A compass needle is not always balance s (2aogg2snzreps0 n ,n7e)v.d parallel to the Earth’s surface, but one end may dip down2nors2 s e07sezp.gg(na v,)n ward. Explain.

Draw the magnetic field lines around a straigh:p g2f.1k iuvojz /pks7 m/eg8t section of wire carrying a current horizontally to thesp2p8kjz7/um/ke o1f : g.ivg left.

In what direction are the magne8 /1pa,va blsmtic field lines surrounding a straight wire carrying a currenbv1,paa/8lm s t that is moving directly away from you?

A horseshoe magnet is held k85tdonp)j +p 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 directippdo8n 5+j)k ton is the force on the wire?

Will a magnet attract any metakha */bam :4lak;ju66 8/1vnx rn mqjqllic object, or only those made of iron? (Try it and see.) Why is this a/aj16/uv 8qax m6*nr4:qlhjnbkkm; so?

Two iron bars attract each other no matt1r m0vtw64b,tn2 tecy er which ends are placed close together. Are both magnets? Explaie62tc vt,w4b ymnrt1 0n.

The magnetic field due to current in wires in your home camt+x2jsk z7 ji, 6kq1p 5liz/xf/li 8bn affect a compass. Discuss the effect in terms of currents, including if they5/ ji1 2x+xk6i z mz/pflslt,kb7j8 iq are ac or dc.

If a negatively charged particle udu :apsj+ 7d4yptv4*enters a region of uniform magnetic field which is perpendicular to the particle’s velocity, will the kinetic energy of the particle increase, decrease, or stay the same? Explain 74pjdy u sdvtapu:*4 +your answer. (Neglect gravity and assume there is no electric field.)

In(Fig. Below), charged particles move in the vicinity of ; fe:s aha zbo9cfr7)1a current-carrying wire. For each charged particle, the arrow indicates the direcco:;7s)ea9rb1fz a hftion of motion of the particle, and the + or - indicates the sign of the charge. For each of the particles, indicate the direction of the magnetic force due to the magnetic field produced by the wire.

Three particles, a, b, and c, enter a magnetic q 5yp;mdzx s*9e4 : uvhfrh9xy06 1bnwfield as shown in Fig. 20–46. What can you say about the charge on eac brnx;wvsz*6 p 09hmuy:qx4 51f heyd9h particle?

A positively charged particle in a nonu oxj+:2wjd wy-+rvshnni7 r z /z*+9ufniform magnetic field follows the trajectory shoxshwin -wnry+7 v*+92/rzj:ou+ jf zdwn 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 rodrgie mtm*m+z+/ vc1a-? What must you consid e/gm1tz+r- a v+icmm*er to answer these questions?

Explain why a strong magnet held near a CRs 9l+nyx) ojn/0w6aytT television screen (Section 17–10) causes the picture to become distorted. Also, explain why the picture sometimes goes 0y /lnxw6 +oy9stnj a)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 are4m*eykh5 hx2+ qcrp+l magnetized but the third is not. How would you determine which two are the magnets without uh5 2h+cr4m q*xp+ elkysing any additional objects?

Can you set a resting electron into motion with a magneticy-n-8v;cw mgskj 8nwf (ioe5p n8:(cf field? With an electric field? Explg 8:f; f n-swi5pj8y(k -ocn (cnew8vmain.

A charged particle is moving in a circle under the influen v-mkegqo;e+vj ahb,m1 u6/o* ce 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 omajve*6 m,;+h kg ob1vu /e-qthe charged particle will take.

The force on a particle in a magnetic field is the idea bwqw .c(w-mdc wz/iy-0p nw b4)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. Belo( q/-ywi.0bpmzc4ww w )cnwd-w). An electric field is applied perpendicular to a blood vessel and to a magnetic field. Explain how ions are caused to move. Do positive and negative ions feel a force in the same direction?

A beam of electrons is directed toward a horizonta2rq6do (1 dtanl wire carrying a current from left to1rtad6d2o(nq right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields that sb ylcq/3gra l357kejrd 4q(h/urround a moving electric charge. heql3 ay(k jq354/cdrl7rg b/

A charged particle moves in a straight line throughquuydh 25*nt(fb :4kg3u t4ee a particular region of space. Could there be a nonzero magnetic field in this reukyb: qfe 34gutn(u2t4e*5dh gion? If so, give two possible situations.

