-3 }\;T$, respectively? What is the radius of the electron orbit if the electric field is turned off? $F_E$    $ \times10^{6 }\;m/s$ $F_{max}$   $ \times10^{ -3}\;m$

  A doubly charged helium atom whose mass: jg;- m0ttpbs 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 rnlg,:n zm09hatw85ycn76v ic9 p:lo wequired for a particle of charge q moving with constant speed v to make one circular revolution in a uniform magnetic field:pgwcm: 5htvnwn,nl 9y 7il90o8 za6 c $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge:n2 shycu7pn knwj-(;m4rv o. q moves in a circular path of radius r in a uniform magnetic o-p7h.;w2nc n vy(s:kuj 4mr nfield B. Show that its momentum is p = qBr .

A particle of mass m and charge q mols0zyg d5j 5eown q,.:ves in a circular path in a magnetic field B. Show that its kinetic energy is n0y,l :zgo5j5.sdwe q proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momzvh (8pnw) j 9a0ozpjb5d -,poentum of the particle in Problem 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’ybd6n m z)f7ya8 v-anb0w8k:rs magneyd awa:-nkr)0vbzn8 8 f6ybm7tic 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 magnetic field at the equator has magni43ughr hd) f 2yjam6o3v,c0rm tude $0.40\times10^{-4}\mathrm{~Т}$ 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 sp2tgq0 8h2 k( wydwd ad(t6s(zpeed $\nu=2.0\times10^5\mathrm{~m/s}$ 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 veho op5we.7(oup5a.t d: m kd2ilicle carries a 65-A current. How strong is thk a o e.md52wopu7po i.5(dtl:e magnetic field 6.0 cm away from it? Compare to the Earth’s magnetic field. $B_{cable}$   $ \times10^{-4 }\;T$ the field of the cable is about    times that of the Earth.

  If an electric wire is xyi2/ pma6e 0b+ewyka m7y7y0allowed to produce a magnetic field no larger than that of th06ye+y07 a paxm i7kyw2mbey/e 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 page towar9mzmve8x ocph2p7 q xfq: +8v/d you. Indicate, with appropriate arrows, the direction of /qf7 h8vmpqxcx+ 2o:v m z9ep8$\vec{\mathbf{B}}$ at each of the points C, D, and E in the plane of the page.

  A vertical straight 3ck,o: w qznn2c+vc9todos-6wire carrying an upward 24-A current exerts an attractive force per unit length of n-w ct qo9cs3 no:d62 vz+k,oc$8.8\times10^{-4}\mathrm{~N/m}$ 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 wire1ikh: nb/ lw7 kxjszv:z48e/ms 35 mi mn:8k4: vlx1h/zwj7ezsk/b long and 6.0 cm apart, each carrying 25 A in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic /3p4l 5ti5a r tmgu4pkfield is being carried out 1.00 m from an electric cable. What is the maximum allowable current in the cable ii5ta4kl 5g4ptm3 pr/u f the experiment is to be accurate to $\pm1.0\%?$    A

  A power line carries a curreh4oq gmp;h- :i*r6hp6 nfu1eer09br pnt 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 does this compare with the Earth’s field of a1pqhgr0 i 6b efp4mp nor*9e: 6hhu;r-bout $\frac{1}{2}G$?    $ \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 6oh5wgp4a* rzxb4h/ q: iyejo9mr)i *currents in the same direction. Determine the magnetic field at point P, 12.0 cm from one wire and 5.0 cm fr9w):a4*iexrqyrbhj i5hmg* o6 4p o z/om the other(Fig. Below).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is -1klr+h5jto d placed 18 cm due south from a straight vertical wire carrying a 35-A current downward. In what direction does the compass needle point at this location?ro-l+1dth j 5k 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 wib7zrk8+ m7jlq re carries 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 point jm7kbql7 r+8zs north but downward, 37$^{\circ}\,$ below the horizontal, and has magnitude $5.0\times10^{-5}\mathrm{~Т}?$
   $ \times10^{-5 }\;T$
$\theta$ =    $^{\circ}\,$ below the horizontal

  A straight stream of protons passes a given point in space at a r wp-jwh4*6/gg;bfps4 oro+ qvate 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 straigh12aqjpln5ul n,4gx0-fga d .it wires 2.0 cm apart in terms of the current I in o- 4 jq.gngaxa5ufnl li,dp 021ne when the other carries 15 A. Assume these currents are
(a) in the same direction,
(b) in opposite directions.

