A compass needle is not always balanced parallel to the Earth’s surface, but ouzqm 93ta*1 tlne end may dip dowtqa mz1 lu3t9*nward. Explain.

Draw the magnetic field lines around a straight section of wirei6ogra/ x78+7oy. gk px yu:ks4n;zhp carrying a current horizontally top.rx z:i+k7os n 48ay pux 67kgyoh/g; the left.

In what direction are the magnetic field lines sud 8r6cao,+2qwfod3o( z fdfr5rrounding a straight wire carryingd rz8oofac2f 5dodf63,q(r +w a current that is moving directly away from you?

A horseshoe magnet is held vertically with the north pole on the o9osih6w *d4n1onslm8, uh3iaf 2 p5jleft and south pole on the right. A wire passing between the pole h6f 92au s ioi,n*p41j 5snl3wdhm8oos, equidistant from them, carries a current directly away from you. In what direction is the force on the wire?

Will a magnet attract any metallic object, or only those made of iron? (Try it an b;3fwm- pi1a:c w+xond see.) Why is th i3m1p+bn-ocx:a fww; is so?

Two iron bars attract eac9yh+1 .azvems;p + zash other no matter which ends are placed close together. Are both magnets? Expms za9 ys++zhve;.p 1alain.

The magnetic field due to current in i2t12gn1 u x lcr26urmwires in your home can affect a compass. Discuss the effect in terms of currents, including if they arm26nuc1 2tui rr21x gle ac or dc.

If a negatively charged particle enters a region of un,, 3hh0)ybst n/d k zqp:*emmwiform magnetic field which is perpendicular to the particle’s velocity, will the kinetic energy of the particle increase, decrease, or stay the same? Explain your answer. (Neglect gravity and assszn hwq ke0/bd:ypm)t* 3,,hmume there is no electric field.)

In(Fig. Below), charged partij0ae-n.zdke(b6 w. d,pz r6licles move in the vicinity of a current-carrying wire. For each charged particle, the arrow indicates the direction of motion of the particle, and the + or - indicates the sign of the charge.ep0a 6bl ,ze(.n ri.j-k w6ddz For each of the particles, indicate the direction of the magnetic force due to the magnetic field produced by the wire.

Three particles, a, b, and c, enter a magnetic field asp)u vn31gd 3gt shown in Fig. 20–46. What can you say about the charge on each pa gpt1n )3dug3vrticle?

A positively charged particle in a nonunifor. 6y0oml;fs7rybi a u, jnr.3wm magnetic field follows the traject.yri7o 0lrnu.m s,f jy;a3w6b 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 attrop pux .:kwp ddm):;s7act a magnet? Can a magnet attract an iron rod? What must you consider to answer these questsm:o dpud)x:wp k7. p;ions?

Explain why a strong magne+,nkqm0y)deox- ,sma lr5*jo t held near a CRT television screen (Section 17–10) causes the picture to become distorted.5-*romeo mys,x)kq ln+,j0 ad Also, explain why the picture sometimes goes completely black where the field is the strongest. [But don’t risk damage to your TV by trying this.][/But don’t risk damage to your TV by trying this.]

Suppose you have three ir3y jb-pn1f4 jton rods, two of which are magnetized but the third is not. How would you determine which two are the magnets without using any additiotjpy3nf b41- jnal objects?

Can you set a resting ebpz9 dmiw-a*.dx+s vtyl -r86 lectron into motion with a magnetic field? With an electric field? ly p *a 96smrdi8dbvxz+-.t-wExplain.

A charged particle is moving in a circle under the inflxanzer8w)5jfs t d93 5uence of a uniform magnetic field. If an electric field that points in the same direction as the magnetic field is xr3d)5f8esa tw j5z9nturned on, describe the path the charged particle will take.

The force on a particle in a magnetic 55ca dv;d;c defield 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 field. Explain a cdvc5d ;de;5how ions are caused to move. Do positive and negative ions feel a force in the same direction?

A beam of electrons is directed toward a horizontal wire cm7j wd2f,;.k wxu.uyp arrying a current from lwf,pw ;k.d7j ymuu. x2eft to right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magneticrkwl0p (6i ai0 fields that surround a moving electric charge.iai( rk l60wp0

A charged particle moves in a straight line through a particular region of spacen./)p :zm*bu7tu -fnqa3 renr. Could there be a nonzero magnetic field in this region? If so, gzar.nfnu:b7qu )te mnr- p 3*/ive two possible situations.

