A compass needle is not always balanced parallel to the Earth’s surfa 5 +29ylxpc u7efhjesl3,)iirce, but one eni72pl u3 )ijexh5,sf9l+ey crd may dip downward. Explain.

Draw the magnetic field lines around a straight section e.h pedxi9kb6ym wrc, dz:.8k. .i5lwof wire carrying a current horizontall e,6ikx.5r .yhz bei.:w p.cdd9w8k mly to the left.

In what direction are the magnetic field lines surrounding a straight wire car faa;e(x+lad9q7w./w t8tp8 owf wf3g rying a current that is moving d(fg qwf awxaedp;a .lft88o3w97+ t/ wirectly away from you?

A horseshoe magnet isun/sn4(xjy 9 g:a*uo x held vertically with the north pole on the left and south pole on the rigux x9u :n(n*jgsao4/yht. 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 metalli 0dz rws7mdv752:y/15gq wpmg:bd m lcc object, or only those made of iron? (Try it and g gv7w w7m:/1mq0d:55lr b2ypzscd mdsee.) Why is this so?

Two iron bars attract each other no matti -ziv sv,n4w. oi5kpy wh++0der which ends are placed close together. Are bo-pvw+.kn5i,wizo yhv d0 s i+4th magnets? Explain.

The magnetic field due to current in wires in your home can affect eivxp618 /r,gcxl9 woj2egj -a compass. Discuss the effect g6 xrve ojwx /c92 jgeip18l-,in terms of currents, including if they are ac or dc.

If a negatively charged particle enters ab8 pbdb)k *ohdq7j/66;mwhoj region of uniform magnetic field which is perpendicular to the particle’s velocity, will the kinetic energj qom* kdw )h;h/db6bj8p7b6oy 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 particlke-fguwf/;k 3nugch yv)r -33es move in the vicinity of a current-carrying wire. For each charged particle, the arrow indicates the direction of motion of the particle,c;-k rkfv- )3g 3wg/ueyhnuf3 and the + or - indicates the sign of the charge. For each of the particles, indicate the direction of the magnetic force due to the magnetic field produced by the wire.

Three particles, a, b, and c, enter a magnetic gywx8*9(whnl field as shown in Fig. 20–46. What can you sayn8 w9*whg(xl y about the charge on each particle?

A positively charged particw v9hd.dbqn79 h)sv659jz ewx le in a nonuniform magnetic field follows the trajectowveq .9) 9jwvh n9ddhs7x 6b5zry 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 attra p4+-6i2wm(khqn4oq x q yeo.gct a magnet? Can a magnet attract an iron rod? What must you conside kynh4pw(io2+mqqq eg 4. -6xor to answer these questions?

Explain why a strong magnet held near a CRT television screen (Section 17–uh0iyn+ew- t3w (c7h5v,ne up10) causes the picture to become distorted. Also, explain why the picture sometimes goes completely black where the fi+73,e5u wnvpew-in( hc0yuth eld is the strongest. [But don’t risk damage to your TV by trying this.][/But don’t risk damage to your TV by trying this.]

Suppose you have three iron rods, two of which are magnetized but the thirgh)*)w yjaf ;jd is not. Ho;yah jg j)wf*)w would you determine which two are the magnets without using any additional objects?

Can you set a resting electron into motion with a magnetic field? With a+-be4a 5gacky n electric field? Expc- y54+ eabgaklain.

A charged particle is moving in a circle under thaz .ren9w9e+o 8jb *whe influence of a uniform magnetic field. If an electric field that points in the same direction as the magnetic rwej+ba *hn9 wz8.eo9 field is turned on, describe the path the charged particle will take.

The force on a particle in a magnetic field is the idea bxcttp,p4e o3oui.9k 2 ehind 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 to a blood vessel and to a magnetic field. Explain how ions are caused to move. Do posii3o,92eu4. ko xtpcp ttive and negative ions feel a force in the same direction?

