A compass needle is not always kqu ) rpq6u5icg /rj5xwx3.u1balanced parallel to the Earth’s surface, but one end may di.q 53gcurrq x )uxikju 6p5w/1p downward. Explain.

Draw the magnetic field lines around a straight secx6x4hcy cl. 4 9)u)hud6kok dytion of wire carrying a current horizontally td) uhxkc.94kc you h)4y6d 6lxo the left.

In what direction are the magnetic field lines surr*dqh)d bb8t:sounding a straight wire carryh)b8q st: d*bding a current that is moving directly away from you?

A horseshoe magnet it l p1pz2 i+fej,k57xur81h kms held vertically with the north pole on the left and south pole on the right. A wir8hp rtx7u1ki5jpkle ,1mz2 f+e passing between the poles, equidistant from them, carries a current directly away from you. In what direction is the force on the wire?

Will a magnet attract any 5d:7hpy9yt 7 o4ilwyo metallic object, or only those made of iron? (Try it and see.) Why is this 7poto y 4y5hd9l:7iywso?

Two iron bars attract each other no matter which ends are placed close toge:l lft,,i)gxzther. Are both magn ltl,gf)i,xz: ets? Explain.

The magnetic field due to currentewj:no. l7 f-p in wires in your home can affect a compass. Discuss the ee7j :.wpn-folffect in terms of currents, including if they are ac or dc.

If a negatively charged particle enters a region of unifor9yeuql,tc ./v m magnetic field which is perpendicular to the particle’s velocity, will the kinetic energy of the particle increase, decrease, or stay thqy9vct.u,le /e same? Explain your answer. (Neglect gravity and assume there is no electric field.)

In(Fig. Below), chargedxyfgjp/r3i 6 : particles move in the vicinity of a current-carrying wire. For each charged partix6:yijf gp3/ rcle, the arrow indicates the 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, + o.ioplimr(c-qec6 )yw,tk f16z2n u6fsji- b, and c, enter a magnetic field as shown in Fig. 20–46. What can you say about the charge on each particle-y .kc6c,2etl)fqf+w(o1i6 p6o-rm ijus zn i?

A positively charged h.m1aq 4 j+rofparticle in a nonuniform magnetic field follows the trajectq+ hr1ojf4ma .ory 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 magnetfh : )d3sr+afu /wwqr0 attract an iron rod? What must you consider to answe: w /3a)dhsrurwq0 ff+r these questions?

Explain why a strong magnet held near a CRT television screen (Section 1fj +oxvmi0c/.( ysb+ )hrjdy-7–10) causes the picture to become distorted. Also, explain why the pictx rh0f( j+j/dv+ yb.)omsy-icure 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 wh w58c(qj4vqinqi- *zwich are magnetized but the third is not. How would you determine which two are the 4w-nwv czj(q 8qii5q*magnets without using any additional objects?

Can you set a resting electron into motion with a magnetic field? -bn,muedyd d/83 3bqbWith an electric field? d d8-/nbu3m ,3bbyqed Explain.

A charged particle i).)h;hjr41 x t2gbvpvw).dq pm wz 4ags moving in 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 pgbpwhm 24 ;xwqhj g vz1))vrdt.a.p4)ath the charged particle will take.

The force on a particle in a magnetic field is the idea behind electromd n8i-5j dz67w/ygv ezagnetic pumping. It is used to pump metallic fluids (such as sodium) and to pump blood in artificial heart machines. The basic design is shown in(Fig. Below). An electric field is applied perpendicular to a blood vessel and to a magnetic field. Expz5dn gvjzyw7 d-/6 ie8lain 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 horz3dza4p4i5q. ni9wv4oy0u qg izontal wire carrying a current from left to righz5w. 0dn4 poig34i q9vqz4uyat
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields thatg 7zn :m4sjb8t surround a moving electric charge.sm n7jtz4b g:8

A charged particle moves in a straight lint ue3h ;:ytn2ve through a particular region of space. Could there be a nonzvute :2hy;t3nero magnetic field in this region? If so, give two possible situations.

If a moving charged particle is deflected sideways ioi*1tcw u.-qtb2mn3v n some region of space, can we conclude, for certain, .ct vm*13o2bwq-it n uthat $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is a uniform-mr v2o,xi /s0rdj3dd 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 ele)nois41el h*pctrons in a certain region of space are being deflected by an electric field or by a mag1)l i4np *hosenetic field (or by both)?

