A compass needle is not always bafotc 1m d,5 -ri+ncd(mlanced parallel to the Earth’s surface, but one end(di+ orn-f1,m cct5md may dip downward. Explain.

Draw the magnetic field lines around a straight section of4 1 on0jd:oqkv wire carrying a current horizontallyk4d:jq 1nv oo0 to the left.

In what direction are the magnetic field lines surrounding a stra2bq-*d8 ;ybpcm2wg 8yliqjg.ym/y a +ight wire carrying2w c82 ayly;py+gg m*8d/-jqyb q. mib a current that is moving directly away from you?

A horseshoe magnet is held vertically with the north pole on mklp74jg b6+u the left and south pole on the right. A wire passing between4p 6b j7umglk+ the poles, equidistant from them, carries a current directly away from you. In what direction is the force on the wire?

Will a magnet attract any metallic object, or only ya 6 cyr6.t1knthose made of iron? (Try it ancky6at1r. 6ynd see.) Why is this so?

Two iron bars attract each other no matter which enh 6 9e+6fs9lj qvoz,gods are placed close together. Are both magnets? Expl,lo feo99vh z+6qsj6gain.

The magnetic field due to curr jv:2sx-yb gm8ent in wires in your home can affect a compass. Discuss the effect in terms of currents, including if they are ac or m : jx-s8b2ygvdc.

If a negatively charg vi;f. 3kqwt sir) ,,vxbj+ksj,fos;*ed particle enters a region of uniform magnetic field which is perpendicular to the particle’s vjowf i .vt)*;brj;ss vq+x,sikk,, f3elocity, will the kinetic energy of the particle increase, decrease, or stay the same? Explain your answer. (Neglect gravity and assume there is no electric field.)

In(Fig. Below), charged partiop:zu83zd (ns cles move in the vicinity of a current-carrying wire. For each charged particle, the arrow indicates the direction of motion of the particle, and the + or - indicates the sign of the charge. For each of the particles, indicate the direction of the magnetic force due to the magnsn:(z 8ou3 dpzetic field produced by the wire.

Three particles, a, b, and c, enter a magneti 7bdb+7i fogva/k ,o.ic field as shown in Fig. 20–46. What can you say about the cod+foi 7g/,7 iabk.b vharge on each particle?

A positively charged particle in a nonuniform magnetic field followgwzurqalkm1t -42/ u:s the trajectory shown in 2t4/q1 grulz :mwu-ka
(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 sg2 )agf/z( gca magnet? Can a magnet attract an iron rod? What must you consider to answer these /c(f g2gzs)a gquestions?

Explain why a strong magnet held nea. alm 9egxa-l7r a CRT television screen (Section 17–10) causes the picture to become distorted. Also, explain why the picture sometimes goes completely black where the field is the strongest. [But don’t risk damage to your TV by tryina mga.-l xe79lg this.][/But don’t risk damage to your TV by trying this.]

Suppose you have three iron rods, two of which are mag a+dpc84-a zfdnetized but the third is not. How would you determine which two are the magnets without using any addit f8c4ad dp-za+ional objects?

Can you set a resting electron into motion with a magnetic field? With an elel1:jt 8 g:zfiokt+m4 mctric fielz tkg4f:tlm18i+:m jo d? Explain.

A charged particle is movic10)p8)wh e-wg:r9 (v0epejcpsd okd ng in a circle under the influence of a uniform magnetic field. If an electric field that points in the same direction as the magnetic field is turned on, describe the path the charged particle will pee )p0)w-(v wseoc:rpg0 8jdcd1k9 htake.

The force on a particle in a magnetic field is the idea behind ev 2 ebm+*. 1vuocqo66)ym4u*z gul zbal u(c-olectromagnetic 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( q(a l2lbz uov+ eu*uo-6b4my6v. cmc)1o*z ugFig. 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 tm/c3bka ps qb0px +u(bf-j: p6oward a horizontal wire carrying a current from leftq-b xcs0mb+ f:pap( kupb36/j to right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields that surround a mozae 9 gsl2n*pb w2p2j2ving electric charge.n2g bszwp2p2l92a j *e

A charged particle m1k/ucmg.w er..)z phzoves in a straight line through a particular region of space. Could there be a no./um.gw p 1zr. ze)khcnzero magnetic field in this region? If so, give two possible situations.