A beam of electrons is directed toward a horizont nj1: jb6;2-mzt mccwval wire carrying a current from left to ricz2-:cbmnmvj wjt6; 1ght
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or makgqelw+f(, (l )1cc*g ,bao ahgnetic fields that surround a moving electric charge.w ,ch(lc ogb,q* )fk g1+leaa(

A charged particle moves in a straight line through a par t5;2 uhtrp/icticular region of space. Could there be a nonzero magnetic field in th/ 5iuprth ;2ctis region? If so, give two possible situations.

If a moving charged par.p 0c7i9vtoyu ticle is deflected sideways in some region of space, can we conclude, for certainyi 7.pu9 o0ctv, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of l 6no*vz+;2i -chl4e4 g xkhldspace 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 wya2s -bmo*)7 ivct4wdhether moving electrons in a certain region of space are being deflected by an electric field or by a magnetic field (or by bot7 dm2*yst-bw)ica 4 voh)?

How can you make a compass without using iron or other ferromagnetic )5z)*afa rblzr sz;2hmaterial?

Two long wires carrying equal currents I are at right85avc 5s npf; +ofu3rw angles to each other, but don’t quite tou3+;5vfpaosrf5 8uwncch. Describe the magnetic force one exerts on the other.

A horizontal current-carrying wire, free to move in Earth’ )g761h m48 zexdct smfow1xj1s gravitational field, is suspended directly above1 djo4x1ztxf6g8)he 7cmmsw1 a second, parallel, current-carrying wire.
(a) In what direction is the current in the lower wire?
(b) Can the upper wire be held in stable equilibrium due to the magnetic force of the lower wire? Explain.

Why will either pole of a magnet p 2oq-f, )z;d+euof *cluqo.yattract an unmagnetized piece of iron?

An unmagnetized nail will not attract an unmagnetized paper clip. Howeveaiz0 g2nc ,2pur, if one end of the nail is in contact with a magnet,n2pg2 zi 0ca,u the other end will attract a paper clip. Explain.

Two ions have the same ma 4 h25 oqvdvx fu;y;c0eeow2)xss, but one is singly ionized and the other is doubly ionized. How will their positions on the film0uwh5qde xfv 4 o2;veco;2) yx of a mass spectrometer (Fig. Below) differ?

What would be the effect on B inside a long i9f dn,vh ;h12um7qtc- 0cggdsolenoid 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 s ymishw)zv1kt1 ,sia*fj6:t 5olenoid 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 curren5t y k* mstj,61)siz1 vahw:fit flowing through the main switch. For example, the starter switch of a car is connected to a relay so that the large current needed for the starter doesn’t pass to the dashboard switch.

  (a) What is the magnitude of the force per meter of length on a straigh0dy 9-v-jbv m +c0l;ifmnzy*wt wire carryn0-bwyv;0*mflmz-y+d9 jci ving an 8.40-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 e*:avebv 4i 8 ;; d lfd3nyyq1eb2p,upa 160-m length of straight wire stretchedv ldpedfev b2:y;n;*a8 i,31pqebyu4 between two 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

  Calculate the magnitude of the magnetic force on a 160-m le;it :3b ab393zest*+jddfly j ngth of straight wire stretched between two towers carrying a 150-A curr;ljz:fa e+s3ddtyt3*b 9jb i 3ent. 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 the m g5qt .zj.q-wvx2r 4qqaximum force on it is .zt2. jvqx q4wqq-rg50.750 N when placed in a uniform 0.0800-T field?    A

  A 1.5-m length of wire carrying 4.5 A of current is oriented horiz9qt35p lnc:d2qibh b 5ontally. At that point on the Eart295l:bqhc3ibqtnd 5 ph’s surface, the dip angle of the Earth’s magnetic field makes an angle of 38 $^{\circ}\,$ to the wire. Estimate the magnitude of the magnetic force on the wire due to the Earth’s magnetic field of $ 5.5\times10^{ -5}\;T$ at this point.    $ \times10^{-4 }\;N$

