A compass needle is not always balanced parallel to the Earth’s surfacex,r dzv-fg ,)i) h;wgw, but one en,d, ; -xggzhr)if)wvwd may dip downward. Explain.

Draw the magnetic field lines around a straight secigw,al ty qlz5*) 25xttion of wire carrying a current horizontally ta w,i5)*z5l xl2qyg tto the left.

In what direction are the magnetic field lines surrounding a straight wire carr6 rl n5,gtlqy :4lqnv:ying a current that is moving directly away from youlnq gn4 y6r:5tl,lv :q?

A horseshoe magnet is ib7djod3noij n2)ci(tx,2kteq2o*8 imrz)/ held vertically with the north pole on the left and south pole on the right. A wire passing between the poles, equidistant from them, carries a current directly away from you. In what direction is thj)o)o2(8e,tbdnz 2t2ixkm3i qj ic d*ori / 7ne force on the wire?

Will a magnet attract any metallic object, or only those made of q5puwq/ 4/lu) hmvxhke k:*br61d )ixiron? (Try it and see.) Whulie m6x/uv1b*h )dph:5 k/q r4w xq)ky is this so?

Two iron bars attract eac dgof shwn:)d 5v5bzox e2y106h other no matter which ends are placed close together. Are bot)5hx 1 0obgd:5ef vsn6zowyd2h magnets? Explain.

The magnetic field dudd/vlk(+zaj oco+ 9 9be to current in wires in your home can affect a compass. Discuss the effect k9bv d9z+ aj o+ld/co(in terms of currents, including if they are ac or dc.

If a negatively charged particle enters a region of uniform magn(dlyomco j bx 817n.q5mj4a.h etic field which is perpendicular to the particle’s velocity, will the kinetic energy of the particle increase, decrease, or.on1. m x58(l hqc7bydjamoj4 stay the same? Explain your answer. (Neglect gravity and assume there is no electric field.)

In(Fig. Below), charged particles h2qz bc9.f/wb 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 pz/ 9fqh bb.wc2articles, indicate the direction of the magnetic force due to the magnetic field produced by the wire.

Three particles, a, 4 q8j vicsp0bx+h)wv1oi3qo1+d l j;h b, and c, enter a magnetic field as shown in Fig. 20–46. What can you say about the charge on each par;1 q++ibo 013hl)pj 4h wxsvcoi8vjqdticle?

A positively chargedz 4)/ qwz/opis particle in a nonuniform magnetic field follows the trajectoryqwz pi/soz /4) 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 a magnet? Can a magnet attract an iron *(5d3 +sknfqe,lroyq rod? What must you consider to answer ,* dy s(f no3qkq5erl+these questions?

Explain why a strong magnet held near a CRT television f,fg r* zyz wg;s4/5x:5dpv)v vuvur-screen (Section 17–10) causes the picture to become d ur zs v,gd5*4zrpg5 /-xvvff:;v)wuyistorted. Also, explain why the picture sometimes goes completely black where the field is the strongest. [But don’t risk damage to your TV by trying this.][/But don’t risk damage to your TV by trying this.]

Suppose you have three iron rods, two of which are magnvv -duozggtb2cn(4(4etized but the third is not. How would you determine which two are the mz-ng v(g d(otv24u4cb agnets without using any additional objects?

Can you set a resting electroi+bxx(s-m l zv35 bza5n into motion with a magnetic field? With an electric fielbvzx+5lb 5s a3-i xmz(d? Explain.

A charged particle is moving intb 1al 46+xzlv 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 char+x az b4v16ltlged particle will take.

The force on a particle in a magn; c mxt7cn. ;cpg4,4dg *fahsqrsdn6+ etic field is the idea behind electromagnetic pumping. It is used to pump metallic fluids (such as sodium) and to pump blood in artificial heart machines. The basic design is shown in(Fig. Below). An electric dp gx4 hr*d.s;4mcng7q fcsn ;6a+,c tfield is applied perpendicular to a blood vessel and to a magnetic field. Explain how ions are caused to move. Do positive and negative ions feel a force in the same direction?

A beam of electrons is directed toward a horizontal wire carrying a ;27,2 trqgliuxv iij7current from left to rit;2xglivji7i2u, 7rqght
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields that surround a movi5ynrq4)ajyk9/0w m jcng electric charge.4 9a5qnw jj0kr c/y)ym

A charged particle movecul;.0u di0bjh g/8r:ff0i6dt nt b2l s in a straight line through a particular region of space. Could there be a nonzero magnetic field in this region? If so,8u;i 0btdf 2 0ijbfh /.nrt:du6 g0lcl give two possible situations.