If a moving charged particlt5fi5eqv +2c*lsj,j pe is deflected sideways in some region of space, can we concludvjjl pcs2q5,ft*5 e+i e, for certain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is a 8j wl. a 1/(.vqyq2ve x,xwu,bk9ufsvuniform 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 czm7fg97ji.ysog 4 g q/ofl9:electrons in a certain region of space are being deflected by an electric field or by a mag4 g.9m7:o/ gs7yfjfq9c z giolnetic field (or by both)?

How can you make a compass without using iron or other fern62eatq swhx/75 u b9 e,8homvromagnetic material?

Two long wires carrying equal cupo): cum6n ,hkauqu8, rrents I are at right angles to each other, but dph, ,)qa o ucknu:mu86on’t quite touch. Describe the magnetic force one exerts on the other.

A horizontal current-carrying wire, free to v92) p:g:mdh+br tmgabb e))kmove in Earth’s gravitational field, is suspended directly above a second, paral dp2kbm:ahb):) etg g )v9m+rblel, 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 ma) c iay)jqllw:p*w2qqlu *yzcy 67.k*gnet attract an unmagnetized piece of iron?

An unmagnetized nail will (m gicp47w* 1 dag*gy1*x-gc)erikrnnot attract an unmagnetized paper clip. However, if one*cpr*i1( *wi my n) ag4-dkxrggc7ge1 end of the nail is in contact with a magnet, the other end will attract a paper clip. Explain.

Two ions have the same mass, but one is singly ionized and t+t :unvrj c cnyxfo0p/33m-y5he other is doubly ionized. How wu0+ 3cf /-5my :cnrxyp3vjt onill their positions on the film of a mass spectrometer (Fig. Below) differ?

What would be the effect on B ipq;bay9 ( u3ky)qhb7knf l,, 2au7f exnside 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 /i4 qdsbzwo f f*+z*t3an 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 switcqsdtf*f+4w / boi*3zzh. A relay is used when you need to switch on a circuit carrying a very large current but you do not want that large current flowing through the main switch. For example, the starter switch of a car is connected to a relay so that the large current needed for the starter doesn’t pass to the dashboard switch.

  (a) What is the magnitude of the force per meter of length on a straigy ed6-(0cbjxms 6 4qrfid-5ssht wire carrying an 8.4 rb i-(ms06sfx6 je-cy4q5dds0-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 (k( 4gqttvx o-of straight wire stretched be(t4- vq toxk(gtween 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 for 8r*uqs 7,piprce on a 160-m length of straight wire stretched betw pq,s*78urpir een 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;njod9+j f o0y long if the maximum force on it is 0.750 N when placed in a uniform 0.0800-Ty0o9njo ;j +fd field?    A

  A 1.5-m length of wire carrying 4.5 A of current is oriented ic rrc0z,es8+:9xp aghorizontally. At that p0az:xsc+rri ,p8 9gceoint on the 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 be6b+5i2qndn k1:xgopm pe 0jj 1tween the pole faces of a magnet. If the pole faces are 55.5 cm in diameter, what is the approximate strength of the magnetic f 2oj m1dpn j:k+6xbeq 1i0n5gpield?    T

  The magnetic force per meter on a wire is measured to be only axu cbg5dlq08r6ctzma3o/ ( 0 35% of its maximum possible value. Sketch the relationship of the wire and the fielxaa( t uccl6gqrdo800 3mzb 5/d if the force had been a maximum, and sketch the relationship as it actually is, calculating the angle between the wire and the magnetic field.    $^{\circ}\,$

  The force on a wire is a mc.q6k ygtug*trvg/ *-vxn t:,aximum 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-diameterzhx9gi*f+f e8 copper wire could just “float” horizontally in air because of the force duz*hf 9g+8 fiexe 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 cmy5x-i9y0 m bdqm n/q gh9w*6zharge $q\,=\,+2e$ 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 force on an electy:+oprwd 1i x)ron 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 eac-v5asae p ;-6m69vzi.yk9rdljul ct4h diagram shown in (Fig. Beloz k6- v ;-9latmas di l9e.jp56r4yucvw), 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 directi r:goxqzj(r hk8 ug0:9on of $\vec{B}$ for each case in(Fig. Below), where $\vec{F}$ represents the maximum magnetic force on a positively charged particle moving with velocity $\vec{v}$.