  The force on a wire carrying 8.75 A is a maximum of 1.28 N when96iozzm snq3paz97b-/j + fz;gm 9hgn placed between the pole faces of a magnet. If the pol9 n 6imzfz;m- g 9zs3hb97nozpajgq +/e 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 measured to be only 35% o obg7se/ dvr-/f its maximum possible value. Sketch the relationship of the wire and the field if the force had been a maximum, and sketch the relationship as it actually is, calculating the angle be /dgs/bover 7-tween the wire and the magnetic field.    $^{\circ}\,$

  The force on a wire is a maximum zhy5c7 g(q 8mrof $ 6.50\times10^{-2 }\;N$ when placed between the pole faces of a magnet. The current flows horizontally to the right and the magnetic field is vertical. The wire is observed to “jump” toward the observer when the current is turned on.
(a) What type of magnetic pole is the top pole face?  ----待选择----North PoleSouth pole 
(b) If the pole faces have a diameter of 10.0 cm, estimate the current in the wire if the field is 0.16 T. $\approx$   A(retain one decimal places)
(c) If the wire is tipped so that it makes an angle of 10.0° with the horizontal, what force will it now feel?    N

  Suppose a straight 1.00-mm-diameter copper wire could just “floa/, uw12an6g kql r--wqfjey2it” horizontally in air because of 2nq-yu kaw/ qir2f,1e wglj6-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 charg8h s9ectqkm 3rhx,u ,:k7k2lke $q\,=\,+2e$ 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 on an electroiye05b.eopg( n 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 fog4iz o:, + lqrurgbimx9)46kbr each diagram shown in (Fig4rq6ir+:gk)z b ig,l u4mb ox9. Below), 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 directionhmx yi1tqy,tx9y n* c2io(-g (o p2a2q 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 with a speeddnf du 4z22qm: 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 fiex, kyc4k 4(ykcld, in a plane perpendicular to the field. What is the rak 4 cyx(4kyc,kdius of its path?    m

  An electron experiences the greatest fors)2l4da.tkk:htgvl;d my 5w s x13 z-igtb-k 8ce 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 elec 1,3dr8hgso n7ni0m, cth u)istrons that go undeflected when passing through perpendicular electric and magnetic fh)1tsouh07 n3,rgs8,dici nm ields of magnitude $8.8 \times10^{3 }\;V/m$ and $3.5 \times10^{-3 }\;T$, respectively? What is the radius of the electron orbit if the electric field is turned off? $F_E$    $ \times10^{6 }\;m/s$ $F_{max}$   $ \times10^{ -3}\;m$

  A doubly charged helium atom whose mass is,ycyue+ k u,7cg/, wre $6.6 \times10^{-27 }\;kg$ 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 .kkyh l-l8yu4q moving with constant speed v to make one circula8luh -l4kyyk.r revolution in a uniform magnetic field $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge x ;ies-+pou+bq moves in a circular path of radius r in a uniform magnetic field B. Show that its momentum is p+oubei +-x;ps = qBr .

A particle of mass m an(lr cbm hri68 s/. pi/r)o5ypmd charge q moves in a circular path in a magnetic field B. Show y)/r6s ri hl(5pr.m /omip8b cthat its 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 3o8,l xrk ah;4exe -q bs:sr3kin 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 perpendiculav;zn uvfx96 t+r to the Earth’s magnetic fitn6x z;fv9v+ueld of $5.00\times10^{-5}\mathrm{~T}$, If the bullet possesses a net charge of $13.5\times10^{-9}\mathrm{~C},$ by what distance will it be deflected from its path due to the Earth’s magnetic field after it has traveled 1.00 km?    $ \times10^{-7 }\;m$

  Suppose the Earth’s magnetic field at the equator has magnitude i 0+szlupp: f2$0.40\times10^{-4}\mathrm{~Т}$ 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 with1nal0 vojp c61 speed $\nu=2.0\times10^5\mathrm{~m/s}$ 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 65-A current. How stro x t)-7eeqp x017rehudng is the magnetic field 6.0 cm away from p xrhxdq0eu7t1-e 7e)it? Compare to the Earth’s magnetic field. $B_{cable}$   $ \times10^{-4 }\;T$ the field of the cable is about    times that of the Earth.