If a moving charged particle is deflected sideways in some regi5z-ih s0mrd1bon of space, can we conclude, for certain, th b s05rd-hiz1mat $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular regipb41g* +5z/zx mu)ehags-:a dq3oqt aon of space there is a uniform magnetic field $\vec{B}$. Outside this region, B = 0 Can you inject an electron from outside into the field perpendicularly so that it will move in a closed circular path in the field? What if the electron is injected near the center?

How could you tell whether moving electrons ins, q 0l(da5owae crz p.ua4/)o a certain region of space are being deflected b z(ucooldwr4 )0 qep5a,a. a/sy an electric field or by a magnetic field (or by both)?

How can you make a compass witho)v(m- rfmu5w hut using iron or other ferromagnetic material?

Two long wires carrying equal currents I p*pb5ohna5)s 7 3dpjaare at right angles to each other, but don’t quite touch. Descriohasdp5)7*b 3 pap n5jbe the magnetic force one exerts on the other.

A horizontal current-carrying wire, frzs 2idvye 6t5 /xa8ho,8hi3 rlee to move in Earth’s gravitational field, is suspended directly above a secondtldx 3y5,ri8 ea/2vz6 hs8iho , 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 a*ve tu4i1vmogk, 9i2p ttract an unmagnetized piece of iron?

An unmagnetized nail will not attract an unmagnetized paper clipe0 w lj0p(7yrm. However, if one end of the nail is in contact with a magnet, the other end will attract a pa 0w7 ymej(rpl0per clip. Explain.

Two ions have the same mass, but one is singly ionized and the other is5l1 gf5shy5wc doubly ionized. How will theiry 5 swhl5gf51c positions on the film of a mass spectrometer (Fig. Below) differ?

What would be the effect on gh:nk3 :xtu9h B inside a long solenoid if
(a) the diameter of all the loops was doubled,
(b) the spacing between loops was doubled,
(c) the solenoid’s length was doubled along with a doubling in the total number of loops?

A type of magnetic switch similar toj1p8 l z.bp me5lv1b5m 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. pl1blebpm 5mv.5j 8z1For 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 o :cuin-v t7k;krbq x xb/q6:l4f the force per meter of length on a straight wire carrying an cu-bk n4: qb x6k; v/xq7i:ltr8.40-A current when perpendicular to a 0.90-T uniform magnetic field?    N/m
(b) What if the angle between the wire and field is 45.0$^{\circ}\,$?    N/m

  Calculate the magnitude of the magnetic force on a 160-m length of hbxin6v,ihb1-8 -yj.k g y8gmstraight wire stretched between two towers carryin nx- k6vi8bh.m1 jybi-, h8gygg 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 a 160-m length of straighz 4gdp5+mqe ira6 +vi13vn qq0t wire stretched between two towers carrying a 151di54viaq 6evg np3r+mqz+ 0q0-A current. The Earth’s magnetic field of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  How much current is flowing in a wire 4- txt ;fnvvj0oznm2;7eif57 rk6 ulr..80 m long if the maximum force on it is 0.750 N when placek6; nrf t5jl ru7-efnvv.z;x ti720 mod in a uniform 0.0800-T field?    A

  A 1.5-m length of wire carrying 4.5 A of current is oriennsi(lrhp:culmb0) x(8 r4h 5oted horizontally. At that point on the Earth’s surface, the dip angle of the Earth’s magnepul8:(x5b o0rr hmnhc)4is l(tic 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 be q53;8kpt/a5dprflu.q/ u cdmtween the pole faces of a magnet. If the pole faces are/5lq duqcmkadp8f3pu/ 5. ;rt 55.5 cm in diameter, what is the approximate strength of the magnetic field?    T

  The magnetic force per meter on a wire is measured to bezhyy.oa3 kv 77 only 35% of its maximum possible value. Sketch the relationship of the wire and the fie7oya vyh3. 7kzld 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 maximubh)5wnu-k /;gzy cc*gm 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-diame:.8gu0dk( iwnp0m gx7cz/y awter copper wire could just “float” horizontally in air because of the foiwdzc7 wgyp nx/.m(g:u 800akrce due to the Earth’s magnetic field $\vec{B}$, which is horizontal, perpendicular to the wire, and of magnitude $5.0 \times10^{ -5}\;T$. What current would the wire carry?    A Does the answer seem feasible? Explain briefly.

