A compass needle is not always balanced -:twtz;t9ilc,k+ m 9r tvbo9gb+9 hmrparallel to the Earth’s surface, but one end may dip downward. Ex,c o+zvrh bmg:999ri-w+tbmlkt t9t ;plain.

Draw the magnetic field lib hh7 +.gax1nqnes around a straight section of wire carrying a current horizontally to the lef q.xg17+hhanbt.

In what direction are the magnetic field lines surrounding a stra l4 t)h;dc,os ,fewt 6bks1jy;ight wire carrying a curro6jw ;f,lyctebdk sh1s;,t)4 ent that is moving directly away from you?

A horseshoe magnet is)8wr ;4 *hwi5xwzdvxogx c; +o 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 the force on dw;wi 85oo c+vr4)wh z*xx;xgthe wire?

Will a magnet attract +2zmkj .n0ezl any metallic object, or only those made of iron? (Try it and s0lj2+ en.zmk zee.) Why is this so?

Two iron bars attract each other no matter which ends awomaa8- s i-z,,*4fktaqi*86 krbh rhre placed close together. Are bothwi-4ao8hrs 8b*m*fai, q-6azt h,kkr magnets? Explain.

The magnetic field due to current in wires in your home can z-/*hd f-;0euy fwh-eh1 nldra*mnd) affect a compass. Discuss the effect in terms of currents, i e1dm /hzh- w*uyd*e-rl -nhdf)fa0n;ncluding if they are ac or dc.

If a negatively charged pargbdc7r924zm oticle enters a region of uniform magnetic field which is perpendicul27z rb c9d4gomar to the particle’s velocity, will the kinetic energy of the particle increase, decrease, or stay the same? Explain your answer. (Neglect gravity and assume there is no electric field.)

In(Fig. Below), charged particles move in the vicinity of a current-cy jvw667js4mqarrying wire. For each charged particle, the arrow indicates 66m4swyq jjv7the direction of motion of the particle, and the + or - indicates the sign of the charge. For each of the particles, indicate the direction of the magnetic force due to the magnetic field produced by the wire.

Three particles, a, b, and c(g6v r74n )8bq(g rhmfxznnr/, enter a magnetic field as shown in Fig. 20–46. What can you say about the charge on each particle? g4v rr 8bz/7(6n)nn rmfxg (qh

A positively charged particle in a nonuniform magnetic fi gzq gnlc*b:ecu 76:bph f-5n-eld follows the trajectory shown zblg bh-f*7u qnp:gce:-65 n cin
(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 magnuy)kuh( vx7 a8et? Can a magnet attract an iron rod? What must you consider to answer these 8)( uuky ahv7xquestions?

Explain why a strong magnet held nea wzt78)62:1ciow jzcj7cp+ f1uq rjfwr a CRT television screen (Section 17–10) causes the picture to become distorted. Also, explain why the picture sometimes goes completely black)wzuow:j6jq7tczpjc+ 1 1cw2r 78ff i 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,oh.+uk/an -rw- lhguq98 ohg1 two of which are magnetized but the third is not. How would you determine which two are the magnets without using any additional obj -no/hg1hragk h wlq8+u-. uo9ects?

Can you set a resting e.co4t0y vcp- biuz-2www8i t6 lectron into motion with a magnetic field? With an electrizbt4 6ww-y.tp uci-2cvow08 ic field? Explain.

A charged particle is moving in a circle under the ):ie +/bikt2zyq3p/u: q:y x emo2boeinfluence of a uniform magnetic field. If an electric field that points in the same direction as the magnetic field is turned on, describe thkxo:b:uiq)/ p2:i 2et qmbeey3oz/y+ e path the charged particle will take.

The force on a particle in da iksor991) aa magnetic 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 field is applied perpendicular to a blood vessel and to a magnetic fielda)a o9 r9i1dsk. 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 horb;xd4jrs1 2 ndce ,dnmdzg9 :tu62ff ;izontal wire carrying a current from left9sdxgc;d, udd1jzn4n2 r:; mbeft62f to right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields that surround a moving electric+7cq.gljj8n g charge.l g7+jg8ncjq.

A charged particle moves in a straight line through a particular region oyk+aky t,k+18 l u0w 7hwvz,e7h w8nbjf space. Ch88w ve77,+ u+bhkk yny1 wk0 lzawt,jould there be a nonzero magnetic field in this region? If so, give two possible situations.