  An electron is projected vertically upward with a som,xr(a x5a):cye 1 k w0nsof,peed 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 ene*3w:uaqqkn xm 7w)30 lwxq *afrgy) proton enters a 0.20-T field, in a plane perpendicular to the field. What is the radius of i0)q 3*3w xl7 f m:qaxwwu*qknats path?    m

  An electron experiences thqfkl t2(r.rkxq+ (4yye 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 kvy :zvgh91t.hu/. p7c gpgl-a beam of electrons that go undeflected when passing through perpendicular electuhk1vv9 ct:zlhgpy- g/p.g7 . ric and magnetic fields of magnitude $8.8 \times10^{3 }\;V/m$ and $3.5 \times10^{-3 }\;T$, respectively? What is the radius of the electron orbit if the electric field is turned off? $F_E$    $ \times10^{6 }\;m/s$ $F_{max}$   $ \times10^{ -3}\;m$

  A doubly charged helium atomn -w53si zthg6 whose mass is $6.6 \times10^{-27 }\;kg$ is accelerated by a voltage of 2100 V.
(a) What will be its radius of curvature if it moves in a plane perpendicular to a uniform 0.340-T field?    m
(b) What is its period of revolution?    $ \times10^{ -7}\;s$

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

Show that the time T requires pt(h q1,)l.vr;gu tad for a particle of charge q moving with constant speed v to make onp qu,)1tas.h gl;rt(ve circular revolution in a uniform magnetic field $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge q movesk/()5jw6oo egfk czn, (r8t zw in a circular path of radius r in a uniform magnetic field B. Show zonw6kg8 t wokec/ (zj()f5r, that its momentum is p = qBr .

A particle of mass m and charge q moves in a y*doh/t ttbwgcm0khcy905)4 circular path in a magnetic field B. Show that its kinetic etw 5mtg ck)0*4yho90ycdh /tb nergy is proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momentum of the particle in Problem q3*y+7 xhvu1t fs 7cqf21 is $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves with a speed of aui7-lwnm 4h9h1o1o7ap 2des 160 m/s perpendicular to the Earth’s magnetic f-o h1 apo94w2u7 amle hd71sniield 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 equ3,thhf . 9v, spbagyeso7 njon-w:-( tator 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 s5o(wif65x upjq. )g c.x rp0dspeed $\nu=2.0\times10^5\mathrm{~m/s}$ 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 ztd;*0n(/cg1k zbx zvstart a stalled vehicle carries a 65-A current. How strong is the magnetic field 6.0 d znbz/cx (;g0tz 1k*vcm 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 magnetic field no larger th/wtv*pgit;qrs9k (epl ;91dsan that of the E;pt9s l dtp9*egirqv;(1/k ws arth $(0.55\times10^{-4}\mathrm{~Т})$ at a distance of 25 cm, what is the maximum current the wire can carry?    A

In (Fig. Below), a long straight wire carries current I out of the page t 2d 2*4 ;quigll,xdzzxoward you. Indicate, with appropriatell*2dq 2zi;,dg xxz u4 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 caj-i+h3zst4)dfm dpgn g(, t-urrying an upward 24-A current exerts an attractive force per unit len+izpgu, - 3d(ts fh-dn j4tmg)gth 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 tmw -1e6( qlnrj t*ac;swo parallel wires 35 m long and 6.0 cm apart, each carrying 25 A in the same directionqem ln(r-a ;st6*c1jw.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’se:1 v7ss pt:ks magnetic field is being carried out 1.00 m from an electric cable. What is the maximum allowable current in the cable if the experiment iets17 p :v:skss to be accurate to $\pm1.0\%?$    A

  A power line carries a cu ncq0awsq,s63fu+8 is3xhd e 2rrent of 95 A along the tops of 8.5-m-high poles. What is the magnitude of the magnetic field produced by this wire at the groun0sn,su ew3d2+ihx8 6c3fqqsa d? How does this compare with the Earth’s field of about $\frac{1}{2}G$?    $ \times10^{-6 }\;T$ The field of the cable is about    % that of the Earth.(retain two decimal places)

  Two long thin parallel wires 13.0 cm apart carry 25-A currents in the 9)s /wl ihf4 4bgitr/bhmn*7qsame direction. Determine the magnetic field at point P, 12.0 cm from one wire and 5.0 cm from the other(Fig. / w q44bbfn)t9i7hlgs*ihr/m Below).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18 cm due south from a stn-gv,v 5 cgj*kraight vertical wire car*v-g nc,k jg5vrying a 35-A current downward. In what direction does the compass needle point at this location? Assume the horizontal component of the Earth’s field at this point is $0.45\times10^{-4}\mathrm{~T}$ and the magnetic declination is 0$^{\circ}\,$.    $^{\circ}\,$ N of W