If a moving charged particle is deflected sideways in some region oft *eclt b:oj -rnwrxb +:tl4ibz9s 9rg ;x.3t0 space, can we conclude, for certain, thacrtr; x b4tt:b o9 xr9:0zj+ng3ise-l. twb*lt $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space ft(f y;-+)xa,ccdok )mw vlz.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 in a certy(zy6hc lu k 5i4ngb66ain region of space are being deflected by an electric field or by a magnetic iu5 yg 6cny4b 6klzh6(field (or by both)?

How can you make a co4-o l ou i++nsi2mc4n:b/ rqxh 6)niobmpass without using iron or other ferromagnetic material?

Two long wires carrying equal currents I are at right angles to ro ;6)m;4q purct*gseuhh:8rjp ph)(each other, but dou) (p cgh;8o;ue hmr:t)rpr 4hs* p6jqn’t quite touch. Describe the magnetic force one exerts on the other.

A horizontal current-carrying wire, free to move in Earth’.bx ljy /o5gvp9p ei,0s gravitational field, is suspended div/ily bp,o e jg.0x9p5rectly above a second, parallel, current-carrying wire.
(a) In what direction is the current in the lower wire?
(b) Can the upper wire be held in stable equilibrium due to the magnetic force of the lower wire? Explain.

Why will either pole of a magnet attrac3z 2vgiyx d 8k;a1urr;t an unmagnetized piece of iron?

An unmagnetized nail will not attract auh a; q0u11ve5v+ rusbn unmagnetized paper clip. However, if one end of the nail is in contact with a magnet, the other end will 5q+ vs0uh;1urv1 bue aattract a paper clip. Explain.

Two ions have the same mass, but one iggh5pt8 ,6*qsx1x: e0 emisa cs singly ionized and the other is doubly ionized. How will their positions on the film of a mass spectrometer (Fig. Belowh1cpm qxg:gx6 se,5ei0*s t8a) differ?

What would be the effect on B 8 lcliqm1iln(p3zq(ir x., e9inside 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 is a 1c/az4+ yh *spwns.rjn 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 larg1 y ns+*srpa/c.j4hz we 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 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 straight *4db z p.de8icwire carrying an db d*c8 .ei4zp8.40-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 strac1 f)g.fww o +ldf .n,gd21opfight wire stretched between two towers carrying a 150-A current. The Earth’s magnetic.f gowd+nd.f,)f og lf c2p1w1 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 )j nmsiif hx0a .uu553tw ul2-160-m length of straight wire stretched between two towers carrying a 150-A currensh)fw3jinilm50a u2. -ut5 xu t. 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 flowing1bt; shf ac 6hs-3,wgf in a wire 4.80 m long if the maximum force on it is 0.c3ta6 1s ;,fgsbwf-hh750 N when placed in a uniform 0.0800-T field?    A

  A 1.5-m length of wir18 ka:3thd knne carrying 4.5 A of current is oriented horizontally. At that point on the Earthn1 8d3kankt:h’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 A88z3n2 ev at;tfyaj-l4:k5t qj-e v6 xxh yp7s 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 approxiax:5jne8xy azt4 l;vk jp8tte-f 6 72yv hqs3-mate strength of the magnetic field?    T

  The magnetic force per mw0cspe3 ts*e 9gq1 ,jgeter on a wire is measured to 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 actually is, calculating the angle between the wire an 1 cgp3*sgq,0e sj9twed the magnetic field.    $^{\circ}\,$

  The force on a wire is a maxi)m 9ul)luhc-72 r)x8uuel98n rbzqs qmum of $ 6.50\times10^{-2 }\;N$ when placed between the pole faces of a magnet. The current flows horizontally to the right and the magnetic field is vertical. The wire is observed to “jump” toward the observer when the current is turned on.
(a) What type of magnetic pole is the top pole face?  ----待选择----North PoleSouth pole 
(b) If the pole faces have a diameter of 10.0 cm, estimate the current in the wire if the field is 0.16 T. $\approx$   A(retain one decimal places)
(c) If the wire is tipped so that it makes an angle of 10.0° with the horizontal, what force will it now feel?    N