If a moving charged particlx,;es h)rav :ae is deflected sideways in some region of space, can we coehsxav) : ,ar;nclude, for certain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region o*6tu 1(nojpkik5*dh sf space there is a uniform magnetic field $\vec{B}$. Outside this region, B = 0 Can you inject an electron from outside into the field perpendicularly so that it will move in a closed circular path in the field? What if the electron is injected near the center?

How could you tell whether moving electrons in a certain regi t2i) z4oq/kipon of space are being deflected by an elet)izp2 qo i/4kctric field or by a magnetic field (or by both)?

How can you make a compass without using iron or other ferromagz7 vqxo7t+l t;netic material?

Two long wires carrying equal currents I are at ri)i 3a3nj3y vpd0 von qd6;ejh:ght angles to each other, but don’t quite touch. Describe the magnetic forcep) 3j3v;hyv ennqaj3d:60i o d one exerts on the other.

A horizontal current-carrying wire, free to move in Earth’s graviceb/ waz+5j, oll1)ndtational field, is suspended directly above a second, llz/5 jed)a1 wc,o b+nparallel, 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 ofe ) bx yr(7 v/lpvdj8v9xk-,bu a magnet attract an unmagnetized piece of iron?

An unmagnetized nail will b9tb h35u -t4 9nl0jhqs j8tqonot attract an unmagnetized paper clip. However, if one end of the nail is in contact with a magnet, the other end will attract hjj543qt0ntbu 9 9lbq- t8 shoa paper clip. Explain.

Two ions have the same mass, but one is singly ionized and the other is doubly t0 gz/as2*wfmionized. How/f 2*gtsm z0aw will their positions on the film of a mass spectrometer (Fig. Below) differ?

What would be the effect s(*lw.ur j 49e4q .i:o5usbud0lsil od/fgr8 on B inside a long solenoid if
(a) the diameter of all the loops was doubled,
(b) the spacing between loops was doubled,
(c) the solenoid’s length was doubled along with a doubling in the total number of loops?

A type of magnetic switch similar to a solenoid is a relay . A relay is an elw,wf f kjdjz5 1-cyiv).c;0 jnectromagnet (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 1 f.kw cfw),v;jnc50 i-jdyzja 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 f))q 7y2 obvgostraight wire carry bv7g)oqoyf )2ing 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 a 160-m length of straight wirej -l mb(8t*tz g:ca.zc stretched betweec-tzzb*:a8 gm ct(.lj n 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 length of straights1u 5oy/laj +,rqfvnd1t ,cy 2 wire stretched between two towers carrying a 150-A current. The Earth’s magnetic field j ,vn51y/tsyqoulc2af1d +r,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 lo zw0duz+tw69 xng if the maximum force on it is 0.750 N when placed i 6u+d9xtww 0zzn a uniform 0.0800-T field?    A

  A 1.5-m length of wire carrying 4.5 A of current is oriented horizontally lh.urwg,9xmb vt*05p. At that point on th9pumrvb.5 wt* h0lx, ge Earth’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 when placed betwel 4*wuw6 /ezhnen the l 6ew 4uzh/*wnpole 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 meter on agx:5 n8o elh294hdk;h3 lzn.5n rotoj 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 be32j o.lxrhhnl:o58t;o nkn 495he dzgtween the wire and the magnetic field.    $^{\circ}\,$

  The force on a wire 6yr iwd kh02/ois a maximum 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 1.8ojt 4qakwph ghnbt 9ff 48gcm4*7y0 400-mm-diameter copper wire could just “float” horizontally in air because of the force due to the Earth’s magnetic field 8tha0w4 j9o*fgynf7 ck4g4 bp8t qmh4$\vec{B}$, 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 charm cu -nu*rnx+r0v2)fx 106xzxdb8l h gge $q\,=\,+2e$ 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 dir2u7f-s;j u9unsfsf 4 k (j6lzdection 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 diagram saxwz6j5oua)z:m oia5 ggy56uu2y2 ) whown in (Fig. Below), whera56mj5wyo)w6)a2x y:2o g 5uagu izuze $\vec{v}$ (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 directio j 5s8 p 3+1jzi r,dur514n2dchwnysszn 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 vertic2ahrnow.dnsvb/ gzs6g g:7 68aj --pnally upward with a speed of $1.7 \times10^{6 }\;m/s$ into a uniform magnetic field of 0.350 T that is directed horizontally away from the observer. Describe the electron’s path in this field.    $ \times10^{-5 }\;m$