  A long horizontal wire carries 22.0 A of current due north. What is the net ur,-tf 8ra pcbmie:+)fi 3k 1umagnetic field 20.0 cm due west of the wire if the Earth’s field there points north but downward, 3ik1b-:rmr ut,e83u+pc iaf ) f7$^{\circ}\,$ 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* i cl/fl3 15)pmbi :ngpgytw0 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 2.0 /5e n1ehoo( syqxt41xvhoq)8cm apart in terms of the current I in one when the othe5 et (/ 8x)q4vxooys 1no1qhher 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 insm4x 2l h)*pw ti6r3xsftrument. If the insulated wires are of negligi3x* )x6mpl2ihr4 fs wtble 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 of the Earth.
   $ \times10^{-6 }\;T$ The field of the wires is about    % that of the Earth.(retain two decimal places)

  A third wire is placed in the plane of the two wires shown in (Fig. Below), a7oo8p 0x t0vrparallel 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 two wires? Assume o 70xpto a0v8rit 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 poinfad; t boq*6.8tm ytv,n0v; hets 23$^{\circ}\,$ E of N outdoors. However, when it is placed 12.0 cm to the east of a vertical wire inside a building, it points 55$^{\circ}\,$ E of N. What are the magnitude and direction of the current in the wire? The Earth’s field there is $0.50\times10^{-4}\mathrm{~T}$ and is horizontal.    A  ----待选择----updown 

  A rectangular loop of wire lies in the same plane as a straighl+cf a /bgx(t1t wire, as shown in (Fig. Below). cfgx+ltb a 1/(There is a current of 2.5 A in both wires. Determine the magnitude and direction of the net force on the loop.    $ \times10^{ -6}\;N$  ----待选择----away from wiretowards wire 

  A long horizontal wire carries a current of 48 *xbhu5p )iz5tA. A second wire, made of 2.5-mm-diameter copper wire and parallel to the first, isp it hb*)ux5z5 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 aruzj lpf-kvd0c 5--(qqe perpendicular to each other. At their closest, they are 20.0 -upz5c- ( l kd-jvq0qfcm apart (Fig. Below). What is the magnitude of the magnetic field at a point midway between them if the top one carries a current of 20.0 A and the bottom one carries 5.0 A?    $ \times10^{-5 }\;T$

  Two long straight parallel wires are 15 cm apart. Wire A carrk 7lolp9vs)73w h;x) rjyuimd r+5, dkies 2.0 A current. Wire B’s cu9s5 p) udrw7yh o7ik;k +d,xl ml)jv3rrrent is 4.0 A 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 olm5)6:h t1.j: gc anjonfl3tare 3.8 cm from one another. (Looking along them, they are at three corners of an equilateral triangle.) The current in etl61n .5o3cfga:l n:o jhtj)mach 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 magni :mqvu/llmodl.q :,rcr 9g0qe)q f5l5 tude and direction of the magnetic field at the midpoint of the side of the tril 0r lgc/ef.u dqq)r::mo lqv59,mlq5angle between wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a distance d apart, carry equal currents I in thhst07bqy gi8b2u i5 mlh01p9he same direction. One wire is at x = 0, the other is at x = d, (Fig. Below). Deb7 uh tib8qmpl0g shh29 105iytermine $\vec{B}$ 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 wirgq5 /alqqafiab 140evw9oi ;.e and carries a current of 5 q1o./0q ;bi 9a 4qlawaeifvg2.0 A. Calculate the field inside near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameter is cr(*gds) (d 2tw) buq5wd sm;oto produce a field of 0.385 T at its center. How much currewg w2dqob*csm;(5d( d) r us)tnt should the solenoid carry if it has 975 turns of the wire?    A

  A 550-turn solenoid is 15 cm long.omawkir 4*63gptkk6 (7 2ksa l 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 wik3 o sl r6k agm27tkp*iwak4(6res that don’t concern us). What is the force on this wire assuming the solenoid’s field points due east?    N

You have 1.0 kg of copper and want to make a practicagaet : ; w3gp-ilnak81l solenoid that produces the greatest possible magnetic field for aga3ilt -a 1eng:wpk;8 given voltage. Should you make your copper wire long and thin, short and fat, or something else? Consider other variables, such as solenoid diameter, length, and so on.

