A compass needle is not always balanced parallel to the Earth’s surface,1g * k xks9vx/3ta6mwz9ht /sr but one end may dip dm9srstt/ w zvg* k9h/k63xax1ownward. Explain.

Draw the magnetic field lines around a strkil;ucd: c 7z6aight section of wire carrying a current hi7: z uc6lkc;dorizontally to the left.

In what direction are the magnetic field lines surroh c-*d8rtkw o,unding a straight wire carrying a current that is movingt- co8rkdhw ,* directly away from you?

A horseshoe magnet is held vertically with . mn gfypz: py1hmh/bq:6;l y6the 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 the wire? 6g1:6;ymym: . /qh phbzlfypn

Will a magnet attract any metallic object, or only those ma,j4dcc/4*/uo;u jgr3ly v kbxde of iron? (Try it and see.) Wdk4 ucj4 *;vrb,3o lxj/y/ugchy is this so?

Two iron bars attract each other no matter which ends are placed close tojt aa9zo6qw2vm j4if09 six;7 gether. Are botwx9joaz 0;tmv 47siij29 q 6afh magnets? Explain.

The magnetic field due to current in wires in your home can affect a ,y9b2; knos tywmm4a(compass. Discuss the effect in terms bm(9ak ;4,mywty n2soof currents, including if they are ac or dc.

If a negatively charged particle enters a region of uniform magnetj zhs g8gj:q3a8oq)db3 7 1votic field which is perpendicular to the p:j qoo)jd88 37ag vq3bsg1t hzarticle’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 t3*vmkf2 td: wm u8to3bhe vicinity of a current-carrying wire. For each charged particle, the arrow indicates the direction of motion of the particle, and the + or - indicates the sign of the charge. For each of the partk8b2m fv: d mt3owu3*ticles, 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 field as shown in Fig. h3glu4fupjm7- wod a:,w0+lb 20–46. What can you say about the charge on eacwlpw:7u3boflau04 ,+jd g-hm h particle?

A positively charged particle in a nonuniform magnetilpr*vpq db755yv fb6j bd4d/b:ty(,rc field follows the trajectory shown in q y5jlb :btdpb67rfd5b drpy *(v/4,v
(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? Ckd:s1 tq tf a6+)365llq.h6 rsc4 c )ckncoeaqan a magnet attract an iron rod? What must you consider to answer these :lt5cs)4sqo3kl6atf6 q+)qdc .c ake1h6cn rquestions?

Explain why a strong magnet held ot 40u9k uza (k)4wo uue72tnsnear a CRT television screen (Section 17–10) causes the picture to become distorted. Also, explain why the picture z9n w20eot4u uk4)u7atku os (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 o2 eoqjei+kp+hk (6g8 qmzg*(dua27f lf which are magnetized but the third is not. How would you determine which two are tei6g2*7 k d(q (uj h ezaplo2fm8gkq++he magnets without using any additional objects?

Can you set a restinkfi,+jjsojg1xu 8 :lyr696b1pq x* v sg electron into motion with a magnetic field? With an electric field? Ex q bpjxr*+1j x9gsf68l y ski1,o:6vjuplain.

A charged particle is moving in a circle under the influence of a uos;o gn1*gjc,b tu 1m;niform magnetic field. If an ,jmcog g ;s11 *t;nbouelectric field that points in the same direction as the magnetic field is turned on, describe the path the charged particle will take.

The force on a particle in a magnetic field is the idea behind electr+nwvnr:xeb 9 5omagnetic pumping. It is used to pump metallic fluids (such as sodium) wv9+x5bren :n and to pump blood in artificial heart machines. The basic design is shown in(Fig. Below). An electric field is applied perpendicular to a blood vessel and to a magnetic field. Explain how ions are caused to move. Do positive and negative ions feel a force in the same direction?