  A 5.0-MeV (kinetic energy) proton enters a 0.20-T field, in a planesi gkg ;r6x(kwm9 9dy+ perpendicular to the rg(9sy;69k +gxmwikdfield. What is the radius of its path?    m

  An electron experiences the greatest force as*gjbjq* ,mxs3z 8/ ckb it travels $2.9 \times10^{6 }\;m/s$ in a magnetic field when it is moving northward. The force is upward and of magnitude $7.2 \times10^{-13 }\;N$. What are the magnitude and direction of the magnetic field?    T ----待选择----EastWest 

  What is the velocity of a beam of electrons that go undeflected when passing cq(+d- . gmk pj(/qphv*m,tpkthrough perpendicular electric and magnetic fik,mgdjq tvc+hp (pp/( k.m-q*elds 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 5 tt0sifgjt u*.u; 7lqis $6.6 \times10^{-27 }\;kg$ 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 chamc q3 n;k czynb1zdh64i-f( 5zrge q moving with constant speed v to make one circular revolution in a uniform magnetic field zq;nc mic ky d5-( zf4nb3hz16$\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge q moves in a circular path of radiuhqh *3l. izakt,. xb/fs r in a uniform magnetic field B. Show that its m hf qblxhi*,.3a.t/k zomentum is p = qBr .

A particle of mass m and charge q moves in a circular path in a magneticuolu8x: xf:4e 1z0/ )wz r9 cjcsi-jpc field B. Show that its kin fzl :xui-xwe09juj)c1/zrc 48 pos:cetic 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 Probll26u 3n1,k ruxy1 uypyem 21 is $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves with a speed of 160 m/s perpendicular to the Earth’s magneo z7f0qbchh jo9 0ht u(u*n.-itic field of cnqz. 9o*7-0b hiujhu0( oh ft$5.00\times10^{-5}\mathrm{~T}$, 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 magni jk2a*: 6y,jee4vhv latude $0.40\times10^{-4}\mathrm{~Т}$ 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 spevm tjloi 6*;m)ci/mb e (sp8d*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 arzkbsd/ bo6: * stalled vehicle carries a 65-A current. How strong is the magnetic field 6.0 cm away from it? C/o szbrb:k *d6ompare 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 sinpj u-l 5g0riq-2)gallowed to produce a magnetic field no larger than that of the E -5gjniq0u- 2l)grs piarth $(0.55\times10^{-4}\mathrm{~Т})$ at a distance of 25 cm, what is the maximum current the wire can carry?    A

In (Fig. Below), a long strai z:xc,)dzu nd-ght wire carries current I out of the page toward you. Indicate, with appropu -, cdxzdz:)nriate 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 upward 24-A current exerts 2w/m, r cuiq5nan attractive fori n 5qmc,/2ruwce 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 two plpb8l pl mph: kmo80 jo5697itarallel wires 35 m long and 6.0 cm apart, each carrying 25 Aoj6l :0 pl ol 8b795mhtk8mipp in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’g.0 rxbelriulj8l*08 73vjyy s magnetic field is being carried out 1.00 m from an electric cable. What is the maximum allowable current in the libj8 *780yrulegylx3r0vj .cable if the experiment is to be accurate to $\pm1.0\%?$    A

  A power line carries a current of 95 A along the tops of jb7s q8/h5z:uezoy 9m95dkpq8.5-m-high poles. What is the magnitude of the magnetic field qszmh5b p 7qz9ju589d/:yeokproduced 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 apajp:pn +t+7 etzrt carry 25-A currents in the same direction. Deter z:pn7jte+p+ tmine the magnetic field at point P, 12.0 cm from one wire and 5.0 cm from the other(Fig. Below).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18 cm due south from a straight vertical wire ca/8rgsoc;y: frj :t)qtrrying a 35-A current downward. In what direction does the compass needle point atj:qyrt;co ft :)rg 8/s 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 north. Whatmh+fib4rpzdbx f3(3ix g o69wq/rvc8((y l 2 y is the net magnetic field 20.0 cm dueidh3lvyz+8(mr42 rf/o3xpi wcb f(y9x b 6q(g 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 in space at a ratelvexu + l.n sohd;7.-m of $1.5\times10^9\mathrm{~protons/s~}.$ What magnetic field do they produce 2.0 m from the beam?    $ \times10^{ -17}\;T$

