A compass needle is not always bal:/wl2vl1o qs zzh 0 8lsxc13fdanced parallel to the Earth’s surface, but one end may dips:2o1l3fd hxlq0wszv/1 c 8zl downward. Explain.

Draw the magnetic field lines around a straight section of wire carry (ksxmylzvx/q5h :;v2ing a current v/qs mx:kyh 2x;5z(lvhorizontally to the left.

In what direction are the magnetic field lines surroh(ofmtg31c z x0.jj i+unding a straight wire carrying a current that is moving directly away o+i13c.(tghzjjxm0f from you?

A horseshoe magnet is held verticav:*5*a d t7zllimvg m1lly 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 f5l1mi*vtz: dvm*a l7 gorce on the wire?

Will a magnet attract any metallic object, or only those+-jixqt0(s ogy) bq :p made of iron? (Try it and see.) Why is this0qjtqs +xoy(b) g:-ip so?

Two iron bars attract each other no matter which ends are pll/n, jy2 9ejr(q hd:tlaced close together. Are both magn:hly9j ledq,( 2/jtrnets? Explain.

The magnetic field due to current in wires in your home can affect awg1 e+xak u35a0sf9cl compass. Discuss the effect in terms of currents, inclc93lx gu+sw5fkaa10 e uding if they are ac or dc.

If a negatively charged particle enters a region of uniform magnetic field26ewbbv wl3hu4p4sou*;6x k0rq vm.s which is perpendicular to the particle’s velocity, will the kinetic energmwb0;6*qu2xo46. e vrpwv4 uk h3sl sby 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 viwm4 6w;c q r3rh:v)tcicinity of a current-carrying wire. For each charged particle, the arrow indicates the direction of motion of the particle, and the + or - indicates the sign of the charge. For each of the parm 64w) ichw; v:q3rctrticles, indicate the direction of the magnetic force due to the magnetic field produced by the wire.

Three particles, a, b, and c, entq7yv0+ij a fifvk2j;4 er a magnetic field as shown in Fig. 20–46. What can you say about the charge on each p4 yf i7q+0vvj f;jik2aarticle?

A positively charged particle in a nonuniform magnetic field w8uwa .5+on 8fj m /+to0aqzvofollows the trajectv8 afa0n+j ot+w /ozmu8qow5.ory 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 attr2a10n/ vjxwu72e3;1l2 b ud bxzzcoko act a magnet? Can a magnet attract an iron rod? What must you consider to answer1luz2 2u avxo3ebcdnobxj 2;71 wk0/z these questions?

Explain why a strong magnet held near a CRT television scree7sy mi,wj1 pi.n (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 ri,.iy w1j7s mipsk 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 mag 1r-a se2n1 v ra+bvtwl,i2d5gnetized but the third is not. How would you determine which two are the magnets without usini1-revt, sar2b2 ld aw1 gv+n5g any additional objects?

Can you set a resting electron into motion with1gxea/;nn i2x a magnetic field? With an electric nan/;i2xge 1x field? Explain.

A charged particle is moving in a 5+ ftf.4 q jxsu3gro*pcircle under the influence of a uniform magnetic field. If an electric fixuqp +3to4 fs.fg5j*reld 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 :5tg(pni yw(q 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 machines. The basic design is shown in(Fig. Below). An electric field is applied perpendicular tqw5y(:i np tg(o 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 px pps8c ek3+)sw ibuv75cy-* toward a horizontal wire carrying a current from left weu5) pp*x8 i-3ypv skb scc7+to right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic ft;o7 i+;kl(lukvb y( t k.fy2zields that surround a moving electric charge.fv(kbt7ou2yk tl;.;zi k l(y+

A charged particle moves in a 6hbx wk(bv4y9s c.c2jzw.my.a /ds y-straight line through a particular region of space. Could there be a nonzero magne .h.4mcksx6by/ vj.wdczsw (ay9 -2ybtic field in this region? If so, give two possible situations.

If a moving charged particle is deflected sideways in so2-/ i- ae/iiszf2atlc me region of space, can we concis/-a2t 2fei ia/lzc- lude, for certain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space therecz- i4q j6n;mxn:)kwh 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 cer2sgl1re* sjdd78+ui ttain region of space are being deflected by an electric field or 8d+tjs7 s *erudli 1g2by a magnetic field (or by both)?

How can you make a compass w :mug;h82 e s8ymf5/n vyo9uivithout using iron or other ferromagnetic material?