A beam of electrons is directed toward a llpta j.)o() 3 +q-fxbnsjrtdw4q13chorizontal wire carrying a current from left tfapxds j br3t41-ql.l oq3) )(cjt+wno right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fi+e7aggyl gctr; j9v 44elds that surround a moving electric charge.7;cgj9rvg alge 4 +y4t

A charged particle moves in a straigh: 4e k- 8xe3mzc3, rwwsle g4o+a/lkrst line through a particular region of space. Could there be a nonzero magnetic field in this region? If so, give two 4l xw33g,z koklar -4+ ese /:8rcsmewpossible situations.

If a moving charged particle is deflected sidewaysyk;* m* 8yavxzlskgx9gw:4w6 in some region of space, can we conclude, for certain, tha zx8v4kskw* 9ayw ;m*:gy6glxt $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is a uniform magneticnbr ye jd* f;7qhz9:8x 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 region of spazxo,yg1f(v2-6xhf *xn o+n gtce are being deflected by an electric field or by a magnetz,yf+of ogx g(tn-vxnx* h612ic field (or by both)?

How can you make a compdgi .:52zxf. tmnbjxju:24 r lass without using iron or other ferromagnetic material?

Two long wires carryiz,+5 zzje ,yc blivb.8c wfb,0ng equal currents I are at right angles to each other, but don’t quite touch. Describe the magnetic,jyz 8fz i.+zl,bebb cc5v w,0 force one exerts on the other.

A horizontal currentk8- -zgfu avm5fu3n p9-carrying wire, free to move in Earth’s gravitational field, is suspended directly above a second, -fupaz8vm f5g9knu-3parallel, 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 an unm.jwx -p9oanwvs r0,7tagnetized piece of iron?

An unmagnetized nail will not attract an unmagnetized papb zx6.: om;wjeer clip. However, if one end of the nail is in contact with a mag. bwojz e:x6;mnet, the other end will attract a paper clip. Explain.

Two ions have the same mass, but one is singly ionized v lo: q*3kyk*u es0ym04 o,kaband the other is doubly ionized. How will their positions on the film of a mass spectrometebukkyev* 3,a00:4 m klo sqy*or (Fig. Below) differ?

What would be the effect on 6jakdh5w(i x3ivv4o 0pi4 s)oB 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 switcros( 3r/m5 lreh similar to a solenoid is a relay . A relay is an electromagnet (the iron rod inside the coil do (s5r m3errl/oes not move) which, when activated, attracts a piece of iron on a pivot. Design a relay to close an electrical switch. A relay is used when you need to switch on a circuit carrying a very large current but you do not want that large 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 pe y: v+jtcs)e6br meter of length on a straight wire carrying an 8.40-A current when perpendicular to a 0.90-T unif:cvte+) sjyb6orm 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 maz;0n:/ em /7-vc9ewpaeme xa1(wyik vgnetic force on a 160-m length of straight wire stretched between two towery/v79m icee/z:x m aaenv wk-0ep1;w( s 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 ma; a nr96a dfjdz)*fln*gnetic force on a 160-m length of straight wire stretched between two towers f*n dz)6;f*nja rlda9carrying 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 fl -;3v: c ww: otzj+dgc2fx;ecxowing in a wire 4.80 m long if the maximum force on it is 0.750 N when placed in a uniform 0.0800-T fieldcdx zcf:w;e+j23wc xv;:o-gt?    A

  A 1.5-m length of wire carrying 4.5 A of current is orient k wgkevwc.tj5+qwbi3 ;z47e 8ed horizontally. At that point on the Earth’s sur+wjw 743;vgz. b8ktw ie5qckeface, 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 pl:yb( tuqfi8wid 9: m7uaced between the pole faces of a magnet. If the pole faces are 55.5 cm in diameter, what is the approximate strength of the magnet:i :mqbi(dt uwyuf87 9ic field?    T

  The magnetic force per meter on a wire is measuraocf, (nak1 ip;74hr:v;pba xed 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 fbx4;:7 p hpoar kva1(can, i;the relationship as it actually is, calculating the angle between the wire and the magnetic field.    $^{\circ}\,$