  If an electric wire is allowed to produce a magnetic field 5va/- ;qrk-zdd6 vli zno larger than that of the5v r k;lvzi/6dd zq-a- 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 sta2nm6lm:wqc (raight wire carries current I out of the page toward you. Indicate, with appropriate alw2c( mq nm6: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 uph3(sc+xclcoqeg x q.0 .c:s9sward 24-A current exerts an attractive forcxss hc9:g.0lcc3o +ex(q s.qc e 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 and direction of the force between 0ab0loi:o7i*f mk;-wz)nk ds two parallel wires 35 m long and 6.0 cm apart, each carrying 25 A in the same directiodisnkoif o * )-lz0;a7k:mw0bn.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic field okvnm s;5 c4ayuk 49a*is being carried out 1.00 m from an electric cable. What is the maximum allowable current in the cable if the e;c ymua*4k k nv94o5asxperiment is to be accurate to $\pm1.0\%?$    A

  A power line carries a current of 95 A along th1z7a 3qwi;6 wut9dngd e tops of 8.5-m-high poles. What is the magnitude of the magnetic field produced by this wire at the ground? How does this comz31d;ti69gw u d7aw qnpare with the Earth’s field of about $\frac{1}{2}G$?    $ \times10^{-6 }\;T$ The field of the cable is about    % that of the Earth.(retain two decimal places)

  Two long thin parallel wires 13.0 cm apart carry 25-A currents in b (4f;7idopbnthe same direction. Determine the magnetic field at point P, 12.0 cm from one wire and 5.0 cm from the other(Fig. Below).b(4nopid f;b7
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18 :2w5 wjz ir)tg,t8hq( mgu+bhcm due south from a straight vertical wire carrying a 35-A current downwardqw+ wit 2:h) ,ggtj(m58zbu rh. 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 wire carries 22.0 A of current duem6 fuo g,ub9wpz5b3cct2ek2 1 north. What is the net magnetic field 20.0 cm due west of the wire if the Eab9efo36,2 t wb k5 uc1mguc2zprth’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 space at a ra.d4myyz k3x 2/iquy+ fte 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 between7 (j vl-u+rk7x fpkrr5 two long straight wires 2.0 cm apart in terms of the current I in one when the other carries 15 Avrj 5k - +r(7xr7kuplf. 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 fwn3 u)p ljiunw 66mo y8jz,3*brom, an instrument. If the insulat)p,6wm unbylw o6uj38z3*ijned 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 Earth.
   $ \times10^{-6 }\;T$ The field of the wires is about    % that of the Earth.(retain two decimal places)

  A third wire is placed yrr0)2n27s /dq u0xjca a+doj in the plane of the two wires shown in (Fig. Below), parallel and just to the right. If it carries 25.0 A upward, what force per meter of length does it exert on each of the other two wires? Assume it is 2.8 mm from the nearest wire, center tj d sxoy70rdq2 0 )2+aaunrcj/o center.
$F_{near}$ =    $ \times10^{ -2}\;N/m$  ----待选择----attractrepel 
$F_{far}$ =    $ \times10^{ -2}\;N/m$  ----待选择----attractrepel 

  A compass needle poinyxk e5zwp;p0 m- + i; ce*y5pnqppem-8ts 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 straighbmhhqisaf 77/o 3+ x,wt wire, as shown in (Fig. Below). There is a current of 2.5 A in both wires. Determine the magxwasbq/h i, m3o7 h7+fnitude and direction of the net force on the loop.    $ \times10^{ -6}\;N$  ----待选择----away from wiretowards wire 