  Suppose a straight 1.00-mm-diameter copper wire could just “f,/ zy kkt0kt c) uurp0*(obln tv2e:4uloat” horizontally in air because of the for:,k u4p) 0/e rlou cbykn (zutvk0t2t*ce 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 charn9p*u+( flg:yvbaa* uge $q\,=\,+2e$ 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 direce 71 (vn n:/0:+n 4gomx)dbwuwlirec ztion of the force on an electron traveling $ 8.75\times10^{5 }\;m/s$ horizontally to the east in a vertically upward magnetic field of strength 0.75 T.    $ \times10^{-13 }\;N$  ----待选择----NorthSouth 

Find the direction of the force on a negative charg1:8mee/91tdmu n7/;.gfym b o fccxjee for each diagram shown in (Fig. Below), wherem1n d:t7bxe 1 mucf;j/e9yc gfmo/.8e $\vec{v}$ (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 directiojuh-:c:tvwfp a0u9eya; cg)g 4 4m2bfn 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 speedxk;lzevmx26 i,/iw 2c of $1.7 \times10^{6 }\;m/s$ into a uniform magnetic field of 0.350 T that is directed horizontally away from the observer. Describe the electron’s path in this field.    $ \times10^{-5 }\;m$

  A 5.0-MeV (kinetic energy) proton enters a 0.20-T field, in a planjrwq7v972 yl ue perpendicular to tyq9u jwrv2 l77he field. What is the radius of its path?    m

  An electron experiencmj d .olq,,.hf jqi:3a1 yut9fes the greatest force as it travels $2.9 \times10^{6 }\;m/s$ in a magnetic field when it is moving northward. The force is upward and of magnitude $7.2 \times10^{-13 }\;N$. What are the magnitude and direction of the magnetic field?    T ----待选择----EastWest 

  What is the velocity of a beam of electrons that go undeflected tdd +4g:dzqpukk5hs+,f3l 9pwhen passing through perpendicular electric and magneticdp:z4u 3ql+hg sp +,t9ddkkf 5 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 hel-tvg):0nss w/ 4 m+d am:vgg/ knaxks4ium 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 q moving with cyemh-r g) wm5/onstant speed v to make one circular revolution in 5hr e gmm/w)-ya 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 oft c6ucap92jo* radius r in a uniform magnetic field B. Sh oa pt*c2cj9u6ow that its momentum is p = qBr .

A particle of mass m and charge q moves in a circular path in a a;lub9cjk0.d magnetic field B. Show that itc.al u; b9dk0js kinetic energy is proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momentum of the particle in Problem 21 is c du)8n;o7yg+hld/ kt $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves with a speed ohu/-ehk lhlv44l ,u38cii , ouf 160 m/s perpendicular to the Earth’s magnetic field o,/,4uu li -8 lvc ouihhh4k3lef $5.00\times10^{-5}\mathrm{~T}$, 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 magnitad/mk:-dz * otude $0.40\times10^{-4}\mathrm{~Т}$ 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 yp-nu f:,ugy tk -hc+,/uwfsy*.gqg9 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 to start a stalled vehicle carries a 65-A current. How30mxxp*ni7cz2g-1 ikz( o o mt strong is the magnetic field 6.0 cm away from it? Compare to the Earth’s m0n(oxxmtzg7k c z-ip3*1 io2 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 n0ak2bg7: xn8s hho*o ho larger than that of the Ehh0:7 8bas2gno h*x koarth $(0.55\times10^{-4}\mathrm{~Т})$ at a distance of 25 cm, what is the maximum current the wire can carry?    A