If a moving charged particle is deflected sideways in some region of space, cazn cdan/ea7 k*ku2pwrc7n44 7,, jcvjn we conclude, for certain, thatu,w7,a7kjj/ep4nkd2nn c ac 7rz*4cv $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space ther/ci5g0gl9-b j6mfs mse 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 lyf9z9ccc t :aa 4gf3- :br8vuc7p:ola certain region of space are being deflected by an electric field or by a magnetic field (oc3l:rfpaf z y4c7abg 9:v -ccuo: 89tlr by both)?

How can you make a compass without using iron or other ferromagnetic ma7fqlldbv 2/h6terial?

Two long wires carrying fa2)o(r mp4vfequal currents I are at right angles to each other, but don’t quite touch. Describe the magnetic force one exerts onrmfoa 2 vf)4(p the other.

A horizontal current-cahl-o o03vewm72jo5y reg zi4sx43k i)rrying wire, free to move in Earth’s gravitational field, is su oy4w02 ee3 oi3lgmo5j ivx4shk7 -zr)spended directly 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 attract a37,x6 -aq2dm ju ar71vrn plb7y zgv0gn unmagnetized piece of iron?

An unmagnetized nail will not ati 1(zijsm -sqbu759c atract an unmagnetized paper clip. However, if one end of the nail is in contact with a magne z 5im c91sjq-bsa7iu(t, the other end will attract a paper clip. Explain.

Two ions have the same mass, but one is singly ionize/zy 9y(/lsnh3 rgxr*bd and the other is doubly ionized. How will their positions onxn9b/ yz/3lsg*(yrr h the film of a mass spectrometer (Fig. Below) differ?

What would be the effect on B inside a lon8mu n0,fann-nastc 3715 jej xu1bfq/g 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 rel qy(c5g ec2vr -:gnbse-d2 93a+ e)w9xbzqgdt ay is an electromagnet (the iron rod inside the coil does not mo92dy z cxwe 325(9 sgv- gqg:ab- dteq)reb+ncve) 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 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 wirm9q m,bjebito r(8:f 3e carrying an 8.40-A current when perpendiculatme9 :om bf3q r,(jb8ir 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 5 :xtpj3 oy9mdg wm6m6the magnetic force on a 160-m length of straight wire stretched between two towers carrying a 150-A current. The Earth’s magnetic field ofpm6yoj3:9x g6 mtwd5 m $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  Calculate the magnitude of the magn 6*hj,hwvuhjg6l 6f+ketic force on a 160-m length of straight wire stretched between two towers carrying a 150-A current. The Earth’lhjuh gv+,6jf6*h6k ws 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 m0l1q 0lu( hmplb;es ,c long if the maximum force on it is 0.750 N when pm q0b (ls;p,cl1e luh0laced in a uniform 0.0800-T field?    A

  A 1.5-m length of wi/x)p7lpx(y5xu o/nrpv zt;8a re carrying 4.5 A of current is oriented horizontally. At that point on the Earth’s surface, the dip angle of the Earth’s x(z5x/8ppuoa; /) lxnpt7 vry 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 maxirp+(n r za8; -ezb-mnfl*p7geat)qt: mum of 1.28 N when placed between the pa -gn( rz:fmqzetlp rn8;t+ e7*a bp)-ole faces of a magnet. If the pole faces are 55.5 cm in diameter, what is the approximate strength of the magnetic field?    T

  The magnetic force per l (/byrp (xze+bk;1*5cbub 1lcrj:qn meter 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 1z x:/ncubk;l lc+p re(y b*b1bq5jr(angle between the wire and the magnetic field.    $^{\circ}\,$

  The force on a wire is a max 6hiz( ;v gm*t/cfla7qu6el 6c t(dsd9imum 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 j3b yw2i7oyn(rr6 bm 3qust “float” horizontally inrrb23 6m7oq(nw 3 ybyi air 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 cwz(n71irp aiv5y l/y 7m9j2ntgk8 n:n harge $q\,=\,+2e$ 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 direm- i96b.hu ,a(ubb scxction of the force on an electron traveling $ 8.75\times10^{5 }\;m/s$ horizontally to the east in a vertically upward magnetic field of strength 0.75 T.    $ \times10^{-13 }\;N$  ----待选择----NorthSouth 

