A compass needle is not always balanced parallel to the Earth’s surface ;c yoat5ptjupsps4rh rw)*p/q67q 51, but one end may dip downo/;t146hau5qjq prpspc p 7y5 s*rw)tward. Explain.

Draw the magnetic field lines around a straight secti*/u+urz5fc+ -+ fufquji er,lon of wire carrying a current hj+q-+/z* rcrueuffif+l,u u5orizontally to the left.

In what direction are the magnetic field lm; gh,w.4bp iputiv i041xhi3ines surrounding a straight wire carrying a current thati, 4 pm3g;xbihw1p.ihutv4 i0 is moving directly away from you?

A horseshoe magnet is held vertically wb5;.lmsbgc 0zj,y1xj ith the north pole on the left and south pole on the right. A wire passing between the poles, equidistant from them, carries a current directly away from you. In what direction isjmsg.c y;05, l jxbz1b the force on the wire?

Will a magnet attract any metallic object, or only y; zqg:k9b p njusnt2)4)ankp8a(q;tthose made of iron? (Try it and see.) Why iz;9);q nn y8ag tqanp) kbusk24p:j(ts this so?

Two iron bars attract each oth-y8dac *aaqg+ e*qk+*)at ul 7iepn*fer no matter which ends are placed close together. Are both magnets?i7fncuq8ad**q*kt+*apl a) y -+eg e a Explain.

The magnetic field due to currgwc wwtorv/ . (npw5g5 )4thm8ent in wires in your home can affect a compass. Discuss the effect in terms of currents, including if they are ac or dc.ht r m/wwo.w5w)8cvp t45(ngg

If a negatively charged particma gg4xlm*63jle enters a region of uniform magnetic field which is perpendicular to the particle’s velocity, will t m*jm6g xalg34he kinetic energy of the particle increase, decrease, or stay the same? Explain your answer. (Neglect gravity and assume there is no electric field.)

In(Fig. Below), charged particles move in the vicinity of a cure8*l3xi rvaba1) +v kvrent-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 particles, indicate the direction o1iv+ )bx*klv er83vaaf the magnetic force due to the magnetic field produced by the wire.

Three particles, a, b, and c, enter a magnetx4n ) mycaq;d5ic field as shown in Fig. 20–46. What can you say about )admx5cn 4y;qthe charge on each particle?

A positively charged particle in ak.f jq6l a80gkdxia7c xt 19j:kpn9n8 nonuniform magnetic field follows the trajectory shown in k:jixx8fa9 9. c7kjagd 81pnnkt 6 ql0
(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 magn(i o/4oreou; cet? Can a magnet attract an iron rod? What must you consider to answer these quoe(ur/ i;ooc 4estions?

Explain why a strong magnet held near a gz ;*onziw,c +CRT television screen (Section 17–10) causes the picture to become distorted. Also, explain why the +gi;*nzzow c, 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 iron rods, twoktr/v8p5;q sy y- 0vvs of which are magnetized but the third is not. How would you determine which two are the magnets wvk0; q-v85rvpy s/sytithout using any additional objects?

Can you set a resting electron into bh0/a9e3q w s /: kcoyus(r.x85v0dphmnpt-wmotion with a magnetic field? With an electrie dhp8ta(mn.srp sob/wu qv yx-9hw0/k 0 :53cc field? Explain.

A charged particle is moving in a circle under the influence ofnlm2mr ,sebkzw*0 h ;( a uniform magnetic field. If an electric field that points in the same direction as the * mznk,(rml eb2;w0shmagnetic 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 electrom y hcrzih6.+ 6com3ttu6 +xm-xagnetic 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 how ions arerim.x 6y x+-th+6 63tchcmuzo 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 carrying a current froq y/v xeu(b2:hm left to rigeq (:byh2xu/vht
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields that sy,(byuejp21o x- pt;turround a moving electric charge.p ,o2u;jt ytep 1(bxy-

A charged particle moves in a straight line through a particzik rg 2(fri+l 3 hn;d;etv97dular region of space. Could there be a nonzero magnetic field in this region? I (n27kidf det glri;rv9+3h;z f so, give two possible situations.