Two long wires carrying equal currents I are uhg mtpk hv /5tufe, :4at6y78at right angles to each other, but don’t quite touch. Desct4ey/gh:u5thmv7fau ,k 8pt6 ribe the magnetic force one exerts on the other.

A horizontal current-carrying wire, free to move in v;rxzxh e/ c e;s)mxk :dj8b,2Earth’s gravitational field, is suspended exs ek , h8z);;jm2b:/dxxvcrdirectly above a second, parallel, current-carrying wire.
(a) In what direction is the current in the lower wire?
(b) Can the upper wire be held in stable equilibrium due to the magnetic force of the lower wire? Explain.

Why will either pole of a l6ynw t6h 8 )z1yc,wz1nlf7xu magnet attract an unmagnetized piece of iron?

An unmagnetized nail will not attract t8*.tt3*n wg nef xfw*an unmagnetized paper clip. However, if one end of the nail is in contact with a m .ttet*nfnxfw **8wg 3agnet, the other end will attract a paper clip. Explain.

Two ions have the same mass, but one ae 0-kpdqz 4a 8z +qz0b/izxq 3c)aoa8is singly ionized and the other is doubly ionized. How will their positions on tha3qo8c k dez+z-0z i/4b )apq0a8xazqe film of a mass spectrometer (Fig. Below) differ?

What would be the effect on B inside a long soleno5gv+-etzr796qrh r. k(s(, jjpgo gioid 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 nxcsisky (-v(fo:0x7 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 t fk07o:-s( vs(nixxyche main switch. For example, the starter switch of a car is connected to a relay so that the large current needed for the starter doesn’t pass to the dashboard switch.

  (a) What is the magnitude of the force per meter of length on a sovr.a8 lkjjh2 4 8zr6straight wire carrying an 8.40-A current when perpendicular to a 0.90-T uniform magnetic fivrrl6oza2 8 ksh4.j8 jeld?    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 le3fuxm4hs suw 2* ir4 mrpj 5ko;,c(v:cngth of straight wire stretched between two towers caf3 xw4u 4c,uriomksv2h: *j5(c;m rsprrying 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 of4k0* hqgddg93 feqeybr2 j2i6 the magnetic force on a 160-m length of straight wire stretched between two towers carrying a 150-A current. The Eartjdb 9i4yg6geq *kfd2 qe r0h32h’s magnetic field of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  How much current is flowing in a wire 4.80 m long if thekg:rftu9 ,o e, maximum force on it is 0.750 N when placed in a uniform 0.,9ro gtkf e:,u0800-T field?    A

  A 1.5-m length of wire carrying 4.5 A of current is oriented horizontally. At .d /((tg 5 pq1qaphwnsthat point on the Earth’s surface, the dip angle of the w hpg(qq1ts.n 5d(a/ pEarth’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 ;g+ ioq dp.5qt7wd7vaof 1.28 N when placed between the poo57p+d vw. qdgi7;qtale 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 meter on a wire is measuryla.zmf - .5+ b (2ikppdbsm3fed to be only 35% of its maximum possible value. Sketch the relationship of y3 .+aklf.sf2piz( bmp5-dm bthe 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 rz-em-7cb+ 3l n*yqvkmaximum 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 copp*oiv3hms*9 a ler wire could just “float” horizontally in air because of the force due to thl3 o9siah mv**e 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 ch5/ mqdjq dlm45arge $q\,=\,+2e$ 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 magnitu/: fv:ll f :ttj4v uw.+0niwavs d6i8vde and direction of the force on an electron traveling $ 8.75\times10^{5 }\;m/s$ horizontally to the east in a vertically upward magnetic field of strength 0.75 T.    $ \times10^{-13 }\;N$  ----待选择----NorthSouth 

Find the direction of the force on a negative charge for each diagram shown in (q6u g:yy0cu , *hqi.huFig. Below), wherq*y:y.0gu, 6i hcuhque $\vec{v}$ (green) is the velocity of the charge and $\vec{B}$ (blue) is the direction of the magnetic field. ($\otimes $ means the vector points inward. $\ odot $ means it points outward, toward you.)

Determine the direction of kg5c cvyt9or ;w )ndul01q6) y$\vec{B}$ for each case in(Fig. Below), where $\vec{F}$ represents the maximum magnetic force on a positively charged particle moving with velocity $\vec{v}$.