  A long pair of wires conducts 25.0 A of dc current to, and from, p/ xe90,0 cezj c5xytean instrument. If the insulated wirxze,0 e0/xjt 5 cpye9ces 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 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 td0 42p mvgw.fawo wires shown in (Fig. Below), parallel and just tg d2wpfm4va0 .o 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 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 298t47od:um b bwex9sb 3$^{\circ}\,$ 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 the7 i.2y;daud11r v1 zs fx-u44gph piv4bru)u n 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.v1-)u brfx giadpu1 u zr7is4hv;1uyd p24n4 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, made of 2cip.t3 c yu-+r w/dj8qh)hx0b.5-mm-diameter copper wire and parallel to the first, is kept in suspension magnetically 15 cm below (Fig. Below-r +)dh b8chw.xq 0u t3/jcypi).
(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 soz j5ni qch3t n8+1p/bggsvi q 3w1*cz0 that they are perpendicular to each other. At their closest, then1nv5+cj*qbqt8h3s z cz /gi1 30wip gy 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 A?    $ \times10^{-5 }\;T$

  Two long straight parallel wires are 15 cm apart. Wire A carries u xn3ol puol/s6 )o-v :;nkzd(2.0 A current. Wire B’s curonl:-o k; 6)nozx/upu( v d3lsrent 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 cgf j eaa5p6 o5/* )zvohq85sccm from one another. (Looking along them, they apv*jf5 6o8gsh5q aoez 5/ca)cre 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 other two.
$\frac{F_\text{M net y}}{l_\mathrm{M}}$ =    $ \times10^{ -4}\;N/m$ =    $^{\circ}\,$
$F_{N\,net}$ =    $ \times10^{-4 }\;N/m$ $\theta$ =    $^{\circ}\,$
$F_{P\,net}$ =    $ \times10^{ -4}\;N/m$ $\theta$ =    $^{\circ}\,$

  In (Fig. Below), determine the magnitude and direction of thqe*h48y7e o elugv96 be magnetic field at the midpoint of the side eg*v9 ee4y6b8 olhq u7of the triangle between wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long paralletecnxe 7))tk4 ,oexjfn ; 1el(l wires, a distance d apart, carry equal currents I in the same directiont )e (t4eln jc1k eo)xfx7,ne;. One wire is at x = 0, the other 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 5x cre(pnr2g*( fvp5 wiv1.( 08hf fx(xgkjeytotal of 420 turns of wire and carries a current of 2.0 A. Calculate the fiepxcvf. e(hwk5(j5fir2px fen(ggryx( 8* 0 v1ld inside near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameter is to produce a fiz6k9b;9x byxz eld of 0.385 T at its center. How much current should the solenoid carry if it has 975 turns of the wire?kxy 96xbz9b ;z    A

  A 550-turn solenoid is eooe9n4 x,fk,jc at27 15 cm long. The 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 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 fiet o cx7 je,f2,4onke9ald points due east?    N

You have 1.0 kg of copper and want to make a prac95m*ka4*43x ,ayusyfrm)kd urmxi 0htical solenoid that produces the greatest possible magnetic field for a given voltage. Should you make your copper wire long ankm umi4 yku0*f94 3xaxm5ra*r)yhsd,d 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 oucd*q w(,v4s df a circle (Fig. Below). Use Ampère’s law along the circular path, s4c(duqvw,*sd hown dashed in (Fig. Below a), to determine that the magnetic field
(a) inside the toroid is $B=\mu_0NI/2\pi r$ where N is the total number of turns, and
(b) outside the toroid is B = 0 .
(c) Is the field inside a toroid uniform like a solenoid’s? If not, how does it vary?

