A compass needle is not always balanced parallel to the Earth’s surface, but,7bbefp b alfw5;c.) ,v.rgtf one end may dip downward. Expf,gap5 ; be7ltrc.w .b vbf,f)lain.

Draw the magnetic field lines around a straight section of wire carrying a cws)zxxct1qg*cr wd)x 4un 49/lxooq5 6l95 ndurrent horizonta/ l51wo ndcq)9tx u4lxo6c4x9d)wq gxns * r5zlly to the left.

In what direction are the magnekf*frb-vi6zz ck:6pzt1gi , .)1 h xygtic field lines surrounding a straight wire carrying a current that is movicvyp*.)ik6-:h rx1 z,ziffk1tbz 6 ggng directly away from you?

A horseshoe magnet is held vertically with ll+-rnq.1 : zwv( w z+cq(doesvba8)jthe north pole on the left and south pole on talq) w8-je(nvv+dszz o.:c1qw+ l b( rhe 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 wire?

Will a magnet attract any metallic object, or only those made of iron? (Try it: di 0,2*isydj;i) z z ;.k;tbbdjpwwb and si w wd ibk.20z *y:ij;;,tsd;b )jdpzbee.) Why is this so?

Two iron bars attract each other no matter which eqcn (oh,h*h7p c+i-bznds are placed close together. Are b h*+pcnhb7,h-i(qzcooth magnets? Explain.

The magnetic field due to current;v6ve gjrr -gf.kwo) ( in wires in your home can affect a compass. Discuss the effect in terms of currents, includjgv;-r(k) fe6. vrgow ing if they are ac or dc.

If a negatively charged particle enters a region of uniform magnetywqa,eg p8f ,:ic field which is perpendicular to the particle’s velocity, will the kinetic energy of the particle increase, decrease, or stay the same? Explain your answer. (Nefye w8q:,ap,gglect gravity and assume there is no electric field.)

In(Fig. Below), charged particles move in the vicinity 28st1rwj :vn tof 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 thet:jvn t2r18w s 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 shog;i -/guaglx 1.tfuph +xd7h1wn in Fig. 20–46. What can you say about the chargat+1idfh-x7uluh.gg ;1pxg/e on each particle?

A positively charged par; q ;fg ykx)c5:lgc)wfticle in a nonuniform magnetic field follows the trajectqgfxwcy)ck: 5 g;);f lory shown in
(Fig. Below). Indicate the direction of the magnetic field everywhere in space, assuming the path is always in the plane of the page, and indicate the relative magnitudes of the field in each region.

Can an iron rod attract e7szjsldvjf-7q q22 -a magnet? Can a magnet attract an iron rod? What must you consider to answer th 2qvfq72jszesd-j7 l- ese questions?

Explain why a strong magnet held neecj7)efjx 2-fb7n87 x3j xeicar 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 yob xx ncej7e xejj)8f237fi7-c ur TV by trying this.][/But don’t risk damage to your TV by trying this.]

Suppose you have three iron rods, two of whic.m1rz t--eehkt( xx*v0eb /hlsm6sofy p 04 :ch are magnetized but the third is not. How would you determine wmcm:xt o/-e4ysh -ezl pkevbh. *06strx(1f0 hich two are the magnets without using any additional objects?

Can you set a restinh*5umfyksmu;; x .m;pg electron into motion with a magnetic field? With an electric ff5. u ;*px;hmku mys;mield? Explain.

A charged particle is movi2p(.e,lyzdnx8gy ,l sng in a circle under the influence of a uniform magnetic field. If an electric field that points in the same directis2 .,8, lzynpedx(y glon as the magnetic field is turned on, describe the path the charged particle will take.

The force on a particle in a magnetic field is the idea behind e2 pq oodbpz*92lectromagnetic 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 to a blood vessel and to a magnetic field. Explain how ions are caused to move. Do positive and negative ions feel a force indo29bzopp*2q the same direction?

A beam of electrons is directed toward a horizontal7e fs1sh /w5sc wire carrying a current from left e1cw57h sss/ fto right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields that surround a moving elecnpc6k 0*nbw)zb k n4onk8v ap(d2(pn9tric charge. zb(wc) *24dknpn8pk0nvn6opka b9 n (

A charged particle mfn3z; yqss8 x/ qywi31xh 7.oyoves in a straight line through a particular region of space. Could there be a nonzero magnetic fie17f; ysyws/ ynozqqxx3 3.hi 8ld in this region? If so, give two possible situations.