In (Fig. Below), a long straight wire carries current I out of the page trh40zlx;bgy ,g*joqu ny 4- (boward you. Indicate, with approprlb;x(gu-y *,4gr y qzbon jh40iate 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 ansf 0xd:gq/,05 6:v bfqaslzn i upward 24-A current exerts an attractive force per unit lenv0nq06,xqg 5:asfs z/b ldf:igth 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 8if01hjx l ,brb ctg4cuxy40*two parallel wires 35 m long and 6.0 cm apart, each carrying 2t0grfj1 4h b ,b4lc8xu0*ciyx5 A in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic field is being carried out 1.00 m from an .t x( rl (jup;bi7t9tkelectri 9tktij7u lt.(xb(p;rc 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 current of glkr jwe .00fisz,:j+az- )ow ma2rbi;5w.cg 95 A along the tops of 8.5-m-high poles. What is the magnitude of the magnetic field 00 a:kab .g -egrrio )52wzcm fijw;z.sj+wl,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 ac 9w *qyv f6mw3z /lj;1z:(*pmy kjozfpart carry 25-A currents in the same direction. Determine the magnetic field at point P, 12.0 cm from one wire and 5.0 cm from the other(Fjocm 91v;k* (/wz6fw zypm:3fzly*jq ig. Below).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placedush**9uyhsg 1 18 cm due south from a straight vertical wire carrying a 35-A current downward. In what directiouughhs y **9s1n 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 01 n.e q fr/sr*iqbp0bz2y6l lA of current due north. What is the net magnetic field 20.0 cm.yn6q* z2fiq1s elbr0/0brpl due west of the 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 iam*lgqd1/ ib 6u (kyp5n 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 bepn q32 ii+yeo o/ w4ll b/;r/q;3vdzmutween two long straight wires 2.0 cm apart in tiw/o z 334dnrvpqo ; u l//+ily;m2ebqerms of the 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 conduct0b bs00ui/b jvs 25.0 A of dc current to, and from, an instrument. If the insulated wires are of negligible diameter but areu0svbjbb 0i /0 2.8 mm apart, what is the magnetic field 10.00 cm from their midpoint, in their plane (Fig. Below)? Compare to the magnetic field of the Earth.
   $ \times10^{-6 }\;T$ The field of the wires is about    % that of the Earth.(retain two decimal places)

  A third wire is placed in the plane of the two wires shown in (Fig. Below), iz;5wp jae 2nj5 x3qb9parallel and just to the right. If it carries 25.0 A upwar;eia wb9x5p5zj 3 j2nqd, what force per meter of length does it exert on each of the other two wires? Assume it is 2.8 mm from the nearest wire, center to center.
$F_{near}$ =    $ \times10^{ -2}\;N/m$  ----待选择----attractrepel 
$F_{far}$ =    $ \times10^{ -2}\;N/m$  ----待选择----attractrepel 

  A compass needle poikec+cjcu( l 9h4x,n 8dnts 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 s sin3t j)iv /v9ctb:jp.b(9jsame plane as a straight wire, as shown in (Fig. Below). bj : )3snvs b(/v.jipci9tjt9There is a current of 2.5 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 a current of 48 A. A second wire, ma.3 p e:ylyoq /p,bxj-qde of 2.5-mm-diameter copper wire and parallel to the first, is kept in suspension magnetically 15 cm below (Fip ,xby:y p/jl-qeo3q. g. 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 otheil,oe/,o x;m)hmvz /wa uu:-nr. At their closest, they are 20.0 cm apart (Fig. Below). What is u,evzxm hi)nlo/uw,/;-a m:othe magnitude of the magnetic field at a point midway between them if the top one carries a current of 20.0 A and the bottom one carries 5.0 A?    $ \times10^{-5 }\;T$

  Two long straight parallel wires are 15 8wc d*f96elmncm apart. Wire A carries 2.0 A current. Wire B’s current is 4.0 A in 9lc* dmwn6e8fthe same direction.
(a) Determine the magnetic field magnitude due to wire A at the position of wire B. $\approx$    $ \times10^{-6 }\;T$(retain one decimal places)
(b) Determine the magnetic field due to wire B at the position of wire A. $\approx$    $ \times10^{-6 }\;T$(retain one decimal places)
(c) Are these two magnetic fields equal and opposite? Why or why not?
(d) Determine the force on wire A due to wire B, and the force on wire B due to wire A. Are these two forces equal and opposite? Why or why not? $\approx$    $ \times10^{-5 }\;N/m$(retain one decimal places)

  Three long parallel wires are 3.8 cm from one another. (Looking along tz;;a* i-gu hethem, they are at three corners of an equilateral triang-* eu;;ihzgatle.) The current in each wire is 8.00 A, but its direction in wire M is opposite to that in wires N and P (Fig. Below). Determine the magnetic force per unit length on each wire due to the other two.
$\frac{F_\text{M net y}}{l_\mathrm{M}}$ =    $ \times10^{ -4}\;N/m$ =    $^{\circ}\,$
$F_{N\,net}$ =    $ \times10^{-4 }\;N/m$ $\theta$ =    $^{\circ}\,$
$F_{P\,net}$ =    $ \times10^{ -4}\;N/m$ $\theta$ =    $^{\circ}\,$