  Alpha particles of chm3zti5e n44 ffarge $q\,=\,+2e$ 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 magnitlnz/+ul;lnyr un- 31m ude 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 nc ti ;i1vrsfbj-gv9+;: m;ph legative charge for each diagram shown in (Fig. Below), c1 ;btl v;fpvi9jmg-si r+h;: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 directioa,2/r5 6lgmznfk)mftqhq 92 zn of $\vec{B}$ for each case in(Fig. Below), where $\vec{F}$ represents the maximum magnetic force on a positively charged particle moving with velocity $\vec{v}$.

  An electron is projected vertically upward wylveps 9:px 82zwtd 4l.al6g6ith 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 ent;/6:czigp d u41yyp/xvla)mo ers a 0.20-T field, in a plane perpendicular to the field. What is theyp igpy6mlazv/d/x ;o4u :1c) radius of its path?    m

  An electron experiences the greaeno .b(ee: vxrw748tlmt7 0 setest 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 gz )e- b9k7ondgo undeflected when passing through perpendiculabge 7-9)kod nzr 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 w mz8y n. y(tt2*m;ilrkhose 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 const9dnul.fz6,n 9xm n5ss ant speed v to make one.nfsnsluz9x 65 dn9m , circular revolution in a uniform magnetic field $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge q moves *0v+ q xjz f7p;emcru/in a circular path of radius r in a uniform magnetic field B. Show that itx p/cq; +jfmvzr u*70es momentum is p = qBr .

A particle of mass m and charge q moves in a circular p u. /e,bydtlf g64q+oxde 4l*bath in a magnetic field B. Show that its kinetic enloee4 g+ bfytd/.q udbx4l 6,*ergy is proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momentum of the particle in Problemjvi*p8l3b io):syway2(9 x s 0.ol jux 21 is $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves with a speed of 160 m/s perpendiw.ov:f fw tz s94omo(ps9( p*qcular to the Earth’s magnetovo(q mps9 w.(f9tf os*4: zwpic 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 e5xjv+zon 0hz 8k6n1 hei0a p8zquator 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 spe;;egj(u 1fpcvlj9q4 led $\nu=2.0\times10^5\mathrm{~m/s}$ 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 vehf0t13 kngghi 0icle carries a 65-A current. How strong is the magnetic field 6.0 cm away from it? Compare to the Ear0nfg1 th0gik3th’s magnetic field. $B_{cable}$   $ \times10^{-4 }\;T$ the field of the cable is about    times that of the Earth.

  If an electric wire imvc ; 8*u +c5zr.uzavws allowed to produce a magnetic field no larger than that of the Eaz;* mvcz r+5wv8acu u.rth $(0.55\times10^{-4}\mathrm{~Т})$ at a distance of 25 cm, what is the maximum current the wire can carry?    A

In (Fig. Below), a long straight wire carries bn2kfm c8o 0kv)d ki0e)-i+u6infea / current I out of the page toward you. Indicate, with appropriate arrows, the direction of n 0 iede+u)n0ca /mi8 f-ki2obv6)kf k$\vec{\mathbf{B}}$ at each of the points C, D, and E in the plane of the page.

  A vertical straight wire carrying an upward 24-A currentwb stp0ebyz(23f ;c ofi6v1:t exerts an attractive fozf v;6etwbbysoif1ct2: 3( 0prce per unit 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 ig5x ,bq;*wasggv* x vpw4des ,u y/51and direction of the force between two parallel wires 35 m weqgs* ygv ;v5sdu4* x5bgiwx1/p, a, 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 field is b;l s ouww)(:dd 4isw21izz38e9 dyjlr eing carried out 1.00 m from an electriwldwl1szue s yo;2: d(r)8zi43djw i9c cable. What is the maximum allowable current in the cable if the experiment is to be accurate to $\pm1.0\%?$    A