  A long horizontal wire carries r3 - r4tc-mhwkq;s:efbif4s, a current of 48 A. A second wire, made of 2.5-mm-diameter copper wire and parallel to the first, is kept in suspeqcmfwe s-tis ;fr4h -4 rb3k:,nsion 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 perpendicular7z c fq/ y+ga3o+td-am/cknm)v: ,.xtfpcb ;m to each other. At their closest, they are 20.0 cm apart (Fig. Below). What is the magnitude of the magnetic field at a point midway between them if the top one carries a current of 20.0 A and the bottom one caa3 +;vand xcm cty kmz +,:/g.topmqfcb)7f/-rries 5.0 A?    $ \times10^{-5 }\;T$

  Two long straight parallel wires are 15;k o, q+jm vp(ey9s0lm cm apart. Wire A carries 2.0 A current. Wire B’s curren,v+plomyqse(90 k j m;t is 4.0 A in the same direction.
(a) Determine the magnetic field magnitude due to wire A at the position of wire B. $\approx$    $ \times10^{-6 }\;T$(retain one decimal places)
(b) Determine the magnetic field due to wire B at the position of wire A. $\approx$    $ \times10^{-6 }\;T$(retain one decimal places)
(c) Are these two magnetic fields equal and opposite? Why or why not?
(d) Determine the force on wire A due to wire B, and the force on wire B due to wire A. Are these two forces equal and opposite? Why or why not? $\approx$    $ \times10^{-5 }\;N/m$(retain one decimal places)

  Three long parallel wires are 3:1p )tw r(ezrk.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,:)r1 (wk erztp 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 magnitud txporq(/5u3m e and direction of the magnetic field at the midpoint of 5u(qrpx3m to/the side of 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, ca627j5efnb2/vbqxqyb-lzc j7 rry equal currents I in the same direction. One wire is at x = 0, the other is/zq2qxy7bce jb2l nb 75 j-v6f 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 420ky*jv-/k3 8op sfw z,t turns of wire and carries a current of 2.0 A. Calculatek8o/v3s-z fyw p,j* tk the field inside near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameter isvbr(if 8ci2 ,1ue.xey to produce a field of 0.385 T at its center. How much current should the sxfibu,ceyi2 (8 1v.erolenoid carry if it has 975 turns of the wire?    A

  A 550-turn solenoid is 15 cm long. The current ic7t78z r; u0epwrpup zd7r v2,n it is 33 A. A 3.0-cm-long straight wire cuts through the center of the solenoid, along a diameter. This wire carries a 22-A current downward (and is connected by other wires that don’t concern us). What is the force on this wire assuming the solenoid’s field points dup8r7770;ruet,v2 w pupzcr dz e east?    N

You have 1.0 kg of copper and 2c6gwzptmkl v.5 bqlg-yx y+v7 m,1:rwant to make a practical solenoid that produces the greatest possible magnetic field for a given voltage. Should you make your copper wire long and thin, short and fat, -:qwy12zlv76.r 5t ,l mym bvckggp+xor 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 Ampèrehmfbq b3 ;*6vs ;5ch35yu shfi’s law along the circul3sb;3hffvu5c hs y*5mq;ih b6 ar 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 between8o 2o3e8wzmk8g y9/ av tnr6gx the conductors of a coaxial cable ag8 6z8/wx 8 2o v3tr9eynkgmo(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 sdkg s/q+j9mq0 nhu1- side is placed with its face parallel to the m10g/-9ssjk hnuqmq+d agnetic 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 def3,t cig-.hqn llects 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 thez )x *+m*zp(hv z -o/vpcf,xze years, what current will give full-scale deflez f),(pz v-o/*z*xx+vpemz hcction if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by what factor does the oe p6. vebshk,e:hyh,w5poo 8smm4nl, wie 6.1utput torque chan6wvp s,e .m4n5h ele,.s,wh8y hb:mp o ko61iege?