How can you make a compass without using iron or tao(: vz fq81iother ferromagnetic material?

Two long wires carrying equal gyxg; 1 tevd mjw v607;xw-(rbcurrents I are at right angles to each other, but don’t quite touch. Describe the magnetic force one exerts on they;; g-vbv 0x7tw w1(mex gj6dr other.

A horizontal current-carrying wire, fupl(v4 j;6( s.1dqjh g1py.f uun(w uvree to move in Earth’s gravitational field, is suspended directly above a second, parallel, wq(yvl; nuujd1fu 64.(jh.gp su (v1pcurrent-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 an unmagneti,/enpe20.g9e u6xy6ildt d h azed piece of iron?

An unmagnetized nail will not attract an unmagnet(vl(mv.o +h zkized paper clip. However, if one end of the nail is in contact with a lzh o+v(m( .vkmagnet, the other end will attract a paper clip. Explain.

Two ions have the same ma;3:4pvqrbf2 lb (wlyass, but one is singly ionized and the other is doubly ionized. How will their positions on the film of a massf(l vw42l;aqb bp3r:y spectrometer (Fig. Below) differ?

What would be the effect on B inside :n8;:mu,iqy s02v sg-iet b pd jlejr-:zk78z 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 similarwgv,7mws 4q)e ;r 0svb to a solenoid is a relay . A relay is an electromagnet (the iron rod inside the coil does not move) which, when activated, attracts a piece of iron on a pivot. Design a relay to close an electrical switch. A relay is used when you neeemvvr w;bsq)7, 0gws4d 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 metere 67r t ep4tl0,4hwthv of length on a straight wire carrying an 8.40-A current when perpendicular to a 0.90-T uniformhept t4wve4hr t,7 0l6 magnetic field?    N/m
(b) What if the angle between the wire and field is 45.0$^{\circ}\,$?    N/m

  Calculate the magnitude of tv)cxcs-n0m ) ihe magnetic force on a 160-m length of straight wire stretched between two towers carrying a 150-A current.0ci)snv )m-xc 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 maj3t1ti1y o2km d*iuj 5gnetic force on a 160-m length of straight wire stretched betweet13u2j 15i kimtd *yjon 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

  How much current is flowing in a wire 4.80 m ws66 iq*lwj jd u)0n8llong if the maximum force on it is 0.750 N when placed in a nqi sju6 l6l*d8j0) wwuniform 0.0800-T field?    A

  A 1.5-m length of wire carrying 4.5 A of curren/+d tgb w+z1c67 )psdy.tae 6cbm;i qjt is oriented horizontally. At that point on the Earth’s surface, the dip angle of the Earth’s magnetic field makes a qmjts;g )wez6 7+t1i.capy+6 bd /dcbn 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 j*xzv71 s,2 fyn tm3tg8.75 A is a maximum of 1.28 N when placed between the pole faces of a magnet. If the pole faces are 55.5 cm in dia*jf ,3t2 mztynv7gx s1meter, what is the approximate strength of the magnetic field?    T

  The magnetic force per meter on a wire is measured to be only 35 9)wlv:+.j:bsq l4;xle zcgts% 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 :xbtelz+: l.c sswl 94v q)jg;angle between the wire and the magnetic field.    $^{\circ}\,$

  The force on a wire is ag2eq5 9bcid9okl n3 n* 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 1.00-mm-diameter copper wire could just “float” horizoblgdfrqk+r5u 267 k* jntally in air because of the force due f65rk+buk rgql 2j*d7 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 cg1otegl8sm:ooy 3rl48v a :3 /br8p vgharge $q\,=\,+2e$ and mass m = $ 6.6\times10^{ -27}\;kg$ are emitted from a radioactive source at a speed of $1.6 \times10^{ 7}\;m/s$. What magnetic field strength would be required to bend them into a circular path of radius r = 0.25 m?    T

  Determine the magnitude and direction of the forceaitk7 80qz. rn 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 neg(n5 l.;xsckg wo p3s :laua):aative charge for each diagram shown in (Fig. Baoll5k; xwnau :p ).ss:g3ac( elow), 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 direction oi 21x6b- h4s(zsy kxrbf $\vec{B}$ 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 witlpzbf qw0i3un -fwgi,g:r7( 1h 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 en+zb h me1aaoer6*x r275v qe8hters a 0.20-T field, in a plane perpendicular to the fieldaqr8vrbh1 7e6o5z*+ he 2xmea . What is the radius of its path?    m