If a moving charged particle is d65v .,oah,lcaqj hba8 eflected sideways in some region of space, can we conclude, for certain j,,68o.hb qhca va5al, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is of,vy)w8 t:v3 g( nwaj7uo 6uxa uniform magnetic field $\vec{B}$. Outside this region, B = 0 Can you inject an electron from outside into the field perpendicularly so that it will move in a closed circular path in the field? What if the electron is injected near the center?

How could you tell whether moving electrons in a certain region of spacma-i-z :y: iaji6zkr,m;d +ige are being deflected by an electric field or by a magnetic f k;:jyzr imimza,ii:a6 g--+ dield (or by both)?

How can you make a compass without using iron or other ferromagnetic z(d ypu8z,8j2um t4ripov )(0ot.z dematerial?

Two long wires carrying equal currents I are at right angles to each otheuj(2opp a,/8o; k(is. m dl+djzt.ecxr, but don’t quite touch. Deskoma, 2 xsc(d.+lij(8 z;e u./tjpdpocribe the magnetic force one exerts on the other.

A horizontal current-carrying wire, fre82rowge/ rk1ne to move in Earth’s gravitational field, is suspended dire1r/n2 k g8orewctly 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 7j89 kku f o.-kfcb3vqa magnet attract an unmagnetized piece of iron?

An unmagnetized nail will not attract an unmagnetized73*0 3ulmesxaetx1 dd paper clip. However, if one end of the nail is in contact with a magnet, the other end will attract a pape t*exls33 mad1d ux70er clip. Explain.

Two ions have the same mass, but one,zvl 3 kd8f9l*2eh gal is singly ionized and the other is doubly ionized. How will their positions on the film of a mass spectr l9egk2,l3l*avfdz h 8ometer (Fig. Below) differ?

What would be the effect on B in0 e9w ldy+yghng0e g f4f3s,3qvwc 9;d2la2twside a long solenoid if
(a) the diameter of all the loops was doubled,
(b) the spacing between loops was doubled,
(c) the solenoid’s length was doubled along with a doubling in the total number of loops?

A type of magnetic switch similar to a solenoid is a relay . A relay iswqsu5exxb456/2,f boyjv 3 w v 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 car is connected to a relay so that the large currento5y bvfvwbq wu s/5,xj423xe6 needed for the starter doesn’t pass to the dashboard switch.

  (a) What is the magnitude of the v(,rn nc ,cm,zsn*s, fforce per meter of length on a straight wire carrying an 8.40-A current when perpensnzsfncm ,,cv(,,r*ndicular 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 forz3pe nr.3t(on- eohj 6ce on a 160-m length of straight wire stretched between two towers carrying a 1506jtre3p- ohz(o3ne n .-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 ojszey 8vp+xv0q sx s6l-/p1/pn a 160-m length of straight wire stretched between t/xy0s1sjvvpe/p-8slp z q+6x wo towers carrying a 150-A current. The Earth’s magnetic field of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  How much current is flowing in a wire 4.80 m long if thmm0 rs4m1;.p:iy-w/ybl )z)lid musp e maximum force on it is 0.750 N when placed in a uniform 0.0800-T iup.rmymw p 0z:/ 1s)-sbli;d4m m)l yfield?    A

  A 1.5-m length of wire carrying 4.5 A of current is oriented horizontally. At tj fl+c- qxpc.*-:ffr juf wt91hat point on the Earth’s surx-9f* fjq crfpu. c:+ft l-j1wface, 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:-4mv mc gtl7uvy )h2 qg-dx(v.75 A is a maximum of 1.28 N when placed between the pole faces of a magnet. If the pole faces are 55.5 cm in diameter, what is the approxtgl) ydhmq4g7c( v:vu-mv-2 x imate strength of the magnetic field?    T

  The magnetic force per meter on a wire is measured mawy5:dp bq /4to be only 35% of its maximum possible value. Sketch the relationship of the wire and the field if the force had been a maximum, and sketch the relationship as it actuay db/45q p:mwally is, calculating the angle between the wire and the magnetic field.    $^{\circ}\,$

  The force on a wire is a m wwytu/1v. z/saximum 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 copper1l. ikpc3 rb9eli y7c6 wire could just “float” horizontally in 3 c re1kp67 lil9cb.iyair because of the force due to the Earth’s magnetic field $\vec{B}$, which is horizontal, perpendicular to the wire, and of magnitude $5.0 \times10^{ -5}\;T$. What current would the wire carry?    A Does the answer seem feasible? Explain briefly.