Show that the magnetic dipole moment M of an electm-;mi kkcsm hk6 uqir2s:* r6*ron orbiting the proton nucleus of a hydrogen atom is related to the orbital angularr kkmmk*i rms6 h ;2:u*-s6qci momentum L of the electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in dw inxa*u+ib6*.t 0g/ q2f ;d g5ryg:uettzbe5iameter and containing nine loops lies flat on the grounagw: .2g5/uett5 i qn *;tux*zfi6+eg dyr b0bd. The Earth’s magnetic field at 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 radiueg0 bd/4aig /ngbzo* ;s 5.10 cm in a 0.566-T magnetic field. What value of elec io e/ngb d;0/bgzag4*tric field could make their paths straight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atoms have radii of curvature equal to 21dy;jy3x 8:mb x.0, 21.6, 21.9, 22.2, and 22.8 cm. The largest radius corresponds to an atomic mass of 76 u. What are the atomic masses of th8dxyx3j :myb;e other isotopes?

  Suppose the electric field between the electri(jwk o * jz1d)i(v61gee5kr (rmudru 4c plates in the mass spectrometer of (Fig. B4v(e eo w (g kz1(5rimru*dujd 1krj)6elow) 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 moypo l-:xm uwx3v0:6t15b cbp initor air pollutants. It is difficult, however, to separate molecules with nearly e 1p-bx:6l w:0vcixtp 3um5oybqual mass such as CO (28.0106 u) and $N_2(28.0134u)$. How large a radius of curvature must a spectrometer have if these two molecules are to be separated on the film by 0.50 mm?

One form of mass spectrometer accelerates ions by a voltage V before thz;s89/ 2en )q rfwmqxoey enter a magnetic field B. The ions are assumed to start from rest. Shem9q)2fs8;w/qrnoxz ow 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 w.wz4y)up9 )ap.mv eb has 430 loops of wire per meter, and a 25-A current flows through the wire. If the permeability of the irone.zwyavb ) 4p)p wm9.u 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 diam-g 3j qot(z9fzeter, and has 640 turns of woq3ft( j-zz9 gire. The magnetic 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 momentum ri q4ahq vrgw83/1s274l wuk8)vunbu $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 energ;0 iycb el5c,sy upon entering a region of constant magnetic field. Wh05; y l,icsbceat is the ratio of the radii of their circular paths?   

  The power cable for an electric trolley (Fig. Belksfs4k(f 7lu ) c:blexza0 v/;ow) carries a horizontal current of 330 A toward the east. The Earth’s magnetic4kcuz(0b7val f /s;sf e)lx:k 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 ai;n lc+oqgd)jjb-qz;,8 vlk 2yrplane 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 points almost horizont9u0tvrx cj6: 5d ,bqxxu1 lqz6ally to the north6lx 9: dctx5v quz1x,6u0b jqr and has magnitude $B=0.50\times10^{-4}\mathrm{~T.}$ What should be the magnitude and direction for the velocity of an electron if its weight is to be exactly balanced by the magnetic force?    $ \times10^{-6 }\;m/s$  ----待选择----eastwest 

  A doubly charged helium atom, whos1x/jn,dm v x61h 0fvzwyt33z a**xhlwe mass is $6.6\times10^{-27}\mathrm{~kg},$ is accelerated by a voltage of 2400 V.
(a) What will be its radius of curvature in a uniform 0.240-T field? $\approx$    m (retain three decimal places)
(b) What is its period of revolution?    $ \times10^{-7 }\;s$

  A sort of “projectile launcya8h vgc61bnt /o 8a+pher” 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 touchbcht na8g6o v/y1ap8+ing the rails. A magnetic field is perpendicular to the plane of the circuit. If the bar has a length L = 22cm, a mass of 1.5 g, and is placed in a field of 1.7 T, what constant current flow is needed to accelerate the bar from rest to 28m/s in a distance of 1.0 m? In what direction must the magnetic field point?
   A
the magnetic field must be ----待选择----updown 