If a moving charged partik6h6smsxd 61 p q2ul7cb:q6gt cle is deflected sideways in some region of space, can we conclude, fpt:66b17sh6gxl6 ksmqucqd2 or certain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of spacehc,b;sag2c 2r there is a uniform magnetic field $\vec{B}$. Outside this region, B = 0 Can you inject an electron from outside into the field perpendicularly so that it will move in a closed circular path in the field? What if the electron is injected near the center?

How could you tell whet8x 05:5zcpwyizt.fip(dkcf -ki :)kl her moving electrons in a certain region of space are being deflected by an electric field or by a magnetidif:lzt8pfw z:kyix -5i)kk. cpc0(5c field (or by both)?

How can you make a compass without using iron or other ferroma5hjruq + 6a p7y w+4gs7r13t wm 0veivccmi9w)gnetic material?

Two long wires carrying equal currents I are at right angles to each other, bukcf w9r09t f0td/jl3 yt don’t quite touchtt k390f9w/rjlcyf0 d . Describe the magnetic force one exerts on the other.

A horizontal current-carrying wire, y0j./* 4bpmsz kl t5xi0 ngje 5bu1d5cfree to move in Earth’s gravitational field, is su55p5ynm .sl1c0i/*dtb zxbg4 0k ejj uspended directly above a second, parallel, current-carrying wire.
(a) In what direction is the current in the lower wire?
(b) Can the upper wire be held in stable equilibrium due to the magnetic force of the lower wire? Explain.

Why will either pole of a sm */h p/txclhddo1o 0w +yf))magnet attract an unmagnetized piece of iron?

An unmagnetized nail will not attract an unmagnetized paper clip. However, if on:2ty8fbp2wo zx ykt4 :+h xwz7e end of the nail is in contact with a magnet, the other end will attractwx x4zkf h:wy8boz+2ytp2: 7t a paper clip. Explain.

Two ions have the same mass, but one is singly ioniqrg;;lu7h v r6/klkd; zed and the other is doubly ionized. How will their positions on thlh;k;;/rg qv du6rl 7ke film of a mass spectrometer (Fig. Below) differ?

What would be the effect on B inside a long solmg3rapofadxut. )9 nc+u hub hq6c,3. 1:f1wgenoid 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 relayzc f0j7 71g3d nyi9 l9eds0wnt . A relay is an electromagnet (the irogfscd 3l1yjz97nn 9 d0et7w0in rod inside the coil does not move) which, when activated, attracts a piece of iron on a pivot. Design a relay to close an electrical switch. A relay is used when you need to switch on a circuit carrying 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,(tusn l2,duu ki5b:s a straight wire carrying a(2s5 u:,nu,bisl dkut n 8.40-A current when perpendicular to a 0.90-T uniform magnetic field?    N/m
(b) What if the angle between the wire and field is 45.0$^{\circ}\,$?    N/m

  Calculate the magnitude of the magnetic force on a 16c/thr-p1hkt30i9 q gk0-m length of straight wire stretched between two towers carrying a 150-A curre19r/0-kq3k c tti hphgnt. The Earth’s magnetic field of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  Calculate the magnitudrx15hsu(wy 3f yn mgm x7u8,k,e of the magnetic force on a 160-m length of straight wire stretched beygmnx,kx1 8hs, uw 3ur(yf 5m7tween 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 long if tha99z49fa/fxuf-5sn f xyr90iiq w m,v r0c.fqe maximum force on it is 0.750 N when placed in a uniform 009i 0uqzxsfq f/mn5i4a 9r9frc.f,ax vw -yf9.0800-T field?    A

  A 1.5-m length of wire carrying 4hw5knp1.s.l h .5 A of current is oriented horizontally. At that point on the Earth15hknhwlp.. s’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 cav.3;lftt- ab brrying 8.75 A is a maximum of 1.28 N when placed between the pole facl-bf ; ttvb.a3es of a magnet. If the pole faces are 55.5 cm in diameter, what is the approximate strength of the magnetic field?    T

  The magnetic force per meter on a wire*ya5g h +ocz up:gflg j,,c(,urspt 5qlk9v 67 is measured to be only 35% of its maximum possible value. Sketch the relationship of the wire and the field if the force had been a maximum, and sketch the relationship as it actually is, calculating the angle between the wire a(lqo gtu z+rc g69j55h,, ypca7ku lgs, f*pv:nd the magnetic field.    $^{\circ}\,$

  The force on a wire is a maximum e,: )s,y-cn7qanlklm 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 “floatb.0ftp9yrp,*g b)gv/r mzrv/” horizontally in air because of the fov y.9,p rgtf*/r gb)mbr/z0vp rce due to the Earth’s magnetic field $\vec{B}$, which is horizontal, perpendicular to the wire, and of magnitude $5.0 \times10^{ -5}\;T$. What current would the wire carry?    A Does the answer seem feasible? Explain briefly.