  Alpha particles of chq4.jx um u-eqi suw-(7arge $q\,=\,+2e$ and mass m = $ 6.6\times10^{ -27}\;kg$ are emitted from a radioactive source at a speed of $1.6 \times10^{ 7}\;m/s$. What magnetic field strength would be required to bend them into a circular path of radius r = 0.25 m?    T

  Determine the magnitude and direction of the force okx,98fcx,khwz*4 l :i j4ik:- 2t 5zxjjgdtmin 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 3*a089ra*maokb mfkl each diagram shown in (Fig. Below), wher9a3fr ka8bma0k m*ol *e $\vec{v}$ (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 t grpdue+8q +*)bdz. ht /rk4sof $\vec{B}$ 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 vertic 0l9lbfa hdce)/ 7nwb-v9 udo7ally 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 ener 8+74rpvinohegy) proton enters a 0.20-T field, in a plane perpendicular to ivo+ 7pr4hne8the field. What is the radius of its path?    m

  An electron experiences the greatest f q2kq fkx0gxf2opy .7w 0.s6mporce 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 paz-xe rhh- j3-dr 9v04i sfn* 7hzziw3yssing through perpendicular electric and magne7z-- r s zxh* wifer3 y-90ndzhvhi34jtic 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 helgo8bnu2g z 7+7f8 dwhgium atom whose 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/hew w8mq5 qr, q moving with constant speed v to make one circular revolution 8/qerw5w m h,qin a uniform magnetic field $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge q moves in a circular path of radius r in a uniform mag aa+jso /9d3o-tha 1aknetic field B. Show that itj-oa /k1 9toas 3+ahdas momentum is p = qBr .

A particle of mass m and charge q moves in a circular p b5jxc*g0vv+ llb43zwath in a magnetic field B. Show that i gjv50 4wxcz+*b3b vllts kinetic energy is proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular mome/tn dj-r pl.b, f:jg1tntum 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 Eart5955ja1laykmf cx5ya h’s magnetic fimc jl5y ay5f91k5a5x aeld 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 hajf+pglo ht u d::p-c;4s 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 spe9u0(pzppx(jv9v k7du jcc)0s ed $\nu=2.0\times10^5\mathrm{~m/s}$ in a field-free region abruptly enters an essentially uniform magnetic field $B=0.850\mathrm{~T~}(\vec{\mathbf{B}}\perp\vec{\mathbf{v}}).$ If the proton enters the magnetic field region at a $45^{\circ}$ angle as shown in (Fig. Below),
(a) at what angle does it leave, $\theta$    $^{\circ}\,$
(b) at what distance x does it exit the field? x    $ \times10^{-3 }\;m$

  A jumper cable used trboq r;xy1 ed.q tn*qnxbv1p- / t5)v5o start a stalled vehicle carries a 65-A current. How strong is the magnetic field 6.0 cm away from it?5ttxr.*bqre1nvdqv5p/x)1oqb ; ny - Compare to the Earth’s magnetic field. $B_{cable}$   $ \times10^{-4 }\;T$ the field of the cable is about    times that of the Earth.

  If an electric wire is allowed to produce a *sx w l0xjia 0m00fiw2magnetic field no larger than that of the Eaa2 00ml0ifxj i0w* sxwrth $(0.55\times10^{-4}\mathrm{~Т})$ at a distance of 25 cm, what is the maximum current the wire can carry?    A

In (Fig. Below), a long straight wirg 5;t,ejg0xa4t0m q *uxzng0 qe carries current I out of the page toward you. Indicate j00ex5 ,q* g4z x;tungm0taqg, 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 upwaruwaeqx jn s+v.2(emg66ph;cdd 7.rl.d 24-A current exerts an attractive force per unit le(pn7ds rg6c+ e xu v.da2qe.lj m6hw.;ngth 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 parallel0qk kx s0cdz;, wires 35 m long and 6.0 cm apart, each carrs qckx,0z0;kd ying 25 A in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth1ddu hood3eh i,t5* h7’s magnetic field is being carried out 1.00 m from an electric cable. What is the maximum allowable currd*t,oo e7 hi35 h1uddhent in the 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 8.5xm:ss meftv53k 3 9z2v-m-high poles. What is the magnitude of the magneesz m2:33vvsk5m xft9 tic field produced by this wire at the ground? How does this compare with the Earth’s field of about $\frac{1}{2}G$?    $ \times10^{-6 }\;T$ The field of the cable is about    % that of the Earth.(retain two decimal places)