  A power line carries a cur oy)ty27vcd a*rent of 95 A along the tops of 8.5-m-high poles. What is the magnitude of the magnetic field produced by this wire ya)72dovcy *t 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 mul o 0a4f 3 r+9ymd8i.7njb z4)mjrsacurrents in the same direction. Determri 70az9yjsorn+j44f8)mm ba 3u .ld mine 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 cx0j*2tunfc 4 nm due south from a straight vertical wire carrying a 3n*xc j24t0nfu5-A current downward. In what direction does the compass needle point at this location? Assume the horizontal component of the Earth’s field at this point is $0.45\times10^{-4}\mathrm{~T}$ and the magnetic declination is 0$^{\circ}\,$.    $^{\circ}\,$ N of W

  A long horizontal wir)hkbkcu(: wq 5e carries 22.0 A of current due north. What is the net magnetic field 20.0 cm due west of the wire ifkq kuc(w )5b:h the Earth’s field there points north but downward, 37$^{\circ}\,$ below the horizontal, and has magnitude $5.0\times10^{-5}\mathrm{~Т}?$
   $ \times10^{-5 }\;T$
$\theta$ =    $^{\circ}\,$ below the horizontal

  A straight stream of protons passes a given (cb;h;oy a .0q/,ybyteb*6jw mf-m ggpoint 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 lobb/l23/mu h rsw 1g 7(qypqwi2ng straight wires 2.0 cm apart in terms of theuq b3glw h7p21/w b/s(qim y2r current 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 vgel- 3dy2,chto, and from, an instrument. If the insulated wires are of negligible diameter but are 2.8 mm ap2 3clye-d v,ghart, 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 two wires shown in tqq4:k ohro.1m )q2z *bbfd .w(Fig. Below), parallel and just to the right. If it carries 25.0 A upward, what force per meter of length does it exert on each of thbwo14dokm):brqqf. .tq* z2h e 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 pointsf4 ditq (4ezwg4 :0ma 0e;ulkd 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 shown 0xn41yj-bobuin (Fig. Below). There is a current of 2.- o uxy4nb0bj15 A in both wires. Determine the magnitude and direction of the net force on the loop.    $ \times10^{ -6}\;N$  ----待选择----away from wiretowards wire 

  A long horizontal wire carries :q(v8ifa(9rc0oo5punx .crv a current of 48 A. A second wire, made of 2.5-mm-diameter copper wire and pacv .qou5i 9foprr (vx0cn :8(arallel 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 othejhjmn(n.yjur;6tjewsg8/x5 *5gj c 7 r. 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 carr j/7j5gj nj;xeus5gmrt*jwy (n.8c h6ies a current of 20.0 A and the bottom one carries 5.0 A?    $ \times10^{-5 }\;T$

  Two long straight parallel wiresxuw f/ixw1 ,hx:bd zw+n-v0e2 are 15 cm apart. Wire A carries 2.0 A current. Wire B’s current is 4.0 A in the same vdxfuzb we21h/i,nxwxw:- 0+ 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 a5u nydchck: 28dwv(td*(j*umre 3.8 cm from one another. (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 magneti**d vk:8 2w(dj(mu ncdt uchy5c 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 s2nzh/nlggeh9-l-e -h6- ema direction of the magnetic field at the midpoint of the side of the triangleg26n-9hsl aeh-lenz - g- meh/ between wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a dis 2+mr ,qou*bi7xa1oo rtance d apart, carry equal currents I in the same direction. One wire is at x7 *oao,1i2rbq +om rux = 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 total of 420 turns of li5k9my3 op5kwire and carries a current of 2.0 A. Calculate the field inside near the ceo mk55lk yi3p9nter.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.jcav;jn )emt 3q6 33qel1 6zxk25 cm in diameter is to produce a field of 0.385 T at its)3q1 6t 6jl3mz3nxq ecva;ekj center. How much current should the solenoid carry if it has 975 turns of the wire?    A

  A 550-turn solenoid is 15 cm long. The current in pe9zi*- t /lprit 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 th/-itp e*rz l9pis wire assuming the solenoid’s field points due east?    N

You have 1.0 kg of copper and want to make a practi qch.g+f2 k/q)f-,mmo 0(bi;l c1b7 c nxqgzeical solenoid that produces the greatest possible magnetic field for a g. zo0 ,mqm ;flk1)-+gcfhcb nqc7i(/ b2eq gxiiven voltage. Should you make your copper wire long and thin, short and fat, or something else? Consider other variables, such as solenoid diameter, length, and so on.