  Alpha particles of chunbw n:.z3 v8farge $q\,=\,+2e$ 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 o3mcafi/rbp17,wi +d 9ki* zakf 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 forcsy 2y3etd :2lse on a negative charge for each diagram shown in (Fig. Below), wheresly2: e23sty d $\vec{v}$ (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 f.)/7r0l wg uabv0vjuon 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 spcts /opu)yputi : w3igm5 4z1fh8;7sheed of $1.7 \times10^{6 }\;m/s$ into a uniform magnetic field of 0.350 T that is directed horizontally away from the observer. Describe the electron’s path in this field.    $ \times10^{-5 }\;m$

  A 5.0-MeV (kinetic energy) proton enters a 0.20-T fieldp-7 ;dy rmv7yb, in a plane perpendicular to the field. What is the radidv-7rp y;b7y mus of its path?    m

  An electron experiences the greatest force as it 3p0t-ee1m3h 6cltyc /vyhl8 wtravels $2.9 \times10^{6 }\;m/s$ in a magnetic field when it is moving northward. The force is upward and of magnitude $7.2 \times10^{-13 }\;N$. What are the magnitude and direction of the magnetic field?    T ----待选择----EastWest 

  What is the velocity of a beam of electrons that go undeflected when paddcd;gj w1;/9 b10w jv amtj.essing through perpendicular electric and mjwa1dd 9/;mgv.bcj d1wj; te0agnetic fields of magnitude $8.8 \times10^{3 }\;V/m$ and $3.5 \times10^{-3 }\;T$, respectively? What is the radius of the electron orbit if the electric field is turned off? $F_E$    $ \times10^{6 }\;m/s$ $F_{max}$   $ \times10^{ -3}\;m$

  A doubly charged helium atom whose mass i 7ccwm6w/ : /(pqrw ;bk/msvzks $6.6 \times10^{-27 }\;kg$ 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 require g1gkfb1pctm. a2pm39 d for a particle of charge q moving with constant speed v to make on9 1.gpgfkc2a 31btm pme circular revolution in a uniform magnetic field $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of chargec v gk 6ezq*.j8;gwkc,;s5keb1-khg c q moves in a circular path of radius r in a uniform magnetic fi5ke qg;8kk1s,cgk.*cc6;h eg -wzbjveld B. Show that its momentum is p = qBr .

A particle of mass m and charge q moves in a circular path inf3 fxcm: uc33m+* n qosh2)yjoby+6uu a magnetic field B. Show that its kinetic eneyu6ob qfh*umc+3 +2 nucx)3m :jyof3srgy is proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular mk4vnvk vd6vdpg5 y.znk7c-qq9 c3ssbgp)(;8 omentum of the particle in Problem 21 is $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves with a speed of 160 m/s perpendicular to the 9hjy:v,awiq-*s cwd-)e; paa Earth’s magnetic field of hc) -;idajw9ap v*-a y,e :qws$5.00\times10^{-5}\mathrm{~T}$, 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 nw*jil23d f* nmagnetic field 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 kgvgmu f v;*j,bdp 6/,speed $\nu=2.0\times10^5\mathrm{~m/s}$ 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 tot)n;qv-z(v xl-qq y47:6m b z:ymyrsz start a stalled vehicle carries a 65-A current. How strong is the magnetic fielxq- z 6:mbv 4z)t :svzl;qm(ry7n-qyyd 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 magnetic field no larger ggw1joo:y ( 96b2krjtombc 4(than that of the b y6 gtr4b1o o:2cw(g(k jom9jEarth $(0.55\times10^{-4}\mathrm{~Т})$ at a distance of 25 cm, what is the maximum current the wire can carry?    A