  An electron experiencek3k 1aqzbzr0 3s 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 -2 15mrrsuut -g(:z*m0eq nd pejlu1delectrons that go undeflected when passing through perpendicular electric and magnetic fields of magnitude -du nd ru-z :jqme21rel mts0g1 up*5($8.8 \times10^{3 }\;V/m$ 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 whomsdrh7 jctubksa /x7 /:/6p3wse 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 Tgo-0elx v t5rrx (fz78 required for a particle of charge q moving with constant speed v to make one circular revolution in a uniform magn7e- tvxzrf58lx0 og r(etic 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 magnetz-a ,ocftbiq) 6ogq, 3ic field B. Show that its momentum is p = qBr qoa,ct6-giqf)z o3 ,b.

A particle of mass m and charge q moves in a circular path in a magneticjbldk6d11vzx ns ej9;g. pb /9 field B. Show that its kinetic energy is proportional tsdpl;vnbgj9j 161dxk b e/9z .o $r^2$, the square of the radius of curvature of its path.

Show that the angular momentum of the partic9 wa7 v(tu3nm5lsh 0rele in Problem 21 is $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves with a speed of 160 6 o0+bl l36afy9jpgno m/s perpendicular to the Earth’s magnetic fi+j0 lf3 6lbpoy 6oa9ngeld of $5.00\times10^{-5}\mathrm{~T}$, If the bullet possesses a net charge of $13.5\times10^{-9}\mathrm{~C},$ by what distance will it be deflected from its path due to the Earth’s magnetic field after it has traveled 1.00 km?    $ \times10^{-7 }\;m$

  Suppose the Earth’s magnetic field )wnrlqr s,(2c slcxkr vyc(b+ g./.y,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 spn+h u+v)ar v3beed $\nu=2.0\times10^5\mathrm{~m/s}$ 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 c gradlu/4fu 7;arries a 65-A current. How strong is the magneticug;d afru /4l7 field 6.0 cm away from it? Compare to the Earth’s magnetic field. $B_{cable}$   $ \times10^{-4 }\;T$ the field of the cable is about    times that of the Earth.

  If an electric wire is allowed to produce a mag l g:+w;qtidb.netic field no larger than that ofldi gw :b;.qt+ the Earth $(0.55\times10^{-4}\mathrm{~Т})$ at a distance of 25 cm, what is the maximum current the wire can carry?    A

In (Fig. Below), a loews800l l8w iu3vyl9t ng straight wire carries current I out of the page toward you. Indicate, with appropriate arrows, the direction si0w08ullte3 y8lvw 9 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 exertsqec;0m xukwmu4x47 r, 6/v mbq an attractive force per unit lengt4xcb u, v04 uxrmkqe67 ;mwqm/h 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 t w(eg3+0cf xezhe force between two parallel wires 35 m long and 6.0 cm apart, each carrying 25 A in the same direction0gefcwx( e3+z.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic field is being carried out 1.00j;vzf:2iyeaxg1 s.a * m from an electric cable. What ae:fgi as2.x1v y j*z;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 95o4s q:rd +.bju A along the tops of 8.5-m-high poles. What is the magnitude of the magnetqb.drjo+:4u s ic field produced by this wire at the ground? How does this compare with the Earth’s field of about $\frac{1}{2}G$?    $ \times10^{-6 }\;T$ The field of the cable is about    % that of the Earth.(retain two decimal places)

  Two long thin parallel wires 13.0 cm apart carryzx ;vfa9t q0 iwwgw:60 25-A currents in the same direction. Determine the magnetic field at point P, 12.0 cm from one wire and 5.0 cm frovwgqx:wwta ;z9 f i060m the other(Fig. Below).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass ii kcc)a3-rm809tlr9pqabe + k s placed 18 cm due south from a straight vertical wire carrying a 35-A current downward. In what direction does the compass needle point at this location? Assua 8)ri3qc-9 9cptkkml ea0 +rbme 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. co 6l,kb fq:o,What is the net magnetic field 20.0 cm due west of the wire if the Ea6f:o , q,bckolrth’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 pt7 h1 bc l,9cp805fljfqm pd4wrotons passes a given point in space at a rate of $1.5\times10^9\mathrm{~protons/s~}.$ What magnetic field do they produce 2.0 m from the beam?    $ \times10^{ -17}\;T$