A toroid is a solenoid in the shape of a circle (Fig. Below). Usf v.b) oz:.jqse Ampère’s law along the circular path, shown dashed in (Fig. Below a), to determine that the magnez.qb .)jf:osvtic 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 thauhx6y *ip6k;rt the magnetic field between the conductors of a co*k;ph6 xiru6yaxial 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 face parallel+/1+wchqaw kc b*am hhz4l7q5 to the magnetic field between thecq bl+qmk* wh4aw/1z hhc+75a pole pieces of a large magnet. When 6.30 A flows in the coil, the torque on it is $0.325\cdot N$. What is the magnetic field strength?    T

  A galvanometer needle dechu p:lx3 3z;aflects 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 the cyl x h9pw wp8dg+n24.years, what current will give full-scale deflection if it originally reywnch2+ .49 g8dlxwp pquired $36-\mu A$ ?    $\mu A$

If the current to a motor dro.qr w6v k86fceps by 12%, by what factor does the output torque chrv8e6c wf6qk.ange?

Show that the magnetic dipole moment M of an e8 o,a2g a/t )zttkayicq6nr:) lectron orbiting the proton nucleus of a hydr6ik g8y qtcr o/z na:at)t,a2)ogen 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 lfd2fl j04a p2aoops lies flat on the ground. The Earth’s magnetic field at this location has mag04flaaj d22 fpnitude $5.50\times10^{-5}\mathrm{~Т}$ 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 z:-k ai 7kfco9a 0.566-T magnetic field. What value of electric field could make their pathsiz-f kk7:o9ca straight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometel/, s 5udzgff5r, germanium atoms have radii of curvature equal to 21.0, 21.6, 21.9, 22.2, and 22.8 cm. The largest radius corresponds to an a ff5sdl g5,u/ztomic mass of 76 u. What are the atomic masses of the other isotopes?

  Suppose the electric field between the e3apktf ay+ ho+yz 6/sd n:ok9,lectric plates in the mass spectrometer of (Fig. d+h3o yo+f t6:a/,aysz9n kpkBelow) 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 mocuj4s h4xbo :6nitor air pollutants. It is difficult, however, to separate molecules with nearlyh4x: cu 4j6obs 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 accelerate vn4x l5 bktha0nq)/0ls ions by a voltage V before they enter a magnetic field B. The ions are assumed to start from rest. Show that the mass of an0tb) l045khnxn ql av/ 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 b*30ume un xb525-A current flows through the wire. If then3 uemub*0xb5 permeability of the iron is $3000\mu_0$ what is the total field B inside the solenoid?    T

  An iron-core solenoid is 38 cm long and 1.8 cm in diameter, and has 6i6 3;e*fzod;q7m2r y*vjnqi w40 turns of wire. The mqq 2mf;i*z n * ;i3wery6dv7joagnetic field inside the solenoid is 2.2 T when 48 A flows in the wire. What is the permeability $\mu$ at this high field strength?    $\times10^{-5}\mathrm{T}\bullet\mathrm{m/A}$

  Protons with momentumt 43ez6-cgzpr $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 havea4f dxp5:av4 6wmve uv)q;t8a the same kinetic energy upon entering a region of constant magnetic field. What is the ratio of the radii6da4a; )xv8m:vfpwq 5teu4va of their circular paths?   

  The power cable for an elehh7+aj74sujf)-y o pu d5zhn-ctric trolley (Fig. Below) carries a horizontal current of 330 Anzoyhphafh - 5uj7s)47u +dj- toward the east. 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 acquireu mnr:gp18 ifor:pbsm5l1e3 jef5b; 6d a net charge of $1550\mu C$ and moves with a speed of 120 m/s perpendicular to the Earth’s magnetic field of $5.0\times10^{-5}\mathrm{~T}$.    $ \times10^{-6 }\;N$

  Near the equator, the Earth’s magnetic field points almoloi965zg wg 2zst horizontally to the north and h9l6igz gz 5ow2as magnitude $B=0.50\times10^{-4}\mathrm{~T.}$ What should be the magnitude and direction for the velocity of an electron if its weight is to be exactly balanced by the magnetic force?    $ \times10^{-6 }\;m/s$  ----待选择----eastwest 