In (Fig. Below), a long straight wire carries cdb k7b,y .cyj x j g-w.9styv/zlck+51urrent I out of the page toward you. tlx-jb c9.ywd.7j+yv5 b c/1kk ,yszgIndicate, with 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 carrying an upward 24-A current exerts an att t q)nvcq5(:zrractive force per unit length )zqc: qv5tr(nof $8.8\times10^{-4}\mathrm{~N/m}$ 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 thexz (r1lp*dl b5*d3 jcr force between two parallel wires 35 m long and 6.0 cm apart, each carrying 25 A in thdrb1 ldc* (l* xrz3j5pe same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic field is being carried fij0izsic/, jw ) 9g0mout 1.00 m from an electric cable. What is the maximum allowable current in the cable if the experiment is to be accuratem jsizj9) /if,0 iw0cg to $\pm1.0\%?$    A

  A power line carries a current of 95 A along the tops of 8.5-m-high polesd9zt9) 7 s1a jxvwi,gt r32qy(hjpsb,. What is the magnitude of the magnetv,bz9j2 x(sa )3j7t,giqdywr p h1s t9ic 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 lex6qv;mv )gy((a-cg apart carry 25-A currents in the same direction. Determine the magnetic field at point P, 12.0 cm fromae6(g v cvqxg;)l(m-y one wire and 5.0 cm from the other(Fig. Below).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18 .p.nspp1vbq . 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? Assume the horizontal component of the Earth’s field at this pqb.psv .p.np1 oint 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. Whalok*w9 x+c2nak 8 hf7j9g cq:at is the net magnetic field 20.0k9 fg:k7aaj*l xnwc 2c+q h9o8 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 pr1ul*kxyg1muj23kp fc+0rjh4 otons 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 magneticpl3 06rms 5odu1,lv af field midway between two long straight wires 2.0 cm apart in terms of the current I in one when the other carries 15 A. Aurl 0 1md,o5fav 6psl3ssume these currents are
(a) in the same direction,
(b) in opposite directions.

  A long pair of wires cond)pfza*rgse4 3 l su,+ij8rxp5ucts 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 field 10.00 cm frr83)l*gpsaez, xp 5+4isj ruf om 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 y-1 a+i3w6l juisfk,p pw;9bgplane of the two wires shown in (Fig. Below), parallel and just to the rig6pw-bf31;w iy pg k,ia9s j+ulht. If it carries 25.0 A upward, what force per meter of length does it exert on each of the other two wires? Assume it is 2.8 mm from the nearest wire, center to center.
$F_{near}$ =    $ \times10^{ -2}\;N/m$  ----待选择----attractrepel 
$F_{far}$ =    $ \times10^{ -2}\;N/m$  ----待选择----attractrepel 

  A compass needle points r(uwg6p; k+yh7tln(p23$^{\circ}\,$ 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 straight whu*d56s ttl g-ire, as shown in (Fig. Below). There is a current of 2.5 A in both wires. Determine the magnitude and directio6udt-h t*l5gs n 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, r/:p*g1z) w+8sj*h bkbkbbfomade of 2.5-mm-diameter copper wire and parallel to the first, is kept in suspension magnetically 15 cmb+w8khpb1 jfz /k o *:*gsbrb) 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 n- juj-k zwvg69xcoi 2* *qv+rthey are perpendicular to each other. At their closest, they are 20.0 cm apart (Fig. Below). What is the magnitude of the magnetic field at a point midwaygjr*6zu x v -c+ji-okq*nw2v9 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 carries 2.0 A current7or lwlop7 -n,oi ,:yr. Wire B’s current is 4.0 A in the s7,pr7in:o- yr, olwloame 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 3.3 t3ai5 zu6wbs8 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). Determine the magnetic force per unit lenw za ib5sut633gth 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 magnicf t a42kdgqs-5a; 8*u rn mm3kqjz/)stude and direction of the magnetic field at the m*48z d qmucaq2 k3akfrjs;s n/ g-t5m)idpoint of the side of the triangle between wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel;b5ofds7qo3w u 4 e(yn wires, a distance d apart, carry equal currents I in the same direction. One wire is at x = 0, the other if5;o4 ewbd3s(u o qyn7s at x = d, (Fig. Below). Determine $\vec{B}$ along the x axis between the wires as a function of x.