(a) Use Ampère’s law to show that the magnetic field between the con wau qi0zorl vt05nu,s6eu f0.86 fm3rductors of a zti,3 n ovfw0ml 0r.f 8ua05suu6r6e qcoaxial 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 with its .o zpbswa5 zl0bwuu,z)j)/(z b:d: gbface parallel to the magnetic field between the pole pieces of a large magnet. When 6.30 0g5bpz:) buz j (sl.)aouz, wdbzbw/ :A flows in the coil, the torque on it is $0.325\cdot N$. What is the magnetic field strength?    T

  A galvanometer needle defbijb9)f /w8iym,x-qo 7 g;almlects 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 weak./rnar;e,vmcqh v6n .ens by 25% over the years, what current will give full-scal,. erqvnv;6mc/ha r. ne deflection if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor dre 5 h8vn 0vlsh(a9vr. 8xaw:zlops by 12%, by what factor does the output torque chxz5 . :vl9l880v vs(aarwhe hnange?

Show that the magnetic dipole moment M of an electron orbiting the protoxo(,ffs4kav 1x*n im5 n nucleus of a hydrogen atom iskmfaxv5 4f,n i(*s1o x related to the orbital angular momentum L of the electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter d/lxb*8z-gt8 fb m)g+)xooa ;asa6cpl1n) ua and containing nine loops lies flat on the ground. The Earth’s magnetic field at6lxaoalzs n18 gmg f*c-a)b +8 x)td;oup a/)b 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 5.53dg fgzi7e .d , sd4j-uxpj2p10 cm in a 0.566-T magnetic field. What value of5 i3gj.s guxzfd 7 -dp2ep,4jd electric field could make their paths straight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atozk- ri e8i)f,ak7 :yuxms have radii of curvature equal to 21.0, 21.6, 21.9, 22.2, and 22.8 cm. The largest radius corresponds to an atomiaie:,ku7 z)yxf ik 8-rc mass of 76 u. What are the atomic masses of the other isotopes?

  Suppose the electric field bet,hn8 offq:u;k ween the electric plates in the mass spectrometer ofuofk;n,q: f8h (Fig. Below) is $2.48\times10^4\mathrm{~V/m}$ and the magnetic fields $B=B^{\prime}=0.68\mathrm{~Т}.$ The source contains carbon isotopes of mass numbers 12, 13, and 14 from a long-dead piece of a tree. (To estimate atomic masses, multiply by $1.67\times10^{-27}\mathrm{~kg.}$)
How far apart are the lines formed by the singly charged ions of each type on the photographic film?
$2r_{13}$ - $2r_{12}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)
$2r_{14}$ - $2r_{13}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)
What if the ions were doubly charged?
$2r_{13}$ - $2r_{12}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)
$2r_{14}$ - $2r_{13}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)

A mass spectrometer is being used to monitor air pollutants. It ise.3 61a9 dm+*e nxtp/ avaco(dt7xboa difficult, however, to separate 1.9toda+db*o etpc/ e 36x maax(v7na molecules with nearly equal mass such as CO (28.0106 u) and $N_2(28.0134u)$. How large a radius of curvature must a spectrometer have if these two molecules are to be separated on the film by 0.50 mm?

One form of mass spectrometer accelerates ions by a voltage V j5b ;7ixwoc*gwcx7 u+before they enter a magnetic field B. Tw7xbg 75x+ijouc;w*c he 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 per meter, and a 25-A currenebcd mi,; 2em-t flows through the wire. If the permeability of the iron is-2eemc; ,dim b $3000\mu_0$ what is the total field B inside the solenoid?    T

  An iron-core solenoid ihval*ro .rg;q :;6 xias 38 cm long and 1.8 cm in diameter, and has 640 turns of wire. The magnetic ai*:.grlra;6ox ;vhqfield 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 momentu9x0o 1wwev,mi8iwl9b 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 kbyqqg8 unjd j317ti3r*d-j vcp++car :0gi 3e inetic energy upon entering a region of constant magnetic field. What is the ratio of the radii of their circular patbqj vcg8 : p*iyt3+d7u1a drjgnq-3 3crje0i+ hs?   