Determine the magnetic field midway between two long straight wires 2.1 x8s5 zzp3zh hm :nt,;tgy4zg0 cm apart in terms of the current I in one when the other carries 15 A. Assume thh34 myng,5;h pg8zs :tzxz1 tzese 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 instrum4 hepfph.myj r84xg 25ent. If the insulated wires are of negligible diameter but are 2.8 mm apart, what is the magnetic field 10.00 cm from their midpoint, in their plane (Fig. Below)? Compare to the magnetic field o.r 5hp4xmy8p f ghe24jf 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 theu-2 dx b 8.l+a3 ikdp2q6wnw52rfpwpp two wires shown in (Fig. Below), parallel and just to the right. I2wn 625rkw-a w2d3dfbpxpp+ qpil 8 .uf 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 poi hex-p1 7c4twmh1z a/xnts 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 th3a au3ig 6y7odrmiw- + +nbep.e same plane as a straight wire, as shown in (Fig. Below). There is a current of 2.5 A7gui ir+o pdyaw+3m6.b3n -ae 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 p- 1s twhxnk a4gfzr3l+.g*)ayp;g x+, made of 2.5-mm-diameter coppxz ;a+fkhlsp * xggr3a41+-yt)wp. nger wire and parallel to the first, is kept in suspension magnetically 15 cm below (Fig. Below).
(a) Determine the magnitude and direction of the current in the lower wire.    A the current is to the  ----待选择----leftright 
(b) Is the lower wire in stable equilibrium?  ----待选择----not in stable equilibrium in stable equilibrium 
(c) Repeat parts (a) and (b) if the second wire is suspended 15 cm above the first due to the latter’s field.

  Two long wires are oriented so that they 75v,f,m+u :l z4nwtfn av5a zuare 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 midwa+ na4m7az:w,uf vu nl5v f,5zty 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 paralle emd2 mkdb64/w0(s rlzl wires are 15 cm apart. Wire A carries 2.0 A current. Wire B’s current is 4.0 A in tbw4/ m k2(der60szdmlhe 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 a7q ehzk s v7:/;tf(juthem, they are at three corners of an equilateral triangle.) The current in hs q(vzk7;ja/tuef7: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 m);r um 54pcjthoy*c); irmk;lagnitude and direction of the magnetic field at the midpoint of the sid;yl iocj)ru r;c *)tm;5mk4h pe of the triangle between wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a distance d apart, carry equ-(1 z n epahca3da6e7lzu 1)mual currents I in the same direction. One wire is at x =(um )a 6hn31le7upz-a dzc ea1 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 solenotu5n*c vrh k9(fjk8 y2id has a total of 420 turns of wire and carries a current of 2.0 A. Calculate the field inside net hkyr28*v( fk5nu 9jcar the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameter is to produce a field of 0.385 T akk6dyui9 (xp )t its center. Hopi)( xk 6k9yduw much current should the solenoid carry if it has 975 turns of the wire?    A

  A 550-turn solenoid is 15 cm long. csq) ew91mn 3r3at,o bThe current in it is 33 A. A 3.0-cm-long straight wire cuts through the center of the solenoid, along a diameter. Thr39,oaw1 csq)tmne 3b is 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 cop45 jrv2ugyy i :thep-,per and want to make a practical solenoid that produces the greatest possible magnetic field for a given voltage. Should you make your copper wire long and thin, short and fat, or something else? Consider other variabup5,rtyyv -j2h g ei4:les, such as solenoid diameter, length, and so on.

A toroid is a solenoid inow.nuw xk 6m;/ the shape of a circle (Fig. Below). Use Ampère’s law along the circular path, shown dashed in (Fig. Below a), to determineu;.woxw/nm 6k that the magnetic field
(a) inside the toroid is $B=\mu_0NI/2\pi r$ where N is the total number of turns, and
(b) outside the toroid is B = 0 .
(c) Is the field inside a toroid uniform like a solenoid’s? If not, how does it vary?

(a) Use Ampère’s law to show t:3 w/ aeeon.u b+yccq+hat the magnetic field between the conductors of a coaxial cable (yb:.+ w n+ qu/ocea3ceFig. Below) is $B=\mu_0I/2\pi r$ if r is greater than the radius of the inner wire and less than the radius of the outer cylindrical braid.
(b) Show that B = 0 outside the coaxial cable.