A toroid is a solenoid in the shaa8 y2z s(cjua6pe of a circle (Fig. Below). Use Ampère’s law along the circular path, shown dashed in (a jayu 8s62zc(Fig. Below 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 ma o e(*q1n9wcqpgnetic field between the conductors of a coaxial cable (nqqocp * w91e(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 ishiy7-d(6(:1ll fetr)th 2)zfgv w lzh placed with its face parallel to the magnetic field between the pol-hl wrz1dfy7zh:tlt2 f )l6ih)(e v(ge pieces of a large magnet. When 6.30 A flows in the coil, the torque on it is $0.325\cdot N$. What is the magnetic field strength?    T

  A galvanometer needle deflects full scale fr57(fdgm mo 9qao-d u0or a $53.0 -\mu A$ current. What current will give full-scale deflection if the magnetic field weakens to 0.860 of its original value?    $\mu A$

  If the restoring spring of a galvanometer weakens by 25% over *czz.+a 2jt;xm )5btprwc u0qthe years, what current wrpbtx0 25z.jcucw zq+t;)m a*ill give full-scale deflection if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, be 0);ubumfh52 az ,erdy what factor does the output torque changeb0 uh)5;,emuz f2r dae?

Show that the magnetic dipole moment M of an electron orbitingr)(p9 p4hnhqt* mjm;v the proton nucleus of a hydrogen atom is related to the orbital angular moqpn 4*hj(vm) htp r9;mmentum L of the electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter and containing nine loops liap cd1w63 fc e6(b3x8 wcdvln2es flat on the ground. The Earth’s magnetic field at this location hfc(w v1w d 62a3nbl8 xpcce6d3as 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 0.5r( nrnmn*ia89 66-T magnetic field. What valunr (mia8*n n9re of electric field could make their paths straight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atoms have radiibkl hwr: b /9)+.bnoamx8xospb 5,h m91kv3ix of curvature equal to 21.0, 21.6, 21.9, 22.2, and 22.8 cm. Theri3x,+/ml bvb.51x8nhaoxhmsw ok) 9:kp 9bb largest radius corresponds to an atomic mass of 76 u. What are the atomic masses of the other isotopes?

  Suppose the electric field betweene .dip;1hf:tg the electric plates in the mass spectrometer of (Fig. Below)1pet: ;d hif.g is $2.48\times10^4\mathrm{~V/m}$ and the magnetic fields $B=B^{\prime}=0.68\mathrm{~Т}.$ The source contains carbon isotopes of mass numbers 12, 13, and 14 from a long-dead piece of a tree. (To estimate atomic masses, multiply by $1.67\times10^{-27}\mathrm{~kg.}$)
How far apart are the lines formed by the singly charged ions of each type on the photographic film?
$2r_{13}$ - $2r_{12}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)
$2r_{14}$ - $2r_{13}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)
What if the ions were doubly charged?
$2r_{13}$ - $2r_{12}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)
$2r_{14}$ - $2r_{13}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)

A mass spectrometer is being used to monitor air pollutai+(2evig:)onpq qi /b :kherx m 8n1w:nts. It is difficult, however, to separate molecules with nearly equal mass (8qvx:+o irhkn): :w2/ i nmgi eeq1pbsuch 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 accele jc8p9co6)l)hm .yuo- :muu5xl8sch crates ions by a voltage V before they enter a magnyl 6mh 8cc.umcso-o ju) 85):hxcplu9 etic field B. The ions are assumed to start from rest. Show that the mass of an ion is $m=qB^2R^2/2V,$ where R is the radius of the ions’ path in the magnetic field and q is their charge.

  A long thin solenoid has 430 loops of wire per meter, and a 25-A cu 6xu4 +4wrh xel6vho3urrent flows through the wire. If the permeability of the irooxe6h xl43u6 w+4rhvun is $3000\mu_0$ what is the total field B inside the solenoid?    T

  An iron-core solenoidmuklyud3, a:1lf;k 3 + bjuqu. is 38 cm long and 1.8 cm in diameter, and has 640 turns of wire. The magnetic field inside the solenoid is 2.2k33alu u+;1 q:ydlfu .jmu ,kb 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 vgy+vsu.ks/mm o.dc4+p n . ;p$4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 babf+w- /jk/c energy upon entering a region of constant magnetic field. What is the ratio of the radii of their circ kabcfjw+b/- /ular paths?   