  Two long thin parallel wires 13.0 cm apart carry 25-A currents 6cu2nsi-+y/or dmbpwk t61 sd.6fif : in the same directi/n6yrdtid2u1 pm is:s.w6f ocfb +-6kon. Determine the magnetic field at point P, 12.0 cm from one wire and 5.0 cm from the other(Fig. Below).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18 cm due south fro8 nd/q,yd. ygdm a straight vertical wire carrying a 35-A current downward. In what direction does the compass needle point at this location? Assume the horizontaqng.yd ydd,/8 l 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 carries 22.0 A of current due north. What is thet5y ow0gvdcdhrg sd/0, . h5o5 net magnetic field 20.0 cm due west of the .5h5r0,t5 d vsgwyd/dc g0ooh wire if the Earth’s field there points north but downward, 37$^{\circ}\,$ below the horizontal, and has magnitude $5.0\times10^{-5}\mathrm{~Т}?$
   $ \times10^{-5 }\;T$
$\theta$ =    $^{\circ}\,$ below the horizontal

  A straight stream of protons passes a given point in 0okzoo-xa1 -b n6hzs7 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 mfk0.c , bhmb,:k+t0vo.n grg59rwuz long straight wires 2.0 cm apart in terms of the current I in one when the w0 9zbnm cgg+k ,rktobrf h..mvu5:0,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 hr)umxh x. y:ts7p,a9 instrument. If the insulated wires are of negligible diameter but are 2.8 mm apart, what is the magnetic field 10.00 cm from their midpoint, in their plane (Fig. Below)? Compare to the magnetic field of the ):r xp7thmhu,x.a s9yEarth.
   $ \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 (Fiqxk( /3eed:zfl5 b e5ig. Below), parallel and just to the right. If it carries 25.0 A upward, what force pefzd eq3e l5b (:k/5iexr 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 2u3 )6kqh tj5en3$^{\circ}\,$ 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 wir0i9i9lrp)5ja5 qlcq 6 xzq fa3e, as shown in (Fig. Below). There is a current of 2.5 A in both wires. Determine the magnitude and direction of thel 6xcz9 p0jq9ari fqal5)5iq3 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 o 4ql (uz9v,kflf 2.5-mm-diameter copper wire and parallel to the first, is kept in suspuqlv(4 9fk,lzension 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 otherot0iw3-.ld )( sq+ewigu y u1g. At their closest, they are 20.0 cm apart (Fig. Below). What is the magnitude of the magnetic field at a point mi0 1owd wsuqggtei(3.yil+)-udway 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 pjwa o1kt3b u3kk5 .b8p4(rhfapart. Wire A carries 2.0 A current. Wire B’s current is 4.0 A in thebu 3kw8b1k at3(hk.rj4o pfp 5 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 area)x gsrwxk.s0qr 36xn js97u- 3.8 cm from one another. (Looking along them, they are at three corners of an equilateral triangle.) The current in each ws6n 9k)js07-3wsur g ra.xxq xire 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 the magnemtb/qm kw:3doh)57 hzk n ;y*ztic field at the midpoint of the side ykh/mzdzkh ;bmw:*5t )3 no7qof the triangle between wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a distance d apart, carry equal s7mm e /0, +gkzdvl-jycurrents I in the same direction. On 7/g kvmlsydj+0,-me ze 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 total of 420 turns of wire and carries a cur2hb: ;xzqm+ kpwgnn(vg46m8 mg 36cy prent of 2.0 A. Calculazxgmh 2c (m+pq4v6gb 6 k8wgn;mpn3 y:te the field inside near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameter is to p0mcpny x 2 ,wiq,ftc21roduce a field of 0.385 T at its center. How much current should the solenoid cart2wx mf y ,1cinp,q02cry if it has 975 turns of the wire?    A

  A 550-turn solenoid is 15 cm long. The current in -c)ub+ *r 5eo- g:.ymfyuhd i+(eupjs6v 9qjwit 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 (- b(r+)9 ph f+vyidgue com uesu qwj:jy65*.-and is connected by other wires that don’t concern us). What is the force on this wire assuming the solenoid’s field points due east?    N

You have 1.0 kg of copper and want to make a practical solenoid that proa leov28du;0 5vmkrf (duces the greatest possible el5f0(vamr 8;2vdou k magnetic field for a given voltage. Should you make your copper wire long and thin, short and fat, or something else? Consider other variables, such as solenoid diameter, length, and so on.