  In (Fig. Below), determine the magnitude andxn/ 2*h kdr:fv direction of the magnetic field at the midpoint of the side of t2 xf* d/:vrnkhhe triangle between wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a distance d apart,6s*/e2 p ,*lrtdlke0dkj v nleq *;,vn carry equal currents I in the same direction. One wire is at x = 0, the other is at x = d, /v*l; ,n*6 d*e 2ekjpv lesl,d rtk0qn(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 tot;9 hj klo ijrx(e:2l,xal of 420 turns of wire and carries a current of 2.0 A. Calculate the f(:xrl9,x ;i2j hjkloeield inside near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in 5l 02 jgxkwvyt) 3eer6rwka93 diameter is to produce a field of 0.385 T at its center. How much current should the solenoid carry if it has 97 vkyr)e9j l t3xe0k6awrgw2535 turns of the wire?    A

  A 550-turn solenoid is 15 cm long. The current in it is 33 A. A 3.0-cm-lo (ma)u-rlwbi2 ng straight wire cuts through the center of the solenoid, along a diab(awm 2il ur)-meter. 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 due east?    N

You have 1.0 kg of copper and want to make a practicac;)exg zlf96c prn- y8l solenoid that produces the greatest possible 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 gyp8ccz fe;96-xn)rl, and so on.

A toroid is a solenoid in the shape of a circle (Fig. Below). Use Ampère’s ljh .c6w dec*v)aw along the circular path, shown dashed in (Fig. Below a), to determine thatc.6* w) jvhdce 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: dievh* (soh, between the conductors of a coaxial cable (Fig. Below) hov: s*ihe,(d 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 par2 disssi 5b b*1mk*cc8any1xg7lv 8;mallel to 1 cmy*i5gvxs8limsbda;b cn* k7182 sthe magnetic 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 deflectsb7xa5wy /w 6hg/cjw4l6cj hh* 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% ovey5j/6c0ben sn4s;ftg6jx1onr the years, what current will give full-scale deflecti1j0 j4fs /tngc;nne xy 65s6boon if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drop e*rsf ;fesi *u)o7miz rv+-/j6owny4s by 12%, by what factor does the output torque changer *i yisz fjn4 f-ouo7e s/w)6e+*m;rv?

Show that the magnetic dipoluwf33x 3cfk5d,t qfq*e moment M of an electron orbiting the proton nucleus of a hydrogen atom is related to the orbital angqtk,3wxd*f33 ucff5 q ular momentum L of the electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter and con5 :e3j giyc332f pl,5vbrp uhc3 6zoeutaining nine loops lies flat on the ground. The Earth’s magnetic field at th 2 63i :b5j3gcehcel 5 zv3purou3,fpyis 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 0.566-Tq3yq-z , lw*ne magnetic field. What value of electric field could make their paths strylze* q,qnw3 -aight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectromet s f)w72v6 lsnpinw74thdfc07er, 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 atomic mass of 76 u. What are the atomic masses of the other0 tdi7w7nflcn fhs) wsp6v742 isotopes?

  Suppose the electric field between the electric plates in the mass n-n w8a e; qnt upig::zmav1,5spectrometer of (tnaez1-5 nv;:, in mqgau:w 8pFig. 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 difficult, 4muae.uf,t,m f2j4sk however, to separate molecules with nearly equal mass such as CO (28.010,uf4t kmm jus24e. a,f6 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 voo8972-yg9qtwfa i ezkltage V before they enter a magnetic field B. The ions are assumed to start from rest. Show that the mass ok teqy g-279zaf8w i9of 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 cfszybfy61k*/5qu j2 i7cc+ rmeter, and a 25-A current flows through the wire. If the p 5*yq6 72rfc1j yf/zscbi+ckuermeability of the iron is $3000\mu_0$ what is the total field B inside the solenoid?    T

  An iron-core solenoid is 38 i+wo; sm;/ zde-xkaz,5 k/fmkcm long and 1.8 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 wimae;wxzk/sm + / f5-kok ,z;dire. What is the permeability $\mu$ at this high field strength?    $\times10^{-5}\mathrm{T}\bullet\mathrm{m/A}$

  Protons with momentubly ,j;vjw9d7m $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ are magnetically steered clockwise in a circular path 2.0 km in diameter at Fermi National Accelerator Laboratory in Illinois. Determine the magnitude and direction of the field in the magnets surrounding the beam pipe.    T

  A proton and an electron have the same kinetic energy upon enterinbjwve 3, p6gl*g a region of constant magnetic field. What is the ratio of the radii of w3vbelp*,g6 jtheir circular paths?   