  The force on a wire is a maximumo xjr0er6 ea:wv;x:jvu a7-y, 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-d7iekbrhxrkj /zw j 6au3+s d0 v),08sjiameter copper wire could just “float” horizontally in air because of the force due to the E)3k07ejkv/wdrss+i 8jzr0 ua,6x jbharth’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 cm9l kp r.80*cpz)ylk5dyl :v. xqxi* mharge $q\,=\,+2e$ 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 direct ubkav-u mdk/u:+,zc+ ion 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 otc)fd +::xh9bqih-ib8z uyg7,z/ ctc n a negative charge for each diagram shown in (F,h:)yitcbq zu ifzhtd /+-87gc:xb9cig. 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 direction t) rdwrg+0w ;gof $\vec{B}$ 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 projecboa wcu ulfn 59(dafeo3x2 42/ted vertically 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 enterdj-v agrb,; 4vs a 0.20-T field, in a plane perpendicular to the field. What is the radius of its path-g4vrv ; db,ja?    m

  An electron experiences the greatest force as ido az1-/euc ka;913qdgxt i: yt 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 b.oikpzb4 algs0 ,;07rnms w8 a beam of electrons that go undeflected when passing through perpendicular electric and magnetic fielarploi80 4., ;k7ns0m gbzwsbds 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 who 5hb ,tdku0+slse mass is $6.6 \times10^{-27 }\;kg$ is accelerated by a voltage of 2100 V.
(a) What will be its radius of curvature if it moves in a plane perpendicular to a uniform 0.340-T field?    m
(b) What is its period of revolution?    $ \times10^{ -7}\;s$

  A proton (mass $m_p$), a deuteron $(m=2m_p,Q=e)$, and an alpha particle $(m=4m_p,Q=2e)$ are accelerated by the same potential difference V and then enter a uniform magnetic field $\vec{B}$, where they move in circular paths perpendicular to $\vec{B}$. Determine the radius of the paths for the deuteron and alpha particle in terms of that for the proton. $r_d$ =    $r_p$ $r_{\alpha}$ =    $r_p$

Show that the time T required for a particle of charge q moving with constant sx6;4joyhiv qi8e* h :hpeed v to make one circular revolution in a ui6h4eq:8 hjyivoh;*x niform magnetic field $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge q svax;a+7 g)bi moves in a circular path of radius r in a uniform magnetic field B. b7ga) xi +as;vShow that its momentum is p = qBr .

A particle of mass m and charge q moves in a circular path in a magnetic fiafbqij 0/2t2geld B. f22b qai g0tj/Show that its kinetic energy is proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momentum of the pae.s z* kvq(qgnj+1k 6frticle 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/nl 9q k7ss4/qcfl /enr( tlcc4a4)0gm s perpendicular to the Earth’s magnetic fie tf04l/lsn)4(9eaq 4 mrgc7 nccs/ qklld of $5.00\times10^{-5}\mathrm{~T}$, If the bullet possesses a net charge of $13.5\times10^{-9}\mathrm{~C},$ by what distance will it be deflected from its path due to the Earth’s magnetic field after it has traveled 1.00 km?    $ \times10^{-7 }\;m$

  Suppose the Earth’s magnetic field at the equat7y1wn pwmwg /3or 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 spe+ 7 lh7n kj3:bgjz2ohked $\nu=2.0\times10^5\mathrm{~m/s}$ 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 vehic uko2tpgx 6 u;wo1snu 5z*f,o(le carries a 65-A current. How strong is the magnetic field 6.0 cm away from it? Compare towognutu65ooxk2zu, 1 ;s p f(* the Earth’s magnetic field. $B_{cable}$   $ \times10^{-4 }\;T$ the field of the cable is about    times that of the Earth.