  A thin 12-cm-long solenoid has a total of 420 turns of wire and carries a curren lr(wq(7sgk4hc /,5z2htvy:8eryfm at of 2.0 A. Calculate the field inside n(w y/z hl,graem:5 fvk428qyrt(sh7cear the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameter is to produce 6x3 q8 fxty4kzx4kms9w(hl7 k a field of 0.385 T at its center. How much current should the sols 9k64wtqkm xzkhx4xf7 3ly8(enoid carry if it has 975 turns of the wire?    A

  A 550-turn solenoid is(io2h3jx/ j q9azz: mjh .xg5v 15 cm long. 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 connect/a9mg2.(h jo5 z hz:xvjj ix3qed by other wires that don’t concern us). What is the force on this wire assuming the solenoid’s field points due east?    N

You have 1.0 kg of copper and want to mai0g 2* -4fmyilcx8nvviq 05q eke a practical solenoid that produces the greatest possible magnetic fig*fic iq 2nyv 45le0-0xvq8mield for a given voltage. Should you make your copper wire long and thin, short and fat, or something else? Consider other variables, such as solenoid diameter, length, and so on.

A toroid is a solenoid in the shape of a circle (Fig. Below). Use Ampère’s lawr rl(v.)2 buc10rw7tckp rkc; along the circular path, shown dashed in (Figt;wpckrc() uv0rkr21 l.rcb 7. 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 magnetic field between the co s3i 5luh ifnh;uf;*2knductors of a c i3k2hluh; is f;uf*5noaxial cable (Fig. Below) is $B=\mu_0I/2\pi r$ if r is greater than the radius of the inner wire and less than the radius of the outer cylindrical braid.
(b) Show that B = 0 outside the coaxial cable.

  A single square loop of wi6 jdr*lg81os;un v )mire 22.0 cm on a side is placed with its face parallel to the magnetic field between the pole pieces of a large magnet. When 6.30 A flows in the coil, th jrs n*1gud86)i mv;ole torque on it is $0.325\cdot N$. What is the magnetic field strength?    T

  A galvanometer needle deflects full scm+byw*q4disexzt9 s1r5y -p /ale 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 galvanol f,6ffwh fcyg c1; wabg;6d. f*fvr74meter weakens by 25% over the years, what current will give full-scale deflection if itbah gf f7 dfr6; wgv1,ccyf46 w;f.f*l originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by what factor does the 4agodsn88j ; nr p16c9+ lx m1i6jqceloutput torque changn; jncp6 x8+6ij 8g corms19d qll4ea1e?

Show that the magnetic dipole moment M of an electron owt: kzui;9ku6 rbiting the proton nucleus of a hydrogen atom is related to the orbital angular momentum L of the ele 6wk;iz9k:utu ctron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter and containd g / n7psg5(jjyyz*5ging nine loops lies flat on the ground. The Earth’s magnetic field at this lo*(yd7ggy5j sjp / nzg5cation 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-T magnet 7h 3jf tcmsob.:+1ci-ucp r3bic field. What value of electric field cocp1jcb o73s3.hf cmi: ru-bt+uld make their paths straight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atoms ha 88orbxczu2qs-yf164 xe x0nnve radii of curvature equal to 21.0, 21.6, 21.9, 22.2, and 22.8 cmryzns- 40f x2u81cqbenx 8xo6. The largest radius corresponds to an atomic mass of 76 u. What are the atomic masses of the other isotopes?

  Suppose the electric field between the electric plates in the massb (d syb hvb-l:c7460sh5 igca spectrometer of (Fig. Be(cha5 y47ihcvs:b-g 6sbb0l d low) 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 fdp fh )q60au.air pollutants. It is difficult, however, to separate molecules with nearly equal mass suchdu 6haf.fq)0p 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 iontfs2ht+ fo9vbv5u )-xisw7e2s by a voltage V before they enter a magnetic fieldvxiufe7 h+2o5 s 2tw-9fst)bv 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,2rpjj1 qn1 7kte,bo ox*+eu2f and a 25-A current flows through the wire. If the permeability of the iron is joe1uqr2 f7tnx,+p2bj*k o1e $3000\mu_0$ what is the total field B inside the solenoid?    T

  An iron-core solenoid is 38 cm long andt nnj8;1)0 2raq4qtjol 0; -peulfwbq3n t t0c 1.8 cm in diameter, and has 640 turns of wire. The magnetic field inside th ft0qoeb c0unw;0l rnpa-2jtjq;3q8l ntt 4 )1e solenoid is 2.2 T when 48 A flows in the wire. What is the permeability $\mu$ at this high field strength?    $\times10^{-5}\mathrm{T}\bullet\mathrm{m/A}$

  Protons with momentumr-ab9t f-:m mh $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 s k+1;sf8ltxerame kinetic energy upon entering a region of constant magnetic field. What itkl sex8rf+1 ;s the ratio of the radii of their circular paths?   