  The power cable for an electric trolley (Fig. Belok ryn9a h 8.) ob1v1iafb0w;zfw) carries a horizontal current of 330 A toward the east. Th8.;hvzbo ff1ab ky1ni a90 )wre 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 acquirb k ke9wjytutvh*lz 83j/k(.:ed 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 horizontalb nssmavwd8; s3b:u(93i,e oply to the north and has mag vis ;s(8nwod9,sbb3 am :3epunitude $B=0.50\times10^{-4}\mathrm{~T.}$ 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+tnqu 9ggu(j - atom, whose mass is $6.6\times10^{-27}\mathrm{~kg},$ is accelerated by a voltage of 2400 V.
(a) What will be its radius of curvature in a uniform 0.240-T field? $\approx$    m (retain three decimal places)
(b) What is its period of revolution?    $ \times10^{-7 }\;s$

  A sort of “projectile launcher” is show4w8+ahf ymay* n in (Fig. Below). A large current moves in a closed loop composed of fixed rails, a power supply, and a very light, almost frictionless bar touching the rails. A magnea4w ym+f8h *aytic 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-diameteri(qag;6pk*6pfe.k e 4(ar lkp copper wire and is suspended in air due to the two magnetic forces from the bottom two wires. The current flow through the two bottom ;pfege lkpa66i(4k* (kpa.rq wires is 95 A in each. Calculate the required current flow in the suspended wire.    A

Two stiff parallel wires es,tqinulqxa /j :-pa9s81;-tctrf j;w* hz*a distance l apart in a horizontal plane act as rails to support a light metal rod of mass m (perpendicular to each rail), ( sai/qap: ttq9th1ulj z-;8;n-r*,fexj s *c wFig. 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+ vdrk:+n avq) the electron beam near the center of a TV )r:vak+n+ vdqscreen 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 elementmecye c+ 0tsx gv*dafut65/+f/l y 1 kx2x,j*oary 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 partcdkvy6t20/*yclxf xg,t*+sum e/ex f1+ aoj5icles are accelerated to higher speeds each time they pass through the gap between the metal “dees,” where there is an electric field E. (There is no electric field inside the hollow metal dees.) The electric field changes direction 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, l jmu.yd 6xu,dri1; ph+ocated at the corners of a square of side l, carry equal cur ;ri+m6uyhddxup.j1, rents $I_0$ 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 l*7aq uip3 )tfkd- 5v;as jc)iuseful in particle accelerators for “beam steering”; that is, the magnetic fields can be used 5k-d 3*)a ;luvspcj)qi itfa7to 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 will a beam of protons traveling at $ 1.0\times10^{7 }\,m/s;$ be bent?    $^{\circ}\,$

  The magnetic field B at the.k f/ k7b4dz2, -yetctm5s- nd-rfbok center of a circular coil of wire carrying a current I (as ir4 t/fns ydkke, d- co7fz2-tb-k5b m.n 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 magnetic field is about 1;0n:qtkui 7dv G($ 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 magnitu7+ fxufh++9ayt1zek y de of magnetic fields produced by overhead power lines. You estimate that the two wires are each about 30 m above the ground and are about 3 m apart. The local power company tells you that the lines operate at 10 kV and provide a maximum of 40 MW to the local area. Estimate the maximum magnetic field you might experience w +1hyy+fz7ux+fta ek9alking 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:qs: ixnht dzv-c -3,sz5u08h:u srqe beam of electrons, traveling to the right at a speed ofhc3-uzrued qv0- s: x:szt:nh 8q5,si $4.8 \times10^{ 6}\;m/s$ 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 fiewq9 tdvsg494 bnak9k.ld 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 r4k4v9tnqsg d b 99aw.kadii 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 pro,,./z-jkh.*n9ay az xkjp2pj 5gf ledduce a 0.30-T magnetic field at its center. If.9xjhk5e, ,gkjypzd-2n/aa.z fl*p j the maximum current is 5.7 A, how many turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, each of diameter 0.50 xy.m;.uqhoe 4i z v:k-mm, carry the same current but in opposite directioi k ;.myov.:zex-qh u4ns. They are suspended by 0.50-m-long strings as shown in (Fig. Below). If the suspension strings make an angle of 3.0$^{\circ}\,$ with the vertical, what is the current in the wires?    A

  An electron enters a uniform magnetic field B = 0.;r 5l s otnm u;v)sxq61wiv(f923 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$