  A doubly charged helium atom, whose mass ist0a1k7kyv 1jbg3qt0 2-lqzk s $6.6\times10^{-27}\mathrm{~kg},$ 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 current movesaoy qyeuf ,6,1 in a closed loop composed of fixed rails, uoey q,,ay61fa 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 wire2.1ui6r-hk 0*vokw0kyshp m+2f tlm r is 1.00-mm-diameter copper wire and is suspended in air due to the two mat22 rp0h-fiy*kr.mo1 l 6h wu+0kv kmsgnetic forces from the bottom two wires. The current flow through the two bottom wires is 95 A in each. Calculate the required current flow in the suspended wire.    A

Two stiff parallel wires a distancefq1t() mygyl.y2i1vbk3-qvc l apart in a horizontal plane act as rails to support a light metal rod of mass m (perpendicular to each rail), (Fig. Below). A magn3-1klt yym gvc 2qb1(yv.)f qietic 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 beam near the lvaxd1/a b+o,gp3;u60z g pww)a/f dlcenter of a TV screen due to the Earth’x0 lldpgbaagwo /du+ /vz fwa1 ;p63),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 devi yoqa:m/+8ev hce 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 higher speeds each time they pass through the gap between the metal “dees,” where there is an electric field E. (There is no el/ :o ha+q8vyemectric field inside the hollow metal dees.) The electric field changes direction each half-cycle, owing to an ac voltage $V=V_0\sin2\pi ft,$ so that the particles are increased in speed at each passage through the gap.
(a) Show that the frequency f of the voltage must be $f\,=\,Bq/2/pi m,$ where q is the charge on the particles and m their mass.
(b) Show that the kinetic energy of the particles increases by $2qV_0$ each revolution, assuming that the gap is small.
(c) If the radius of the cyclotron is 2.0 m and the magnetic field strength is 0.50 T, what will be the maximum kinetic energy of accelerated protons in MeV?

Four very long straight parallel wires, located at te9g tuftd;3h5 he corners of a square of side l, carry equal currengdu3t59;th efts $I_0$ 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 park x9rh;(,betqtsa d7.ticle 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 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 wqdr,ka9.x(t;e tbhs7 hat angle will a beam of protons traveling at $ 1.0\times10^{7 }\,m/s;$ be bent?    $^{\circ}\,$

  The magnetic field B at the center of a circular coil of wire carrying a ct ou+eubf5zvy2 uq qy;8/ l11olpih1 1urrent I (as in Fig q1uevyh8i/ut p1 oqlf51 lobuy1 ;+z2. 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 magnetipvk.l2 0* lqcper3,ksc 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 magnitude of lro k,5y1 mgde uq13c+ -yxf*cmagnetic 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 t *ocqykx3el +,dcfgr1 15-umyhe 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 elenly xgm/,ct2(rj,rgww4gt*x 5 ;2z 5kl oeih;ctrons, traveling to the ri2 ;rxtg/*je 2r4, lt ,g;ynwl o(hxmkg5wzci5ght 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 in a magnetic fi ts v5zc yo2q3trfx7ozr0.;ux4owr+ 8 eld of 0.010 T, perpendicular to the plane of the spiral, as shown in (Fig. Below). In two successive loops, at po74 x3 vf sr;r28u0tz +oc.y5trzooxqw ints 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 produce a 0.30-T mag 8k g.zfd1;(2pglv8s jhx4 inznetic field at its center. If the maximum currngszxgi 8;2 lf8v1 d zh(.4pkjent is 5.7 A, how many turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, each of diameter 0mf.pdri2:hf w4yc+ ;.ly q3y15/c qhorjfe o2.50 mm, carry the same current but in opposite directions. They are suspended by 0.50-m-long strings as shown in (Fig. Below). If the suspension strings make an angle of j.wyo1qc 5q3+he 4poff2lf my2 r.yr:/hi ;c d3.0$^{\circ}\,$ with the vertical, what is the current in the wires?    A

  An electron enters a ,ljkj(w 3 jl:ptik5m0uniform magnetic field B = 0.23 T at a 45$^{\circ}\,$ angle to $\vec{B}$. Determine the radius r and pitch p (distance between loops) of the electron’s helical path assuming its speed is $3.0 \times10^{6 }\;m/s$. See (Fig. Below).
r $\approx$    $ \times10^{-5 }\;m$ (retain one decimal places)
p =    $ \times10^{-4 }\;m$