Determine the magnetic field midway between two lonzpczm b)9c+d9lhdhpr 9 +-v6 bg straight wires 2.0 cm apart in terms of the current I in one when tm6)r d+b +-vphzh9dl9cpzb c9he 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 instresop,v 8:/eeo) pasc6u -ca6lcd2)lbument. If the insulated wires are of negligible diameter but are 2.8 mm apart, what is the magnetic field 10.00 cm from their midpoint, in their plane (Fig. Below)? Compare to the magnetic ee2sp6occ -6becl8a uv ) ad,olsp/:) 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 ofro++k s3;gz g20txr 7nf3qgd p the two wires shown in (Fig. Below), parallel and7nrg;+z g3dofsk t+pgx0r3q 2 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 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 poihn9ha(9 -slhm.q zjr 9nts 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 samdxn;9i2jg s 0fe plane as a straight wire, as shown in (Fig. Below). There is a current of 2.5 A infsnix20g dj ;9 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 wic2nm hq11u. ycre carries a current of 48 A. A second wire, made of 2.5-mm-diameter copper wire and parallel to the first, is kept in suspension magnetically 15 cmu1qyn.c2c1m h below (Fig. Below).
(a) Determine the magnitude and direction of the current in the lower wire.    A the current is to the  ----待选择----leftright 
(b) Is the lower wire in stable equilibrium?  ----待选择----not in stable equilibrium in stable equilibrium 
(c) Repeat parts (a) and (b) if the second wire is suspended 15 cm above the first due to the latter’s field.

  Two long wires are oriented so that they are perpendicular to each other. At ti(tq+ 7z)uw fvheir 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 f+i t)v7z qu(wA and the bottom one carries 5.0 A?    $ \times10^{-5 }\;T$

  Two long straight parall8hs*rh, 1hp.8:4a s fmelxavrel wires are 15 cm apart. Wire A carries 2.0 A current. Wire B’s current is 4.0 A in the same directi h h8*le1sxamp84v h.f,r:rsaon.
(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 alon ua vc(2h3hg*d.9qqnl g them, they are at three corners of an equilateral triangle.) The current in each wire is 8.00 A, but its direction in wire M is opposite to that in wires N and P9anc 2qu d.lh* (3qvgh (Fig. Below). Determine the magnetic force per unit length on each wire due to the other two.
$\frac{F_\text{M net y}}{l_\mathrm{M}}$ =    $ \times10^{ -4}\;N/m$ =    $^{\circ}\,$
$F_{N\,net}$ =    $ \times10^{-4 }\;N/m$ $\theta$ =    $^{\circ}\,$
$F_{P\,net}$ =    $ \times10^{ -4}\;N/m$ $\theta$ =    $^{\circ}\,$

  In (Fig. Below), determine the magnitude and dirte/v -q h:fh3* 0vxwtlection of the magnetic field at the midpoint of the side of the triangle between wire M anhfvqh :*vxt3wet-l0 / d wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a distance d apart, carr-l92wx cz3 0wzvs;ea.y tltj3y equal currents I in the savw; 0 wc29l3jetzs .xt3y-zlame direction. One wire is at x = 0, the other is at x = d, (Fig. Below). Determine $\vec{B}$ along the x axis between the wires as a function of x.

  A thin 12-cm-long solenoid has a total of 420 turns of wire and carries e29 ux90a2q3nxdc9f yy 6/3znktis f bpk, :rla current of 2.0 A. Calculate the fielil0snxxcd92 2upk:rk6fz3 yeq9n,t 3yfb / a 9d inside near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in ;v sy-:(gvs+lm)vysxg yzs3v0(r 2ej diameter is to produce a field of 0.385 T at its center. How much current should the solenoid carry if it has 975 tur yg mlsys yz(jg2esv+(30v ;:-vrv)sx ns of the wire?    A

  A 550-turn solenoid is 15 cm longud z9ft(dron) 3- 7fbp. The current in 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 p 3oz9d(7f) udtfbr-nconnected 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 want4z+ fdoi4 clu7 to make a practical solenoid that produces the greatest possible magnetic field for a given voltage. Should you mak+4io df7 ulz4ce your copper wire long and thin, short and fat, or something else? Consider other variables, such as solenoid diameter, length, and so on.