  A single square loop of wire 22.0 cm on a side is placed wixj4jc2 .v,*4vd ay*eahiy kth(y- keept7t-: th its face parallel to the magnetic field between the pole pieces of a large magnet. When 6.30 A flowst:i-k7 h-ptj 4 *ejv4hv2td(acyyyae* k. ex, in the coil, the torque on it is $0.325\cdot N$. What is the magnetic field strength?    T

  A galvanometer needle deflecjmh rz/pqos khlm )f5-m;a,vm7n7y.,ts 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 galvanng l7 q1pz9qgouh9 w:r f5h86fometer weakens by 25% over the years, what current will give full-scale def6zrfuqgh9 :8 lw1q9nop7g5h flection if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by)uosi+, i5i q6yl7wvx what factor does the output torque chan ,wu5)i+ lqxyivo i67sge?

Show that the magnetic dipole moment M of an electron or xl7h pw5uu b*l+(+qhf* wpll4biting the proton nucleus of a hydrogen atom is related to the orbital angular momentum L of thelql* 5lp+f7u h+w*4pubx l(wh electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter and contain 5z 5b,cyqsxh/ing nine loops lies flat on the ground. The Earth’s magnetic field at this location has mahyz bq ,c5xs/5gnitude $5.50\times10^{-5}\mathrm{~Т}$ 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 l( j(t+ goc8p9zaecdc yzcz 9)zv3:s)in a 0.566-T magnetic field. What value of electric fieldvoy3p9z)j c+ 9zdz(aes( z8c)c cg:lt could make their paths straight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germaniumt e): mna4ylm:. 3eb/:ifs nwy atoms have radii of curvature equal to 21.0, 21.6, 21.9, 22.2, and 22.8 cm. The largest radiuy/::e msb4 t n:)fl .nma3iweys corresponds to an atomic mass of 76 u. What are the atomic masses of the other isotopes?

  Suppose the electric field between the j9y*acx-t +sc,uw j2oelectric plates in the mass spectrometer of w9y c-t ,c xa*ou2jjs+(Fig. 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 mg 1k0vrurftj w4k /*+ponitor air pollutants. It is difficult, however, to separate molr0vr / jkgk4wpt+1uf*ecules 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 accelerates ions by a m2ue e5op6s6xvoltage V before they enter a magnetic field B. The ions are assumed to start from rest. Sp62e ms6ouex5how that the mass of an ion is $m=qB^2R^2/2V,$ where R is the radius of the ions’ path in the magnetic field and q is their charge.

  A long thin solenoid has 430 loops of wire per meter, and a 25-A current f l c/i(v)mox2cyv a6o+lows through the wire. If the permeability o avo2x6cil/cyo+)m v(f the iron is $3000\mu_0$ what is the total field B inside the solenoid?    T

  An iron-core solenoid is 3kr2u/4xmwueodj mf 3**kl,j- 8 cm 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 wire. mo d3 k2j,uu4me**xrkw j/-fl What is the permeability $\mu$ at this high field strength?    $\times10^{-5}\mathrm{T}\bullet\mathrm{m/A}$

  Protons with momentuin (- yyjj co1qdq7 v36q7pw5hm $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 e9/4-mas f3hdoaqa z q/ntering a region of constant magnetia-a maoqh z fs4q//9d3c field. What is the ratio of the radii of their circular paths?   

  The power cable for an electric trolley (Fckrxb eq-2m*49ad a1z ig. Below) carries a horizontal current of 330 A toward the east. The Earth’s x m1ba9z4 kqr*dc-e2amagnetic 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 acquired a net chargedb1gl4lvyd; odfnf lq8s3eu+ ,,9ux2 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 horizont8 *m0j*nyevc f09g+nfke/ n qou;.gvq ally to the north anc0oen9* mq;+n8f/gngejvqk yv*f.0 ud 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 7wy tm1psh80k.eqb.b 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 lansg+--knc s 2uuncher” is shown in (Fig. Below). A large current moves in a closed loop composed of fixed rails, a power supply, and a very light, almost frictionless bar 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+un-g k2n- css 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 wire and is suspenbse01yb3 f ;phgi8/yveoux/ +ded 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 in the suspesyip+ o/v8f; eu1/xyhebg b03nded wire.    A

Two stiff parallel wires ) 7tp+2uxy4*lnzgvrx iw ft60a distance l apart in a horizontal plane act as rails to support a light metal rod of mass m (perpendicular to f7lt *6ztw) vxxn+pgu4ri20yeach rail), (Fig. Below). A magnetic field $\vec{B}$, directed vertically upward (outward in the diagram), acts throughout. At t = 0, wires connected to the rails are connected to a constant current source and a current I begins to flow through the system. Determine the speed of the rod, which starts from rest at t = 0, as a function of time
(a) assuming no friction between the rod and the rails,
(b) if the coefficient of friction is $\mu_k$.
(c) Does the rod move east or west if the current through it heads north?