  If an electric wire is allowed to produce a magnetic fielzp3),.br qrteiv5ey( d no larger than that of the Ea)bizyter.5 er 3,pv( qrth $(0.55\times10^{-4}\mathrm{~Т})$ 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 out0;mgu/cmypm j.qvt78 of the page toward you. Indicate, wt7my qmgv;jm/8u. c0p ith appropriate 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 carrys cdk 7ns92s9iing an upward 24-A current exerts an attractive forcek9id7 ssn 2s9c 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 lu(s py. 96)dypd-0sqvohck*of the force between two parallel wires 35 m long and 6.0 cm apart, each carrying 25 A in y0dpoq *k d(6c9)su -ph.sylvthe same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic field is being carried out 1.00 m from an fvzapa3ag;pnd e+ro 3 / -::kselectric caf aea3:3drp sn+;-aopvg:z/ kble. What is the maximum allowable current in the cable if the experiment is to be accurate to $\pm1.0\%?$    A

  A power line carries a current of 95 A along 7lz:6yxt(i9 n iz5 kcpthe tops of 8.5-m-high poles. What is the magnitude of the magnetic field produced by this wire at the ground? How does this compare with the Earth’s fp6likz5c( x :9in zy7tield of about $\frac{1}{2}G$?    $ \times10^{-6 }\;T$ The field of the cable is about    % that of the Earth.(retain two decimal places)

  Two long thin parallel wires 13.0 cm apart carry 25-A currents in the same a)ta z0 dn0xb ,i(ufi3e -zec:direction. Determine the magnetic field at0dxzat 3-:iecz u,0b)ef(ian 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 a7 xw94ir8ezml straight vertical wire carrying a 35-A current downward. In what direction does the compass needle point at this location? Assume the horizontal component of the Earth’s fieem lxi8rz749wld 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. What is the nplo*1- a fj -o;2np o8kksrb0o l;nv-bet magnetic field 20.b 1l jko-of08- ap*onrsb- olp; kvn;20 cm due west of the wire if the Earth’s field there points north but downward, 37$^{\circ}\,$ below the horizontal, and has magnitude $5.0\times10^{-5}\mathrm{~Т}?$
   $ \times10^{-5 }\;T$
$\theta$ =    $^{\circ}\,$ below the horizontal

  A straight stream of protons passes a given point in space at a rate 6oz bcz12f;p ca w+or,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 betwee25kn6gz c4s bzn two long straight wires 2.0 cm apart in terms of the current I in one when the other carries 156bgkzs z425nc A. Assume these currents are
(a) in the same direction,
(b) in opposite directions.

  A long pair of wires conduct3td u0rr) )fkns 25.0 A of dc current to, and from, an instrument. If the insulated wires are of negligible diameter but are 2.8 mm apart, what is the magnetic fielu )dr)0r n3tkfd 10.00 cm from their midpoint, in their plane (Fig. Below)? Compare to the magnetic field of the Earth.
   $ \times10^{-6 }\;T$ The field of the wires is about    % that of the Earth.(retain two decimal places)

  A third wire is placed in the plane of the two wires shown i(+gt d41xg yvxn (Fig. Below), parallel and just to the right. If it carries 25.0 A upward, what force per meter of length does it exert on each of the other two4vt1gy+d(x gx 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 poinzh8rm-q 9 .qkhts 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 liev4s .8 jacyw7 p*6hdgx-i+8y)tqm v fgs in the same plane as a straight wire, as shown in (Fig. Below). There is a current of 2.5 A in both wires. Determine the magnitude and directi.v tv-ai8shjy c4d8)+ mygw76*xgfqpon 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 of 2.5-mm- w) xcnor +/rck;y*7ws s45 obkx 6m.xm/k-afbdiameter copper wire and parallel to the first, is kept in suss mra- bx)+7mo.c c4k/xk*kx b5n 6/sfroyw;wpension magnetically 15 cm below (Fig. Below).
(a) Determine the magnitude and direction of the current in the lower wire.    A the current is to the  ----待选择----leftright 
(b) Is the lower wire in stable equilibrium?  ----待选择----not in stable equilibrium in stable equilibrium 
(c) Repeat parts (a) and (b) if the second wire is suspended 15 cm above the first due to the latter’s field.