  In (Fig. Below) the top wire is 1.00-mm-diameter copper wiv91je(*i 76vg1f 8pwsn yypj1ipjkg;re and is suspended in air due to the two magnetic forces from the bottom two wires. The currev1pv; 6p1n*ig1 wy7jpji9 ygfes8( jknt 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 app 52kr( ps.y1qows( pdg-u 2zlart in a horizontal plane act as rails to support a light metal rod of mass m (p gwr(5 (y22p.1ks s-lzup podqerpendicular to each rail), (Fig. Below). A magnetic field $\vec{B}$, directed vertically upward (outward in the diagram), acts throughout. At t = 0, wires connected to the rails are connected to a constant current source and a current I begins to flow through the system. Determine the speed of the rod, which starts from rest at t = 0, as a function of time
(a) assuming no friction between the rod and the rails,
(b) if the coefficient of friction is $\mu_k$.
(c) Does the rod move east or west if the current through it heads north?

  Estimate the approximate maximum deflection of the electron b47xu,sh.q ipdeam near the center of a TV screen due tq4pu s,xhd.7io 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 parr d gq6-ji e*yeo6 txr)9w-ky8ticles 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 me -k6qi 9wdtrr y6ex g-ey*oj)8tal “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 o) zowf5 /7k-jrux5rumf a square of side l, carry equak/ 7)xrmj-fwuzor55 u l 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 s20t1u2 olcrj) 7bbyuw i nh0t3,6 tkmrteering”; that is, the magnetic fields can be used to change the beam’s direction without altering its speed (Fig. Below). Show runu0tb, kl oy71t 0m )2 62rhbitjc3whow this works with a beam of protons. What happens to protons that are not moving with the speed that the magnetic field is designed for? If the field extends over a region 5.0 cm wide and has a magnitude of 0.33 T, by approximately what angle will a beam of protons traveling at $ 1.0\times10^{7 }\,m/s;$ be bent?    $^{\circ}\,$

  The magnetic field B at the center of a circular coil of wire hxc duc 1;ev+;carrying a current I (as hc1 cv ud+;;exin Fig. 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 magne;*)obj/z om+.udsl *fn zms p)tic 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 lciqy588symmr* 1gs 6 magnetic fields produced by overhead power lines. You estimate that the two wires are each about 30 m above the ground and are about 3 m apart. The local power company tells you that the lines operate at 10 kV and provide a maximum of 40 MW to the local area. Estimate the maximum magnetic field you might experience walking under these power lines, and compare to the Earth’s field. [For an ac current, values are rms, and the magnc8 lg i5yms8 rs*1qy6metic field will be changing.] $B_{net}$ $\approx$    $ \times10^{ -5}\;T$(Round to the nearest integer)

  (a) What value of magnetic fielseztd6-d+j d l5*oqi ,d would make a beam of electrons, traveling to the,+o-dd5id6 jz esqt *l right 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 magnr2 t4ba5xvpryxr1a * c..:rfjetic 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 change in the kinetic energy of the proton as it travels from P to Q. r*rx1 .jb2a5c.fv p4tra:xry    $ \times10^{-20 }\;J$

  A 32-cm-long solenoid, 1.8 cm in diameter, is,iuwoasw3+ zhtzd8kbd /6.;o a+h3 io to produce a 0.30-T magnetic field at its center. If the maximum cur o 8 to +kszid/b;hd6+w33wi zoha.ua,rent 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, caa bhp,a8lofj9p7-t lm5xx31vx1w o/ arry the same current but in opposite directions. They are suspended by 0.50-m-long strings as shown in (Fig. Below). If the suf3v8 / 15oomt1xwb,j lpx al xpha-79aspension 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 field B = 0.23 T at 202.7x1(hs h /irt hqgqueqvzg6u7yn 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$