  An electron is projected vertically upward with a speed r u3ke3x0(daif06 dzsih)z9k 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 perpendiculhso; oamh:44dqiwmj49e ;b2 4xcr s h;ar to the field. What is the rad4o soc je; :m;;q4bwx4mrhh s a29dh4iius of its path?    m

  An electron experiences the r5b+hik-hwx s.rj86vutm .b-greatest force as it travels $2.9 \times10^{6 }\;m/s$ in a magnetic field when it is moving northward. The force is upward and of magnitude $7.2 \times10^{-13 }\;N$. What are the magnitude and direction of the magnetic field?    T ----待选择----EastWest 

  What is the velocity of a beam of electrons that go undeflected when passinlz / bafq m,4mw 338cz4mlr+hig through per,4 83mm3amzhq c/wlbilr+f4 z pendicular 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 whosj;4zehao by 40e 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 +4e lqnt4 ymc. ukac+(9llz 0eof charge q moving with constant speed v to make one circular revolution in a uniforqc9z 0l km.uet4(ey++ n4cllam magnetic field $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge q moves i pysgc r+fo9mj.s v.6)n a circular path of radius r in a uniform magnetic field B. Show that its momentum is9 +.f yp.gvmjs 6)scor p = qBr .

A particle of mass m and charge q moves in a circular path in a magnetiw4 pvp:e;a,g,gaxr6 q c field B. Show that i gvg;x4a6 paepw :r,,qts kinetic energy is proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momentum of the particle in Problem 2w vh )st.4+fl 5zxx33vv9cecr1 is $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves w bjqh- pe4wv 90l8fn(qith a speed of 160 m/s perpendicular to the Earth’s magnetic4 ehq8vln(- jw9p f0bq 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 equatoxoo ;tn(zi7z,r 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 sbm6jns:sv m l+p9:t 2q.s6r lkpeed $\nu=2.0\times10^5\mathrm{~m/s}$ 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 6x.g3hx u )b7ft5-A current. How strong is the magnetic field 6.0 cm away from it? Compare to the Earth’s magneti7 ug3xh.b fxt)c 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 no larger tha9n ci.(gu0 2 nhjzgkd*n that of the (inj2*0g9cukgh zdn .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+6 t yhe.s bimff+f;3o current I out of the page toward you. Indicate; h3fiyts6b.+ m+f eof, 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-A current exerts an attyllpfw 5g0, la :97 esdpyqf8,ractive force per unit lyp s,, gd:8l0q9e5w al7f lyfpength 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 wi6qkte1m: r1i02 fkka ires 35 m long ak 6ietrakk 121mi:q0fnd 6.0 cm apart, each carrying 25 A in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic field is b);y5qezx cu /oag, m+reing carried out 1.00 m from an electric cable. What is the maximum allowable current in tme+g )/o ;, 5yarzqucxhe cable 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-m-high poles. Whatz*k6 fl8mumr/ is the magnitude of the magnetic field produced by this wire at the ground? How does this compare with the Eartmk*u/m f rl8z6h’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 parallkmfk+ ,u/ pb 2xpy7txi /y1c:rel wires 13.0 cm apart carry 25-A currents in the same direction. Determine the magnetic field,iy m/xy:x1c bpp 7/k+2krfut 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 j*b dvd*2y m2yefx23oplaced 18 cm due south from a straight vertical wire carrying a 35-A current downward. In what direction does the compass needj e3myxv2od*b f2 2*ydle 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 carrie56ohj2j/s. y mfgc3jes 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 downward,mc 3h5 jj2 j6osf./egy 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 giveg:v pm*.sf /d*f jyyn8n 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 lon(knl. 4kddgad tg ssvdt8w;s lho 50/;75z9gag straight wires 2.0 cm apart in terms of the cgg4w/z9.t k d da5nkaodsvh;ts5l8 g7 l( 0;dsurrent I in one 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, an instrument. gw(tx9misi23 6y2r s6 dxk/hg If the insulated wires are of negligible diameter but are 2.8 mm apart, what isgixwsythr6 / 3629 d(ksmx i2g 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 two wires shown in (Fig. Below), hwqm;-/kx on/ parallel and just to the right. If it carries 25.0 A upward, what force per meter of length does it exert on each of tho ;mqn k/w-/xhe 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 point3; 0w wuf cw-5jx,twqos 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 same plane as a straight wire, as sh3hr4a yip;bsfx n0* w-own in (Fig. Below). There is a current of 2.5 A in both wires. Determine the ;nbpa* hix-3y f4r0s wmagnitude and direction of the net force on the loop.    $ \times10^{ -6}\;N$  ----待选择----away from wiretowards wire 

  A long horizontal wire carries a current of 48 A. A second wire,n44cud + *paqp made of 2.5-mm-diameter copper wipn*4 +ucadq4p re and parallel to the first, is kept in suspension magnetically 15 cm below (Fig. Below).
(a) Determine the magnitude and direction of the current in the lower wire.    A the current is to the  ----待选择----leftright 
(b) Is the lower wire in stable equilibrium?  ----待选择----not in stable equilibrium in stable equilibrium 
(c) Repeat parts (a) and (b) if the second wire is suspended 15 cm above the first due to the latter’s field.