  The power cable for an electric trolley (Fig. Below) carries;7s qq -vbha)-ud3yfhdu 3(jk a horizontal current of 330 A toward the east. The Earth’s magnetic field has a stb h3-37sqdjuk)fu y(ahq-; dvrength $5.0\times10^{-5}\mathrm{~T}$ 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 .1dh+ 4gwevr6 f)*ib:b ovf2vt9axgznet charge of $1550\mu C$ and moves with a speed of 120 m/s perpendicular to the Earth’s magnetic field of $5.0\times10^{-5}\mathrm{~T}$.    $ \times10^{-6 }\;N$

  Near the equator, the Earth’s magnetic field points almost ho k f3zslc;pe9(6cm3 yerizontally to the north ak; 9sc3pmye(f 3lzc6 end 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 tz* d)tbd +kzs-wa yzvhh.1/.is $6.6\times10^{-27}\mathrm{~kg},$ is accelerated by a voltage of 2400 V.
(a) What will be its radius of curvature in a uniform 0.240-T field? $\approx$    m (retain three decimal places)
(b) What is its period of revolution?    $ \times10^{-7 }\;s$

  A sort of “projectile launcher” is shown in (Fig. Below). A1tdtzgy/uv 21 akwg3 + large current moves in a closed loop composed of fixed rails, a power supply, and a very light, almost frictionless bar touching thu23yzv 1wa t gk+/1gdte rails. A magnetic field is perpendicular to the plane of the circuit. If the bar has a length L = 22cm, a mass of 1.5 g, and is placed in a field of 1.7 T, what constant current flow is needed to accelerate the bar from rest to 28m/s in a distance of 1.0 m? In what direction must the magnetic field point?
   A
the magnetic field must be ----待选择----updown 

  In (Fig. Below) the top wire is 1.00-mm-diameter copper wire yn,hsu; 63tnem.jdlvw (.k v;and is suspended in air due to the two magnetic foj us.v ;nltkv, y3;h6dmwen( .rces 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 w/ 1yjo53ks hzzp8aw w7ires a distance l apart in a horizontal plane act as rails to supportoz z7/3aksh 5wy8p1 wj a light 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 defl3/:xl* x0qwt mxm/ nraection of the electron beam near the center otx/axw* xl3 /nm:qm r0f 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 to accelerate elementaryw2t:w mbqy j27y;a-hb 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 h; 2ytaybjwb :-mw2qh 7ollow metal dees.) The electric field changes direction each half-cycle, owing to an ac voltage $V=V_0\sin2\pi ft,$ so that the particles are increased in speed at each passage through the gap.
(a) Show that the frequency f of the voltage must be $f\,=\,Bq/2/pi m,$ where q is the charge on the particles and m their mass.
(b) Show that the kinetic energy of the particles increases by $2qV_0$ each revolution, assuming that the gap is small.
(c) If the radius of the cyclotron is 2.0 m and the magnetic field strength is 0.50 T, what will be the maximum kinetic energy of accelerated protons in MeV?

Four very long straight parallel wires, located at the corners ovwj(,z i)2hia)k qz8v f a square of side l, carry equal curre, )i 8v vwzqhi2)jkz(ants $I_0$ 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 xxhtrh.xb 5r8g8/g.g in particle 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. Whabrhxg.5grx./xht g88 t 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 4ti k,dz2a0xe.(no(nt, t z bsthe center of a circular coil of wire carrying a current I (as in Fian.tk,etnt2z ( ,4(xbsdozi0 g. 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 xqmw1-b;ut 7 p9eqqf8( -q zwzthe 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 bg6f,u1 uq8*q;olzjssz7 4 mx cy overhead power lines. You estimate that the two wires are each about 30 m above the ground and are about 3 m apart. The local power company tells you that t7, g; c14zol xqzu* sqsjmuf86he 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 b1eigc*. f7 jodeam of electrons, traveling to the righ.d7efg oi *jc1t 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 a magnetic field of 0.01 c+2plod ws+4r0 T, perpendicular to the plane of the spiral, as shown in (Fig. Below). In two successive loops, at points P and Q, 2dslwco4r + +pthe 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 (6 7hpdu;vdvw in diameter, is to produce a 0.30-T magnetic field at its center. If the maximum cwd 6uvh (7pd;vurrent 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 the su. lw z*z0;qleame current but in opposite directions. They are suspended by 0.50-m-long strings as shown in (Fig. Below). Ifl 0z.ul ;*zqwe the suspension strings make an angle of 3.0$^{\circ}\,$ with the vertical, what is the current in the wires?    A

  An electron enters a uniform magnetic field B = 0.23 T tgiprel6d-hd: p9 6o-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$