  Two long wires are oriented so that they are perpenoy/yl4 r d29d h8ttk,bdicular 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 on4 t9bodk/yydl8 ,rht2e carries 5.0 A?    $ \times10^{-5 }\;T$

  Two long straight parallel wires are 15l65t))ai 5 mf3dalew zsmjf-1+.8wi qe m 3dnb cm apart. Wire A carries 2.0 A current. Wire B’s current is 4.0 .+q6 53w l1ndms)dlafi zm t3fb8-em j)i5we aA in the same direction.
(a) Determine the magnetic field magnitude due to wire A at the position of wire B. $\approx$    $ \times10^{-6 }\;T$(retain one decimal places)
(b) Determine the magnetic field due to wire B at the position of wire A. $\approx$    $ \times10^{-6 }\;T$(retain one decimal places)
(c) Are these two magnetic fields equal and opposite? Why or why not?
(d) Determine the force on wire A due to wire B, and the force on wire B due to wire A. Are these two forces equal and opposite? Why or why not? $\approx$    $ \times10^{-5 }\;N/m$(retain one decimal places)

  Three long parallel wires are 3.8droy s lm1 bqkv/)d.)z:-bqm 3 cm from one another. (Looking along them, they are at three corners of an equilateral triangle.) The current in each wire is 8.00 A, but its direction in wire M is opposite to that in wires N and P (Fig. Below). Det3zdbd-k/o)sq )v m r q1mb.l:yermine 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 direction of the magnetic field ateaa/fknv2qz0 pk1 eg maf*5f 5a1s5+h the midpoint of the side of the triangle between 5ff5 zfs ngva5aem 1aqkpe k/1 2*+ha0wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a distance d apartepkf y05p2ql:0 (ai0g /h l zjrrmru(+, carry equal currents I in the same direction. One wire is at xg/(hlri2 urrea:0kq5p (00mjp+ly zf = 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 totam /f jnx-5wexftz f*bx7**v-vl of 420 turns of wire and carries a current of 2.0 A. Calculate the field insidv ffmf v *x t-*we*znxb7xj-5/e near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameter is to produce a field im:s-r k.l/a rof 0.385 T at its center. How much current should the solenoid carry if it has/rmal:i.srk - 975 turns of the wire?    A

  A 550-turn solenoid is 15 cm long.;q46bf(u: d d+ggdyee 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 connected by other wires that don’t concern us). What is the force on this wire assuming the solenoid’s: eye;f bdq (u6+dd4gg field points due east?    N

You have 1.0 kg of copper andj (jm1ymv igi7c ii;8 ae.qe:5 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 variaq ecvia( jj;i85.ig1: eymim7bles, such as solenoid diameter, length, and so on.

A toroid is a solenoid in the shape of a circle (Fig. r.aef 7fljyfpj:4 *5pBelow). Use Ampère’s law along the circular path, shown dashed in (Fig. Be.* e j f4:pfpaljryf75low a), to determine that the magnetic field
(a) inside the toroid is $B=\mu_0NI/2\pi r$ where N is the total number of turns, and
(b) outside the toroid is B = 0 .
(c) Is the field inside a toroid uniform like a solenoid’s? If not, how does it vary?

(a) Use Ampère’s law to show that the magnetic field between t o,7 cs)xlapq:he conductors of a coaxial cable (Fi7,:)ao sqxpc lg. 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 w ae3 /njtdd))with its face parallel to the magnetic field between the pole pieces of a large magnet. When 6.30 A flows in the coil, tht3)na / ed)jdwe torque on it is $0.325\cdot N$. What is the magnetic field strength?    T

  A galvanometer needle deflects full 3j18-zp+aizad s1if gscale 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 weakys4dn c i )wl74j-r(g/ sbn,ykens by 25% over the years, what current will give 4 gr/c4yy dssj, wn-l(7)inbk full-scale deflection if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, byzxft :+ig+a)c what factor does the output torque cha++ca ftgx)zi: nge?