A toroid is a solenoid in the shape of a circle (Fig. Below). Use Ampère’s la)mdqwby3:hw ;/ gcdf- w along f);/-b dww ycdhm:q g3the circular path, shown 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 conductors u,gqfh;p* ye,h(gw /oa4ztw + of a cyeq+pf,z*t /,wg wg(;ha4h ouoaxial 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 p2d4 8;p8jx lgeju7ynplaced with its face parallel to the magneticxu;4yj8e7p8pld gjn2 field between the 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 deflec4j k18 m0ej,h :mr 4j1rh)ah)iko mugpts 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 years, what cts( z(++ o(grp :tn 3gd7bjjsvurrent will give full-scale deflection if it origina3ggtpjdnjs+ ( +(tbv:sr oz( 7lly required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by what factor does the output td,zsn2i 6l+lo h0y2ftorque chanfynld2t60,2 z l o+hsige?

Show that the magnetic dipole moment M of an electron orbit gyf+a kx)1bg oth+*k)u7qj6ting the proton nucleus of a hydrogen atom is related to the orbital angular momentum L of the t6xugk)ojqfk*ab+ 17)thy+ gelectron by
$M=\frac{e}{2m}L.$

  A circular coil 16.09b2bc et-h.thj4+ylm cm in diameter and containing nine loops lies flat on the ground. The Earth’s magnetic field t ht+jl.by9m 4-2hb ceat this location has magnitude $5.50\times10^{-5}\mathrm{~Т}$ and points into the Earth at an angle of 56.0$^{\circ}\,$ below a line pointing due north. If a 7.20-A clockwise current passes through the coil,
(a) determine the torque on the coil,   $\times10^{-5}\mathrm{m}•\mathrm{N}$
(b) which edge of the coil rises up: north, east, south, or west?

  Protons move in a circle of radius 5.10 cm in a 0.5+, yje6ivaw ((c kpx3n66-T magnetic field. What value of electric wn yvk + a(ji(c36ex,pfield could make their paths straight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanib82k*qvu) g mapppq0+f t.bkm91;l5vyd 7duz um atoms have radii of curvature equal to 21.0, 21.6, 21.9, 22.2, and 22.8 c 7b 9 ;bdkv d2l8* kpfzp.0)qyt5av1qpumumg+m. 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)b)bl z+yw;fmb( qc8 s electric plates in the mass spectrometer of (m w;bl( z bsby))f+q8cFig. 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 is difzhh ,rue3 );rvficult, however, to separate molecules with nearly equal mass such as CO (28.0106 u) az,rru;h 3h)evnd $N_2(28.0134u)$. 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 before they eni p0wv;hxtz9kvp-;sjz,q ;;1u.wg cp ter a magnetic field B. 9w;sv1 qwt,hc; v jzp xp0g;z.;k i-upThe 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 cu.p :skh:v;hm.j attv 7o va;jnn*f*2g rrent flows through the wire. I:a t72hkgs*.nvojvtvj :pah.;; f *mn f the 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 1i u2;x9oh f(xj.8 cm in diameter, and has 640 turns of wire. The magnetic field inside the solenoid is 2.2 T when 48 A flows in the wire. Wha2jh 9o;fu( xixt is the permeability $\mu$ at this high field strength?    $\times10^{-5}\mathrm{T}\bullet\mathrm{m/A}$

  Protons with momentumr j8 g,ajmyqm* 65gn4yj*ko n8 $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 thkuue+i m,+wn t-1: lf op(aytp6- +xzee same kinetic energy upon entering a region of constant magp-w +puxfim :-te+yt16z( kuo,aeln+netic field. What is the ratio of the radii of their circular paths?   