  Two long wires are oriented so that they are perpendicular to each other. zs z:j,s9h(nxAt their closest, they are 20.0 cm apart (Fig. Below). What is the magnitude of the mz(j9 xs:h s,nzagnetic 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 twf w)y+ *9fbl p 0zm3xc9;hvqcarries 2.0 A current. Wire B’s cur*+xh bmt wfv9cqf039;ylw)pzrent 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 another. (Looking along thh xf:9;im g9htem, 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 :;t 9hfmi9hx gwires 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 the 8ofdci tbs(/ilyl 1,2 magnetic field at the midpoint b,ll(yi/i f8 csdt1o 2of the side of the triangle between wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wziu + nz6h4j8tx7ob7,5map esires, a distance d apart, carry equal currents I in the same direction. One wire is at h7xmejtsb, p u7in4azz+5o 68x = 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 h40f)p/f4y qn8mgt qnoixp ,8 pas a total of 420 turns of wire and carries a current of 2.0 A. Calculate the fi fn 4o8 tp)xyng40fp mq8p/,iqeld inside near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameter is to produce a field of 0.385 T )ixxbo 2sjsqi-4* 8dhat its center. How much current should the solenoid carry if it has 975 turns of the j2odqi*sh sx)-i84 xbwire?    A

  A 550-turn solenoid is 15 cm long.+1umo uqq0+xmdc3 w lai*3vtn ;/rm5y The current in it is 33 A. A 3.0-cm-long straight wire cuts through the center of the solenoid, along a diameter. Thisim ouxc3q 3;r0 /+uw*dn5yl vmt q1a+m wire carries a 22-A current downward (and is connected by other wires that don’t concern us). What is the force on this wire assuming the solenoid’s field points due east?    N

You have 1.0 kg of copper and want to : cph t:y4y8 ript3n8k)oz*tpmake a practical solenoid that produces the greatest possible magnetic field f:yr nyip:8)4 pkz tt*cht38poor 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 ayt8vfc bxb0 8y;w-q7circle (Fig. Below). Use Ampère’s law along the circular path, shown dashed in (Fig. Below a), to determine that thvay 7f8b- ybw08txqc;e 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 conductonu5s xb s,,5lo,uji 1ors of a coaxl s,5x51j, uo,binous ial 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 cb d,e/gfekc 5y(ol.5um on a side is placed with its face parallel to the magnetic field between the pole pieces of a large magnet5lgf5(/bco. ueyek, d. When 6.30 A flows in the coil, the torque on it is $0.325\cdot N$. What is the magnetic field strength?    T

  A galvanometer needle deflects full scale for a hye kgn- 6b0zfw-/8ca a 3gxkq4-bg;x$53.0 -\mu A$ 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, wmsgiuyc u+19 j *39ee yh6yhb0hat current will give full-scale deflection if it9h+ge buyy3 i j*016emchy9 us originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by what factor does the output tovpmg1l u 2-gc1*,i nsxrque changm1n,cx* l 2sug 1pvg-ie?

Show that the magnetic dipole moment qatz v/pjx/y21 aj+ md(* 01hwywv 8evM of an electron orbiting the proton nucleus of a hydrogen atojvtz wjpd8y/+ehxv mqya12*/w0a 1(vm 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 lies flat on qo a)jo/i7 :jrthe ground. The Earth’s magnetic field at this locatiro7i :/joa) jqon 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 0.56;vbu1qkdia1s9 . xw*y6-T magnetic field. What value of electric field could make their paths straight? In what dir1db kav y9i;uqx1*ws. ection must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atoms have radii of curvature eq fvpyhn2 2;i(qual to 21.0, 21.6, 21.9, 22.2, and 22.nf;vh qy2(2ip 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 speq l,zgv1)kg8 dctrometer of (Fig. B,8qgdl1g) zv kelow) 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 is difficult, h;g3unc3pl3:5c8ymwim qh j 7nowever, to separate molecules with nearly equal mass such as CO (28.0106c33 7ul8c ywjn5mqn:g m;hp 3i 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 o j; bl)vox.y/;a5jdovoltage V before they enter a magnetic field B.jlxa; )/by.voo; do5j 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 per meter, and (apya l:p7 j1y o)5inpa 25-A current flows through the wire. If the permeability 7p y j)op1a:y5ainpl(of the iron is $3000\mu_0$ what is the total field B inside the solenoid?    T