  Estimate the approximate maximum deflection of the electron beam near t.l0cjpyt1 ejzn1xg 47 he center o1lztjp.1n xgyce j470f a 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 fmwgg)ce .*bjox na./+gkn )/to accelerate 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 “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,g ngxnoc f.)mkj/w. ga*)eb/ + owing to an ac voltage $V=V_0\sin2\pi ft,$ so that the particles are increased in speed at each passage through the gap.
(a) Show that the frequency f of the voltage must be $f\,=\,Bq/2/pi m,$ where q is the charge on the particles and m their mass.
(b) Show that the kinetic energy of the particles increases by $2qV_0$ each revolution, assuming that the gap is small.
(c) If the radius of the cyclotron is 2.0 m and the magnetic field strength is 0.50 T, what will be the maximum kinetic energy of accelerated protons in MeV?

Four very long straight parallel wires, located at the x.ap9r(/lap8umw 5e g i hh tg(vcz+:6corners of a square of side l, carr6 :l t.c(9 h w/ erxi58paggpm(h+uvzay 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 particle acceleraq qbdu5g0;v; 6i0nj nttors 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 q qb6;ituj00nn 5vd;g protons. What happens to protons that are not moving with the speed that the magnetic field is designed for? If the field extends over a region 5.0 cm wide and has a magnitude of 0.33 T, by approximately what angle will a beam of protons traveling at $ 1.0\times10^{7 }\,m/s;$ be bent?    $^{\circ}\,$

  The magnetic field B at the center of a circular coil of wire carrying ax:kfd us)jno /cn:/r5 current I (as od nk cf5x:):unsrj//in 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*(ucdmxjf z3 fw0+ji 8 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 y:z 6 wir8ss*/(y znwb2r 9a+ f4 .zg6rnniwefof magnetic fields produced by overhead power lines. You estimate that the two wires ar.rgz ai iw 2znwez: rby*+694r8ynns(/sf6 wfe each about 30 m above the ground and are about 3 m apart. The local power company tells you that the lines operate at 10 kV and provide a maximum of 40 MW to the local area. Estimate the maximum magnetic field you might experience walking under these power lines, and compare to the Earth’s field. [For an ac current, values are rms, and the magnetic field will be changing.] $B_{net}$ $\approx$    $ \times10^{ -5}\;T$(Round to the nearest integer)

  (a) What value of magnetic field would make a beam of electrons, traveling to cn 8rg3;wq)vlxs-dhqaao sa ,w: 20 k /+xq6yvthe r )x8 yv s6q xkg0-+a ;qc :a,23rosa/hvwdnwqlight at a speed of $4.8 \times10^{ 6}\;m/s$ go undeflected through a region where there is a uniform electric field of 10,000V/m pointing vertically up?    $ \times10^{ -3}\;T$(retain one decimal places)
(b) What is the direction of the magnetic field if it is known to be perpendicular to the electric field?
(c) What is the frequency of the circular orbit of the electrons if the electric field is turned off?    $ \times10^{7 }\;Hz$

  A proton follows a spiral path through a gas in + k qlpka:70 ltrbxn;(a magnetic field of 0.010 T, perpenda;lr qkk:bnl 0 xp7+t(icular 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 produ8 9-z z3.*ivqsjmm t f 1fymd5t4m2j8hfp3z mqce a 0.30-T magnetic field at its center. If the maximum current is 5.7 A, how many turns must the soleno8m- jf8mztqm pz 9fs*433mtf.v5j qyh 12 mdizid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, each of diameter 0.50 mm, car/ 2i-jx,/c,rv b .fxub+pcaa ury the same current but in opposite directions. They are suspended by 0+x.2b jcur /vba ,/c-uapxf, i.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 magnetqhu b,ub8y*i/bup )iu93qv+ric 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$