Find the direction of the force on a negative charge for each di/5fgc:c neq 2p3t6wpi agram shown in (Fwp g:qi53 /c6ptc2 nefig. 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 directioni(q0lj 9iuoe+dh 5h, w 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 spjfslhn3589jrm4 .zkbl, e f2sz,zf*veed of $1.7 \times10^{6 }\;m/s$ into a uniform magnetic field of 0.350 T that is directed horizontally away from the observer. Describe the electron’s path in this field.    $ \times10^{-5 }\;m$

  A 5.0-MeV (kinetic energy) proton enters a 0.20-T field, in a plane peyiaf 6c ) auc+)la-o6 njyyl6;rpendicular to the field. What is the radius o+acal n f)6j-ycliuy)oy ;6a6f its path?    m

  An electron experiences thmiy.ui. k4(xy4xipf4 +ls-bv9+t mid lr-x 0oe 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 udj9k;j+mnmt6 ndeflected when passing through perpendicular e6j+td;9 mmn kjlectric and magnetic fields of magnitude $8.8 \times10^{3 }\;V/m$ and $3.5 \times10^{-3 }\;T$, respectively? What is the radius of the electron orbit if the electric field is turned off? $F_E$    $ \times10^{6 }\;m/s$ $F_{max}$   $ \times10^{ -3}\;m$

  A doubly charged helium atom whose ma 6dybsvbo z40yz61ij 3ss 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 partiz;7h5+uq gehm cle of charge q moving with constant speed v to make one circ7hh5eqzu ; +mgular revolution in 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+g bl sq9rd:s;netic field B. Show that its momenss:9+bdg;lr qtum is p = qBr .

A particle of mass m and charge q moves in a circular)h o5 )7hgx.p5kyq p 19stttfr path in a magnetic field B. Show that ix7ro ptts . yk)hh595)pfq1tg ts kinetic energy is proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momentuwr z.7m*8hra eb5p j71t ugnn7m 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 perpz;wkldlaz* m80 ak5c2endicular to the Earth’s magnetic fi;0ac2a8z* kmlklzwd5 eld 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 fi 6y6(auw3 if 1dcbwmz2eld at the equator has magnitude $0.40\times10^{-4}\mathrm{~Т}$ and a northerly direction at all points. Estimate the speed a singly ionized uranium ion $(m=238\mathrm{u},q=e)$ would need to circle the Earth 5.0 km above the equator. Can you ignore gravity? $F_B$    $ \times10^{ 8}\;m/s$ $\frac{F_B}{F_g}$    $ \times10^{8 }\;$

  A proton moving with spee 19hp5v/urm ned $\nu=2.0\times10^5\mathrm{~m/s}$ 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 tiy+r0 vuckfu4-(+ hvko start a stalled vehicle carries a 65-A current. How strong is the magnetic field 6.0 cm away from it? Compare to thehucfkr y v 4v-ui++k0( 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 algh h+ar q6li2:lowed to produce a magnetic field no larger than that of the Earth gahhl+6qi r:2 $(0.55\times10^{-4}\mathrm{~Т})$ 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 ou kttim*tn9a v /knv1;+p0/a jxpwpt+ :t of the page toward you. Indicate, with appropriate arrows, p1 jt;v+: xwttpm+9nan0//vp a ki*tkthe direction of $\vec{\mathbf{B}}$ at each of the points C, D, and E in the plane of the page.