  The power cable for an electric troll5qrl +br ;:cfkc33r evey (Fig. Below) carries a horizontal current of 330 A toward the east. The Earth’s magnetic field has a str+rq;r5bfv c k3ercl3:ength $5.0\times10^{-5}\mathrm{~T}$ 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 wh8ho9m9p+kj xo*.mxj ;pp1 onet 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 almost horjom) i5r wjjo:v3+z+ sizontally to the north and has majsjo :m5j+ wv+3r)ziognitude $B=0.50\times10^{-4}\mathrm{~T.}$ 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 rk2 5gm/+qk /v ycqp0wis $6.6\times10^{-27}\mathrm{~kg},$ 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 b4jfe 6puc8 t9large 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 need6fc8b4epu jt9 ed 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-( ck oe8fm(6brmm-diameter copper wire and is suspended in air due to the two magnetic forces from the bottom two wires. The6fbc (8mroke( current flow through the two bottom wires is 95 A in each. Calculate the required current flow in the suspended wire.    A

Two stiff parallel wires a distance l apart in a,bbekznjd xazg *o20 7iip +zc i.)l39 horizontal plane act as rails to support a light metal rod of mass m (perpendicular to each rail), (Fig. Below). A magneticjanl,9dbz 7 0x+ *gpzi3i z)ick.oe2 b 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 centerxvlm866mzbv 5 of bxv zv8lm66m 5a 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 accelerate elementary 72i*q +imlqffyi1 ehdk *b13l 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 eqyiiq1i3 kl f*bf1 hm *l2+7dhigher speeds each time they pass through the gap between the metal “dees,” where there is an electric field E. (There is no electric field inside the hollow metal dees.) The electric field changes direction each half-cycle, owing to an ac voltage $V=V_0\sin2\pi ft,$ so that the particles are increased in speed at each passage through the gap.
(a) Show that the frequency f of the voltage must be $f\,=\,Bq/2/pi m,$ where q is the charge on the particles and m their mass.
(b) Show that the kinetic energy of the particles increases by $2qV_0$ each revolution, assuming that the gap is small.
(c) If the radius of the cyclotron is 2.0 m and the magnetic field strength is 0.50 T, what will be the maximum kinetic energy of accelerated protons in MeV?

Four very long straight parallel wires, located at the corners of a squarf 2 liltp0yr9s,.z s.se of side l, carry equal0zsri. 9t.lp ,ss l2yf 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 int rgw5r 92+sbjgjl 3z*o;p9im 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 beam of protons. What happens to protons that are not moving with the speed that the magnetic field is designed for? If the field extends over a region 5.0 cm wide and has a magnitude of 0.33 T, by approximately what angle wjt*w2go9pbzl3i rjs gmr95+;ill a beam of protons traveling at $ 1.0\times10^{7 }\,m/s;$ be bent?    $^{\circ}\,$

  The magnetic field B at the center of 4*b y1 0qhalrv,15rsl gyw2wd a circular coil of wire carrying a current I (as in Fig. Below)*ay 1 ,gh0l 5wylbwqr rvs2d41 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 magnp:mncx5y*pa. iem/ bz(j*w ; tetic 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 them avdd2c+ z 9am476mqh magnitude of magnetic fields produced by overhead power lines. You estimatemh742dqza m ca6 vm+9d that the two wires are each about 30 m above the ground and are about 3 m apart. The local power company tells you that the lines operate at 10 kV and provide a maximum of 40 MW to the local area. Estimate the maximum magnetic field you might experience walking under these power lines, and compare to the Earth’s field. [For an ac 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 b25xthcd u; 6yz*gy izq)1e 3weeam of electrons, traveling to the right at a speg5wtq6zy*ze3);1 id y2hec u xed 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 field of 0.bu a uuywm(4f cq-,t)70 n7yfu5mhm+r 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 change in the kinetic ener5 uwy+)7uf4tmurqm ,mufc0n -h y(a7bgy of the proton as it travels from P to Q.    $ \times10^{-20 }\;J$

  A 32-cm-long solenoid, 1.8 cm 8aunwnz(u8 z 6in diameter, is to produce a 0.30-T magnetic field at its center. If the maximum current is 5.7 A, how many turns must the solenoid havw a( u8n8nzzu6e?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires 7 w/f; 66 g o-ngrw.5g1vdqwdhiqomf5, each of diameter 0.50 mm, carry the same current but in opposite directions. They are suspended qg5middf rw ;.6goq5v-h 7w/1 ng owf6by 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 undx9(444zcs (kp3rrmfhoog*kd m5( *hcyo x4 miform 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$