  The power cable for an electric trolley (Fig. Below) carries )v08: qw7ke*svzgniga horizontal current of 330 A toward the east. The Earth’s magnetic fieldsn7v8i*0)qw ge: vgkz 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 ofsp ,acfb x6u.:o,ey2hd0yhx ; $1550\mu C$ 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 moe-bq-d)dc ajo7p53 dp*4m klagnetic field points almost horizontally to the north and hao -)ab 5 q3dm7jcdedokl4*-p ps 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 heliu- yun: nbc2aac9s vg( 5n0xn*4mqms g.m 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). A large cuirg7,jge gug: d+(g8frrent moves in a closed loop composed of fi:i f8dgggurgjge+7, ( xed 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 copper pr f1dv*r5 v))jgq*lkwire and is suspended in air due to the two magnetic forces from the bottom two wires. The current )rlvv*qgf pr)1 *5djkflow 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 horizb-t1jm- .zct jontal plane act as rails to support a light meta -1zb -t.tmcjjl rod of mass m (perpendicular 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 elenk o2kqne2sl;d (d (xj;:5lllctron beam near the center of a TV scree5;skdlxq:ol2(k(nl lend2j; n 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)x271g kjsszqz 4 cg+w5 is a device used to accelerate elementary particles such as protons to high speeds. Particles starting at point A with some initial velocity travel in circular orbits in the magnetic field B. The particles are accelerated to highe4wxqkc2z s5sg7 +z1 gjr 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, ldm7m4i*efhhx )*2n b lo p-i1t( nfq2docated at the corners of a square of side l, carry*i d f(l -n) ot de1*f27mihn2q4pmbxh 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 ve g:tsd d7awk3m77cb sh8k81v a;ykpk1ry useful in particle accelerators for “beam 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 beamh vdpgsb1sd77;: 1 ackma tyk 87w8k3k 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 circularr.o::4(a1 ,yc cn( 5rsewb bvfz,dod x0 lvvv; coil of wire carrying a current I (as in Fvyl.,df d; r swx0ncoe1b(:ba4,v oz r (v5c:vig. 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 field is tkdku+o*2+m 9r7 3ao +eht lzyabout 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 ide3fjk;42 fo4ggro5 m0dr0n zc ba of the magnitude of magnetic fields produced by overhead power lines. You estimate that the two wires are each about 30 m above the ground and arfo 5kmzgocr0 n44g j2;r0bdf3e about 3 m apart. The local power company tells you that the lines operate at 10 kV and provide a maximum of 40 MW to the local area. Estimate the maximum magnetic field you might experience walking under these power lines, and compare to the Earth’s field. [For an ac current, values are rms, and the magnetic field will be changing.] $B_{net}$ $\approx$    $ \times10^{ -5}\;T$(Round to the nearest integer)

  (a) What value of magnetic field would m6 zx*emb q)+tzm 6jun/i7,vbiake a beam of electrons, traveling to the rightm+)x7ein* /6iqb 6uzj tzvm ,b at a speed of $4.8 \times10^{ 6}\;m/s$ go undeflected through a region where there is a uniform electric field of 10,000V/m pointing vertically up?    $ \times10^{ -3}\;T$(retain one decimal places)
(b) What is the direction of the magnetic field if it is known to be perpendicular to the electric field?
(c) What is the frequency of the circular orbit of the electrons if the electric field is turned off?    $ \times10^{7 }\;Hz$

  A proton follows a spiral path through a gas iy0vco* 7s , qj(xdh*ikn a magnetic field of 0.010 T, perpendicular to the plane of the spiral, as shown in (Fig. Below). In two successive loops, at points P and Q, the radii are 10.0 mm and 8.5 mm, rhy,0(oc 7k *qid* sxjvespectively. 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 produce a 0.30-T magnetic fd:y4uz sv jc)2ield at its cen v)2z:sy ujcd4ter. If the maximum current is 5.7 A, how many turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, each of diambtl9h cq- m9,zkp w/0meter 0.50 mm, carry the same current but in opposite directions.99bm/tmhl0kqp - z cw, 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 mag6gu n/ ffo 93nwet39dxnetic 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$