  A vertical straight wire car/ dxphb+y)r,gcnkd 61 rying an upward 24-A current exerts an attractive force per unit lengthyg1b ),rdxhn c k+/d6p of $8.8\times10^{-4}\mathrm{~N/m}$ on a second parallel wire 7.0 cm away. What current (magnitude and direction) flows in the second wire?    A  ----待选择----upwarddownward 

  Determine the magnitude and direction of the force between two parallel wires 3r4c),ee eqmi 85 m long and 6.0 cm apart, each car)m4e, 8ieq crerying 25 A in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic field is being carried two7: d)k09 :wu stunsout 1.00 m from an electric cable. What is the maximum allowable current in the cable if the9tts o7nwu0u)d :ws:k experiment is to be accurate to $\pm1.0\%?$    A

  A power line carries a current of 95 A along the tops of 8.5-m-hig0up8pll eux .okf:r8 ,h poles. What is the magnitude of the magnetic field produced by k f8: ,p xop0ul.lr8uethis 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-w-w bubp/qi7my; 1b y8A currents in the same direction. Determine the magnetic fieldq8b1yub - ;bwmiy/ 7wp 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 duxx/qjvcxd6bo 8/5(b w e south from a straight vertical wire carrying a wx5c jq(dxb /8vx 6/ob35-A current downward. In what direction does the compass needle point at this location? Assume the horizontal component of the Earth’s field at this point is $0.45\times10^{-4}\mathrm{~T}$ and the magnetic declination is 0$^{\circ}\,$.    $^{\circ}\,$ N of W

  A long horizontal wire carries 22.0 A of current due ntx*rbf fa-g) 0orth. What is the net magnetic field 20.0 cm due west of the wire if b0)rg- ffxta *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 spa6l, v +nyt3hv35tgo9oxuq1 h bce 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 magneti9mkxjn ;2:q5ofiv zke1*fj c5c field midway between two long straight wires 2.0 cm apart in terms of the current I in 55i:f;j 1c xkov92 emf jk*znqone when the other carries 15 A. Assume these currents are
(a) in the same direction,
(b) in opposite directions.

  A long pair of wires conducts 25.0 A of dc current to, and from, an oi+l-u veowv4r 1fc ey5 31+r,oeqc.yinstrument. If the insulated wires are of negligible diameter but are 2.8 mm apart, what is the magnetic field 10rveol 41o5 ur1,iw3 qocc-e.+e vy+yf .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 ja d2 h*s+6ez 3zeyyz-in the plane of the two wires shown in (Fig. Below), parallel and just to the right. If it carri-+zhzz yy dj6*seae2 3es 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 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:nb4wylx 20h;w2r fm.eonyj 7 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 sb rl 7vrk/c7w4r7 x(bdtraight wire, as shown in (Fig. Below). There is a current of 2.5 A in both wires. Determine(clrd7brv7x kbw4r/7 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, made (rj dkr o9.z1nof 2.5-mm-diameter copper wire and parallel to the first, is kept in suspension mag (.nzdk9r roj1netically 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 oriente q8(mz jcjpxq;0r1eh3d so that they are perpendicular 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 carrizh( 8xjjcmr;qq1 p03e es 5.0 A?    $ \times10^{-5 }\;T$

  Two long straight parallewltm ja (l4gs+f46l8 dl wires are 15 cm apart. Wire A carries 2.0 A current. Wire B’s current is 4.0 A in thll8 wf64sl+md( 4ja gte 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 anot : 7:7ppadvgz3c9y drbher. (Looking along them, they are at three corners of an equilateral triangle.) The current in each wire is 8.00 A, but its direction in wire M is opposite to that in wired r3pgpyvazd: 9bc: 77s 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 arakt d-02c)azx-hh -c k amp..nd direction of the magnetic field at the midpoint of the side of .)d2pc mhrh.x-- ka0aaz-c tkthe 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 curr tscyrhm1pb x/v.v+mkaug30 8w;: j y:ents I in the same direction. One wire is at x = 0, the other is at x = d, (Fig. Bejs+w tm/bu 1m: : ax;kv0r.cgy3hpy 8vlow). 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 wir ck7fmlfu-j4 ul -3f7me and carries a current of 2.0 A. Calculate the field u-ulm47 f7 kfc3mfj-l inside near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diame d 3qj5 lgn9:l:3rsazxter is to produce a field of 0.385 T at its center. How much current should the solenoid carry if it hdqxl3 :z95a 3:nrljgsas 975 turns of the wire?    A

  A 550-turn solenoid is 15 cm long. The current in it is 33 A. A 3.0-czi o5w,2 ug.qam-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 donq,izag. owu52’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 prb n 8k*ul. j;r hv41wk/+yuoqyoduces 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, lengthh *.kjy ;rkl + /q4ub8unvw1oy, and so on.