A toroid is a solenoid in the shape of a circle (Fig. Below). Use Ampère’a76f n/1/pmxr+ nez.dgzwwd/ oe,4. g) qv otys law along the circular path, shown dashed in (Fig. Below a), to determine that the magneey 6/x7.. feq,+p/dt 1/ado )wr4m gw zgnvozntic 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 vpofndp6 wjj)6l:f71uq9+ yfmagnetic field between the conductors of a coaxvq+ ) 6f9y ffp1njjlo:76puw dial 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 (,e re nz-r9fzpz1zaj+x1d )b7l;fm iis placed with its face parallel to the magnetic field between the pole pieces of a large magnet. When 6.30 A flows in the coil;+ r afr7mi-xfdze (bznp1z9lz1e),j, the torque on it is $0.325\cdot N$. What is the magnetic field strength?    T

  A galvanometer needlekn ;mzohp.;*w qyh7i - 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 gch +k1(/su pjgfj9+ wweakens by 25% over the years, what current will give full-scale deflection isu+/kg9 pg+wc1hfj j(f it originally required $36-\mu A$ ?    $\mu A$

If the current to a mi)k82hm:peve83l20s dh/bxf r nu1 iin40jjwotor drops by 12%, by what factor does the output torque changeheblvi rdkj1n0uenpxj/)82fsi mh4: w 830 i2?

Show that the magnetic dipole;ryj+zg s +0x2 ynomovu*p.czf+.uj8 moment M of an electron orbiting the proton nucleus of a hydrogen atom is related to ymo2snfr.puyz*jxo vg+ +zj+c 80u;. the orbital angular momentum L of the electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter and containing nine loops lies fl35w, ze s 1urn78hnwtkpz :gb)at on the ground. The 1w3zg, u7 :tehr5nw8zs bn) pkEarth’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 radiuss)h,l7so+ w ire9fm/k0o;y0fn/ fco5zw9cpc 5.10 cm in a 0.566-T magnetic field. What value of electric field could make the cf w7fpfe/nyisc cr/,ho5ls +;9k)o9m00owz ir paths straight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atoms have radiiug xud)1kxuohjd)tp r8)y15+ 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 auo)g+urdd 1ktp yjx1 ))8 h5uxre the atomic masses of the other isotopes?

  Suppose the electric field between the electric plates in the mass zt,-o (ddgjks79tx 6h spectrometer of (Fig. Below) is ojtsdkh69t x,dz(g-7$2.48\times10^4\mathrm{~V/m}$ 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 iyk;x hlfsxh5 t)a:-e n*22gzws difficult, however, to separate molecules with nearly equal m 5 2wyhh*x za;-s)g: xleknft2ass 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 acceley zcyb vgpu /t ,9,ll6/h4nsw*1/ vfqfrates ions by a voltage V before they enter a magnetic field B. The ions are assumed to start from rest. Show thz9y1w,fgq clul4* vp b/hytf/vs 6/,n at the mass of an ion is $m=qB^2R^2/2V,$ where R is the radius of the ions’ path in the magnetic field and q is their charge.

  A long thin solenoid has 430 loops of wire per meter, and a 25-A cpdq90l9 e pm6fp4nq9aurrent flows through the wire. Iepp d699 4plmaq9fn0qf the permeability of the iron is $3000\mu_0$ what is the total field B inside the solenoid?    T

  An iron-core solenoid is 38 cm long an66ni8xau2idbu* p4nt d 1.8 cm in diameter, and has 640 turns of wire. The magnetxnb8i *u2p6ndi64ut a ic 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 s; v 6kqbnwrlo,m8,f3 $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 energlk7e77h i7vqh-zz3cl y upon entering a region of constant magnetic field. What is the ratio of the radii of their circl7c73hiz7 lh- kz 7qevular paths?   

  The power cable for an electric trolley (Fi, rd2 94 bhh1b txosii1x5mqr,g. Below) carries a horizontal current of 330 A toward the east. The Earth’s magnximt rs,1ih5or42qh d, x91bbetic 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 whicy0f yj- .xhf 0;lnkf7fh 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 pointsf yia5 hu44xg-qce+h +dnr0l) almost horizontally to the nort5440gcaqr+ hyhx duil+e f-)nh 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, whose mass ixmu/oh1njvp)py4. m, s $6.6\times10^{-27}\mathrm{~kg},$ is accelerated by a voltage of 2400 V.
(a) What will be its radius of curvature in a uniform 0.240-T field? $\approx$    m (retain three decimal places)
(b) What is its period of revolution?    $ \times10^{-7 }\;s$