Show that the magnetic dipole moment M of an electrr0pkzy: v2)g lon orbiting the proton nucleus of a hydrogenv :kg)r0 p2ylz atom is related to the orbital angular momentum L of the electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter an i(,a6jjl niv5.5jr1 yy*vgtk d containing nine loops lies flat on the ground. Thekgijvaj( r6*v. 5t5y jyi ,1ln Earth’s magnetic field at this location has magnitude $5.50\times10^{-5}\mathrm{~Т}$ and points into the Earth at an angle of 56.0$^{\circ}\,$ below a line pointing due north. If a 7.20-A clockwise current passes through the coil,
(a) determine the torque on the coil,   $\times10^{-5}\mathrm{m}•\mathrm{N}$
(b) which edge of the coil rises up: north, east, south, or west?

  Protons move in a circle of radius 5.10 cm in a 0.566-n4ycyl c /bb-dq:sfr d 497.zeT magnetic field. What value of electric field could make their paths straight? In what direction must it n9.z yrycd- 4eb:4b c7 sf/qdlpoint?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atoms have radii of2pb3utom1q /bx 72 nle curvature equal to 21.0, 21.6, 21.9, 22.2, and 22.8 cm. The largest radius corresponds to anqbu/tmeb32l 2p1 x7n o atomic mass of 76 u. What are the atomic masses of the other isotopes?

  Suppose the electric field betly 8qc5lg3e9ycqxu+ /ween the electric plates in the mass spectrometer of (Fig. Belowccyg53 +x8e y/lq ql9u) 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 ub:y(e0xrs+8yt(tu na sed to monitor air pollutants. It is difficult, however, to separate molecules with nearly equal mass such as CO (28.0(br0ua e:8st +xy (ynt106 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 spectrom6gxj92zgw)1g o ngj*tp(jm 2 weter accelerates ions by a voltage V before they enter a magnetic field B. The ions are assumed to start from9j2ngw g2jxm* w)zt go(gj 1p6 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 430f zcpw0xxnz51)**n pp loops of wire per meter, and a 25-A current flows through the wire. If the permeabilit5*n z0xxpp np)1* czwfy 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 ancqenpv51j *2 ud 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. What ispue c1j2*5nq v the permeability $\mu$ at this high field strength?    $\times10^{-5}\mathrm{T}\bullet\mathrm{m/A}$

  Protons with momentum ad p 1.t61bv(fncui,q $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 mapfw1l m s+k 7(kz./1-vtn9jr (gthk same kinetic energy upon entering a region of constant magnetic field. What is the ratio of the radii of their circul7 /whjpt.(k ( 1s1mngf +zvrlkmt9ak -ar paths?   

  The power cable for an electric trolley (Fig. Below) carries a horizozcy * sz*: ztwph)v8o*ntal current of 330 A toward the east. The Earth’s magnetic field has a stre pz**ztwvzhc8s: *)oy ngth $5.0\times10^{-5}\mathrm{~T}$ 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 ackp qq*nn4;h6j *r 3avtquired 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 g 8, kglg* vdgz tjf37g3)mew6Earth’s magnetic field points almost horizontally to the north and h ,g*g7fv kmwd63jgz t lg)e8g3as 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 heli x0tlp- if3ze3ckzy8(qo8ki- um atom, whose mass is $6.6\times10^{-27}\mathrm{~kg},$ is accelerated by a voltage of 2400 V.
(a) What will be its radius of curvature in a uniform 0.240-T field? $\approx$    m (retain three decimal places)
(b) What is its period of revolution?    $ \times10^{-7 }\;s$

  A sort of “projectile launcher” is showb7h9q b4hs)kwnyg: +in 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 placed in a field of 1.7 T, what constant current flow is needed g:bbik9n+yw47 h ) sqhto 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 t+- dd+k kidx(ey vx3aia4mo9 2op wire is 1.00-mm-diameter copper wire and is suspended in air due d +xk(me 4 +-dk9odyix 2aia3vto 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 suspended wire.    A