A toroid is a solenoioe9qi2g b)pt9d in the shape of a circle (Fig. Below). Use Ampère’s law along the circular path, shown dashed in (Fig. Below a), to determine that thetp 9 o2q)ebig9 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 betqgngg8 yeq3,a. a7q/r8m 7 gjaween the conductors of a rqjq 8n7a.gqygg/,38ga ma7 e coaxial 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 isn e:64p os;zka-(l gda placed with its face parallel to the magnea -4lsnoz; :kg e(apd6tic 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 needlesm/:w :tis6/du x o+jgnq3k;s deflects 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 weakensitnk ; 7q(c6gqvt) vq0 by 25% over the years, what current will givcqvq0) tg(7tqi; nkv6e full-scale deflection if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motorcq qpvn:g (:uik6+q5q drops by 12%, by what factor does the output torque chanq(nvq5iuq6 kc:g: +qpge?

Show that the magneti7dsi.+ wvw iy ,awh*(pri4 lzy6+8e5fnlgru1 c dipole moment M of an electron orbiting the proton nucleus of a hydrogen atom is related to the orbital piw+rslif*uw,z54de iy 8h6( y1 +.arw lv7gn angular momentum L of the electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter and containing nin40ron/.x8j y3 wzlbaub 0uhm(e loops lies flat on the ground. The Earth’s magnetic field ( 84bjn y 0 b/0auu.roxzm3lhwat 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 cml,3ep;emdnimo h+*pqg c24i i;k5kn. in a 0.566-T magnetic field. What value of electric field could make their paths straight? In what dirii ;g pn,k2.qik+*p dhn e;oe mclm453ection must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atoms haz v6/mw:dbkk0r0 u kfv,x )1vpve 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 other isotopes?zwkk/:k)m6 ,vvfr xv0 0 1upbd

  Suppose the electric field between the electric plates in the jw;6vo/u - xf8xb kb4pmass spectrometer of (Fixpwo;b bxkuv4f/ 68- jg. 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 cwfc5 ) 0bfgk7m3oa2 tis being used to monitor air pollutants. It is difficult, however, to separate bcw3fo fm52ck0a )7 gtmolecules with nearly equal mass such as CO (28.0106 u) and $N_2(28.0134u)$. How large a radius of curvature must a spectrometer have if these two molecules are to be separated on the film by 0.50 mm?

One form of mass spectrometer accgtswh7idey+v73 c*l .elerates ions by a voltage V before they enter a magnetic field B. The ions are assumgwil.7ev*h+37 tcd syed 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 l gm faxz ,v70msy+p0dh.w-x0 a 25-A current flows through the wire. If the permeabim+z.0w, xpmh ly -gxdf0a07svlity of the iron is $3000\mu_0$ what is the total field B inside the solenoid?    T

  An iron-core solenoid is 38 cm long and 1.8 cm in diameqoo2y22 b itef)u,l5z 5z t6yrter, and has 640 turns of wire. The magnetic field inside the solenoid is 2.2 T when 48 A flows in the wireb 2yt6 le2urf),5iy qo o25tzz. What is the permeability $\mu$ at this high field strength?    $\times10^{-5}\mathrm{T}\bullet\mathrm{m/A}$

  Protons with momentum nv1kwn39j u 7dnws/e; $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ are magnetically steered clockwise in a circular path 2.0 km in diameter at Fermi National Accelerator Laboratory in Illinois. Determine the magnitude and direction of the field in the magnets surrounding the beam pipe.    T

  A proton and an electron have the same kinetic energy upon entering ) l bwkuern//p41cpp/a region of constant magnetic field. What is the ratio r1bpe n/pk)w/lup/4cof the radii of their circular paths?   