  A sort of “projectile launcher” is shown in (Fig. Below). A large current moves2gdsaj1+z2h e a.w+v a in a closed loop composed of fixed rails, a power supply, and a very light, almost frictionless bar touching the rails. A magnetic field is perpendicular to the plane of the circuit. If the bar has a length L = 22cm, a mass of 1.5 g, and is placed in a field of 1.7 T, what constant current flow is needed to accelerate the bar from rest to 28m/s in a distance of 1.0 m? In what direction must the magnetic fjaa.zv d2+ +s21geh awield point?
   A
the magnetic field must be ----待选择----updown 

  In (Fig. Below) the top wire is 1.00-mm-diameter copper wire and pihd1y - kr)s3qp/x8 pis suspended in air due to the two magnetic forces from the bottom two q81i p-3physrkxdp/ ) wires. The current flow through the two bottom wires is 95 A in each. Calculate the required current flow in the suspended wire.    A

Two stiff parallel wires; ol-i( a35evsxklwf0b0nj 9q a distance l apart in a horizontal plane act as rails to support a light metal rod of m 50b;x09 osfe ll(ajv-qni w3kass m (perpendicular 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 u8buplus 5g c sdll l542w5r;e586pcxdeflection of the electron beam near the center of a l8 bgdc4lu68use ruxpp525lc 5sl;5w TV screen due to the Earth’s $5.0\times10^{-5}\mathrm{~T}$ field. Assume the CRT screen is 22 cm from the electron gun, where the electrons are accelerated
(a) by 2.0 kV,    mm(Round to the nearest integer)
(b) by 30 kV. Note that in color TV sets, the CRT beam must be directed accurately to within less than 1 mm in order to strike the correct phosphor. Because the Earth’s field is significant here, mu-metal shields are used to reduce the Earth’s field in the CRT.    mm(Round to the nearest integer)

The cyclotron (Fig. Below) is a device used to accw.tl n1 io,h6 de(j )4fh,rfrkelerate elementary particles such as protons to high speeds. Particles starting at point A with some initial velocity travel in circular orbits in the magnetic field B. The particles are accelerated to higher speeds each time they pass through the gap between the metal “de,fi1(ro4l,heh6.jrd tnw )kf es,” 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 straigh0ga /46vk4 oy6bli( apg(ebjmt parallel wires, located at the corners of a square of side l, carrbk o/gpv6lig(ay ajm4e60b4(y equal 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 .w xs/ml-8 oy0xu dcncq1 .wd9particle accelerators for “beam steering”; that is, the magnetic fields can be used to change the beam’s direction without altering its speed (Fig. Below). Show how this works with a beam of protons. What happens to protons that are not moving with the speed that the magnetic field is designed for? If the field extends over a region 5.0 cm wide and has a magnitude of 0.33 T, by approximately what au9nlsy/xx m0 - .o.1qww dcc8dngle will a beam of protons traveling at $ 1.0\times10^{7 }\,m/s;$ be bent?    $^{\circ}\,$

  The magnetic field B att s1.b3iopn.p,6a j(yngymm . the center of a circular coil of wire carrying a current I (as in Fig. Below) i6p js3mg.n .tpa( yn, yi.ob1ms
$B=\frac{\mu_{0} N I}{2 r},$
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 tufxcq n9u,0j: he magnetic 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 produced by overhfhk/:l1lx c x2ead power lines kh2x /:xcl1fl. 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 be changing.] $B_{net}$ $\approx$    $ \times10^{ -5}\;T$(Round to the nearest integer)

  (a) What value of magnetic fc g xa++k6j1toield would make a beam of electrons, traveling to the right at a speed 1g6at o x+j+kcof $4.8 \times10^{ 6}\;m/s$ 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 ies9pd +6. t7*raypkn path through a gas in a magnetic field of 0.010 T, perpendicular .kn ptar6y9*7 ipsd+e 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.    $ \times10^{-20 }\;J$

  A 32-cm-long solenoid, 1.8 cm in diameter, is to prody1aa w, 7j kff e0p-vp2/rla2+k rbos2uce a 0.30-T magnetic field at its center. If the maximum current is 5.7 A, how many turns must t po2r-a,wl/ kye1+f b02rpsja v2af7khe solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, eachyki5xi1- mzl mv6.k)f of diameter 0.50 mm, carry the same current but in opposite directions. They are suspended by 0.50-m-long strings as shown in (Fig. Below). If the suspension strings make an anglvi1f -z.m) xiyl 5mkk6e of 3.0$^{\circ}\,$ with the vertical, what is the current in the wires?    A

  An electron enters a uniform magn cc.s6y la1:ja3zq j8vx;6v ojetic 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$