Two stiff parallel wires a distance l apart in a horizonth *x+2 ijyh, xxc+/dks gvdy1*mxg9 nr 7ni(j:al plane act as rails to support a l7d* v+gdxx j2 ymx,9s+:1*nckn/h( hijxr gyiight metal rod of mass 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 deflection of the electron beam near the 0:xk : i dgcs-mwzk(u hi3m32hcenter of a TV screen due to tkz0iw:dxs2ikg3um(h : 3m -hc he Earth’s $5.0\times10^{-5}\mathrm{~T}$ field. Assume the CRT screen is 22 cm from the electron gun, where the electrons are accelerated
(a) by 2.0 kV,    mm(Round to the nearest integer)
(b) by 30 kV. Note that in color TV sets, the CRT beam must be directed accurately to within less than 1 mm in order to strike the correct phosphor. Because the Earth’s field is significant here, mu-metal shields are used to reduce the Earth’s field in the CRT.    mm(Round to the nearest integer)

The cyclotron (Fig. Below) is a device used to accelerate elementary par96 w/x6t ysiqyticles 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.) Thy66 /9itwqys xe 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 paraly9 1fogj:s.wb lel wires, located at the corners of a square of side l, carry equal c9 wb jys1go:f.urrents $I_0$ perpendicular to the page as shown in (Fig. Below). Determine the magnitude and direction of $\vec{B}$ at the center C of the square.

  Magnetic fields are very useful in particle accelerators for “beam smp8/s me;)pa8 ; r( yadgfe1jmteering”; 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 angle will g1ym8ada;/p)s (m j e;f p8mera beam of protons traveling at $ 1.0\times10^{7 }\,m/s;$ be bent?    $^{\circ}\,$

  The magnetic field B at the center o3 p,aq-n ovq4dnm77 qcf a circular coil of wire carrying a current I (as in Fig. Below)cd4o7 a nm,qp qv3n-7q 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 magneti+ i;mt fxa5hc:3j9h ebc 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 prody3ry-d0sn3 fj uced 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 powe3s- 0nfyj 3dyrr 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 fiel u+)w) lgqcwaa7.nyq)v*9zwp d would make a beam of electrons, traveling to the right at a speln ga).q+aw)y7zc)9* qwv puw ed of $4.8 \times10^{ 6}\;m/s$ go undeflected through a region where there is a uniform electric field of 10,000V/m pointing vertically up?    $ \times10^{ -3}\;T$(retain one decimal places)
(b) What is the direction of the magnetic field if it is known to be perpendicular to the electric field?
(c) What is the frequency of the circular orbit of the electrons if the electric field is turned off?    $ \times10^{7 }\;Hz$

  A proton follows a spiral path through a gas in a magnetic field of 0dljy2dk1f4h 0;b hd3lyi3 t j:.010 T, perpendicular to the plane of the spiral, as shown in (Fig. Below). In two successive loops, at points P and Q, the radii are 10.0 mm and 8.5 mm, respectively. Calculate the change in the kybkdl 02fj 3;dy1j:l ih4hd3tinetic energy of the proton as it travels from P to Q.    $ \times10^{-20 }\;J$

  A 32-cm-long solenoid, 1.8 cm in;nqo.xkd n;)z,8z naf diameter, is to produce a 0.30-T magnetic field a, ;.fznqd)a kn;xz8on t its center. If the maximum current is 5.7 A, how many turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, each of diameter 0.50 mm, carry thr092u hyk (yqye same current but in opposite directions. They are suspery2qh(u9y y k0nded by 0.50-m-long strings as shown in (Fig. Below). If the suspension strings make an angle of 3.0$^{\circ}\,$ with the vertical, what is the current in the wires?    A

  An electron enters a w u*.cxqum58suniform 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$