  An iron-core solenoid is 38 cm long and 1.8 cm in diameter, an1aprfqh13ou4y *rbgjfxre y ;x3; - 2md has 640 turns of wire. The magnetic field inside the solenoid is 2.2 T when 48 A flows in the wi13fyh- exa4 ;urq1j og3brfy xm2r;*p re. What is the permeability $\mu$ at this high field strength?    $\times10^{-5}\mathrm{T}\bullet\mathrm{m/A}$

  Protons with momentuhanh8kt)cuv )b*2 ;nuyz. zt6m $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 re 9xvb8 s;p.gqbgion of constant magnetic field. What is the ratio of txb ;v9psqg8b. he radii of their circular paths?   

  The power cable for an electric trolley (Fig. Below)m7akk sq14y5yf 3vrc0(ft,ea carries a horizontal current of 330 A toward the east. The Earth’s magnetic field ha3rask70q, f v4aet my( k1cfy5s 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 . sagh6pq:ge mc1,dg-t f8zf4on an airplane which 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 Earth’s magnetic field p 5t 1av nt;9 ngt*5bzb 4t:bxrj,x)qxsoints almost horizontally to the north and has magnitq9b1xn:5tvn tg br* x4 a,t5;sx)bzj tude $B=0.50\times10^{-4}\mathrm{~T.}$ 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 masstcs jrh6-61jbqxw9 8fs1rg - c 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 jy e55p3t jkc;launcher” is shown in (Fig. Below). A large current moves in a closed loop composed of fixed rails, a power supply, and a very light, almost frictionless bar touching the rails. A magnetic field is 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 kj3ye p 5tcj5;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 wire iwd *a83zjw+4 pob( rsand is suspended in air due to the two magnetic forces from the bottom two ja w+b8idswpzr*3( 4 owires. 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 am :61e bjapaq4 horizontal plane act as rails to support a light metal rod of mass m (perpendicular to each railaem :p6bq1ja4 ), (Fig. Below). A magnetic field $\vec{B}$, directed vertically upward (outward in the diagram), acts throughout. At t = 0, wires connected to the rails are connected to a constant current source and a current I begins to flow through the system. Determine the speed of the rod, which starts from rest at t = 0, as a function of time
(a) assuming no friction between the rod and the rails,
(b) if the coefficient of friction is $\mu_k$.
(c) Does the rod move east or west if the current through it heads north?

  Estimate the approximate maximum deflection of the electron bet +-bd76. jlnhbcol0cam near the center oflbbc.6tndjl-+ ho07 c 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 acce * mac,bwkqs3-r8a3 cxlerate 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 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 eac-* mr8x,qws3 bca k3cah 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 wig1q xb+/8uuka res, located at the corners of a square of side l, carry equ+ u81a /ukxgqbal 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 nt me3 )m*iv/w po(sq1steering”; that is, the magnetic fields can be used to change the beam’s direction without altering its speed (Fig. Below). Show how this works with a beam of protons. What happens to protons that are not moving with the speed that the magnetic field is designed for? If the field extends over a region 5.0 cm wide and has a magnitude of 0.3n*qto)/ves wp31mm (i3 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 j u)j1wu4iekaom(q:: of wire carrying a current I (as in Fig. Below) isj4i) emou ::(q1wajuk
$B=\frac{\mu_{0} N I}{2 r},$
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 iseos1 j 77oc-y wgtc8i)+ru(rjvg r1 / xx9iy7f 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 magn6r s l.7dcs8mxitude 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 prl srs78.m6d cxovide 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 make a beam of elect0/vgjl c fg.)f 6q,hanrons, traveling to the right at a spe .6fjanh,v/ l)fc qg0ged 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 th5q9m ny5diei5al4 i x .4rvop6rough a gas in 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, respectively. Calculate the changen.5eo4piyd 45qmai56vir x 9l 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 0.3f3q 2r9 *. in4dwquozf(scw-c0-T magnetic field w*.n3o-zw9id4sfc (qcur2qf at its center. 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 diameter 0.50 mm, carry th bw4er 4dvwey7 69jsy1e same current but in oppoys4e6wr v7j de49 1ybwsite directions. 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 magnetic field4gzzd 1l, *z dpsrdi9(.b bxjo b6,z3s 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$