  The power cable for an electric trolley (Fig. Below)*2vrg6mc 9p, bc7ptzj sy)9yf carries a horizontal current of 330 A toward the east. The zrjy6yg 72*9cbp 9vm) tfcps,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 n 3 jer7((52zpcqsz+4bvng cbon an airplane which has acquired a net charge of $1550\mu C$ and moves with a speed of 120 m/s perpendicular to the Earth’s magnetic field of $5.0\times10^{-5}\mathrm{~T}$.    $ \times10^{-6 }\;N$

  Near the equator, the Earth’s magneticqfsgg*q ,nh:j:t7s*g field points almost horizontally to the north and ha:f*sjsg,* 7qt: qh gngs 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,,wpo jh -t2:m dtq)f :3a*eeei 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 shown in (Fig. Below). A lanjd83os e)8 4 eg7eyoarge current moves in a closed loo4 e8yoaejd83)one 7s gp composed of fixed rails, a power supply, and a very light, almost frictionless bar touching the rails. A magnetic field is perpendicular to the plane of the circuit. If the bar has a length L = 22cm, a mass of 1.5 g, and is placed in a field of 1.7 T, what constant current flow is needed to 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 wiret+*nmmbi;g vowy +qnsu3 qi,z ; t7*c) and is suspended in air due to the two magnetic forces from the bottom two wires. The current flow through the two bottom wires is 95 A in each. Calculate the required current flow *; * itncq y n+,3w;tg+i vzm)7sbqmuoin the suspended wire.    A

Two stiff parallel wbmha;u-7v5e slby ooty8ry8i 7s5 ;,fires a distance l apart in a horizontal plane act as rails to support a light metal rod of mass m (perpendicular to each rail), (Figoh- 85;;sb,7 l7oy8muytiyfvsa eb 5r. 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 db ioe;wn49 n(nf9v f(gb 98bcfeflection of the electron beam near the center of a TV screen d((bw9ec b9f9;f 4 bn8nfoigv nue 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 x5 r)tcfx )qu3ii ryu 3ly9h4.accelerate elementary particles such as protons to )x5 4.x9yui3iq)f tcrl3h ruyhigh speeds. Particles starting at point A with some initial velocity travel in circular orbits in the magnetic field B. The particles are accelerated to higher speeds each time they pass through the gap between the metal “dees,” where there is an electric field E. (There is no electric field inside the hollow metal dees.) The electric field changes direction 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 wnj* /o nlax1n4hzz7a :ires, located at the corners of a square of side l, carry equal curre nao7:1jz a4zn x*lh/nnts $I_0$ 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 usefulhf. fj k,qz-5 +*vlor9lpca e, in particle accelerators for “beam steering”; that is, the magnetic fields can be used to chaolc k. ,zfp*+qher va,9f5 l-jnge 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 cenab x6h yeb21-zter of a circular coil of wire carrying a current I (as in Fig. Below) is61 ehza2-byb x
$B=\frac{\mu_{0} N I}{2 r},$
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 fd)73( 4(yequsjofyetic 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 magnetic fields pft,cnk- tbvu7( 8z 3asvmw+9hroduced 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 magnetic field will(vvm,tc 8wzbtu7 f+-k3 sn ha9 be changing.] $B_{net}$ $\approx$    $ \times10^{ -5}\;T$(Round to the nearest integer)

  (a) What value of magnetic field woulanch sz+(n ykr269tzqu e31)59 zjt xyrts.g+d make a beam of electrons, traveling to thehzg1+ +z jx)5(utt zsqk r2cs y.ea6tn399 ryn 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 ab- ys;u7r8t, pk sjx0gas in a magnetic field of 0.010 T, perpendicular to the plane of the spiral, as shown in (Fig. Below). In two successive loops, at points P and Q, the radii are xsya0 b 8rup-sk, 7jt;10.0 mm and 8.5 mm, respectively. Calculate the change in the kinetic energy of the proton as it travels from P to Q.    $ \times10^{-20 }\;J$

  A 32-cm-long solenoid, 1.8 cm in diameter, is to produce a 0.30-T magnetic fi u-d:ugimar75h ;u4+ sqmu kn74 *ybreeld at its ce54meuruar:g*myu7 7s - bn hd;+quk 4inter. If the maximum current is 5.7 A, how many turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight alut5xx5b65 qljqh /nx cpt60a f.minum wires, each of diameter 0.50 mm, carry the same current but in opposite directions. They are suspended by 0x tbn.f5l/cpt 5q6a60hx 5jqx .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 unifod 1q-o*f.q2r4nvg qut rm 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$