  The power cable for an;v 70, rzlqo5c .y d-tbr urff3wj2,vw1rb:f e electric trolley (Fig. Below) carries a horizontal current of 330 A towtufv7;2w.,o5l: c r 1r w0bvy 3f,jfr rebq-dzard the east. The Earth’s magnetic field has a strength $5.0\times10^{-5}\mathrm{~T}$ and makes an angle of dip of 22$^{\circ}\,$ at this location. Calculate the magnitude and direction of the magnetic force on a 15-m length of this cable.    N the force on the wire is  ----待选择----southerlynortherly  and   $^{\circ}\,$ above the horizontal .

  Calculate the force on an airplane which has acquie;4d g .ec6vvored a net charge of $1550\mu C$ and moves with a speed of 120 m/s perpendicular to the Earth’s magnetic field of $5.0\times10^{-5}\mathrm{~T}$.    $ \times10^{-6 }\;N$

  Near the equator, the Earth’s magnetic field pkv0t.b3d :pl/mka +hzoints almost horizontally to the north and has magnit. vz +kptk0:madlb h3/ude $B=0.50\times10^{-4}\mathrm{~T.}$ 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,xn;qr xd,b73aubp z 9k897kwr whose mass is $6.6\times10^{-27}\mathrm{~kg},$ is accelerated by a voltage of 2400 V.
(a) What will be its radius of curvature in a uniform 0.240-T field? $\approx$    m (retain three decimal places)
(b) What is its period of revolution?    $ \times10^{-7 }\;s$

  A sort of “projectile launcher” is shown in (F1bps-ku;a v*z(hs 2vyig. Below). A large current moves in a closed loop composed ofhp1av 2ky;s*b- uzsv( fixed rails, a power supply, and a very light, almost frictionless bar touching the rails. A magnetic field is perpendicular to the plane of the circuit. If the bar has a length L = 22cm, a mass of 1.5 g, and is placed in a field of 1.7 T, what constant current flow is needed to accelerate the bar from rest to 28m/s in a distance of 1.0 m? In what direction must the magnetic field point?
   A
the magnetic field must be ----待选择----updown 

  In (Fig. Below) the top wire is 1.00-mm-diameter copper wire and is suspended iq8mj5/kf5 xfxo/j* utn 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 suspended wirf8j/f oq ujmtx55*/x ke.    A

Two stiff parallel wires a dista qumi.xsy1 ga 4)e nuzqevd/1 6l73g4unce l apart in a horizontal plane act as rails to support a light metal rod of mass m (perpendi6sn11 meqvg.axl4uq/)i4g u7 yz3eu dcular 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 deflecti)l4jpswrypf) ps2d7 mme7 le 8e;d.8uon of the electron beam near the center of a TV screen due to the Earth pe pfl8d78ls)4w)72.y u premm;jsde’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 kk7drjlt. ,;mf-e3e mused 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.d jfe,klr;7-3memt k is no electric field inside the hollow metal dees.) The electric field changes direction each half-cycle, owing to an ac voltage $V=V_0\sin2\pi ft,$ so that the particles are increased in speed at each passage through the gap.
(a) Show that the frequency f of the voltage must be $f\,=\,Bq/2/pi m,$ where q is the charge on the particles and m their mass.
(b) Show that the kinetic energy of the particles increases by $2qV_0$ each revolution, assuming that the gap is small.
(c) If the radius of the cyclotron is 2.0 m and the magnetic field strength is 0.50 T, what will be the maximum kinetic energy of accelerated protons in MeV?

Four very long straight parall0mz)rl9i-f zfoar4y .el wires, located at the corners of a square of side l, cly-0 .aomifz 49f rzr)arry 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 accelerators for “be41zyf m9o 27o*qliu (c0u lluhqe;)vf am steering”; that is, the magnetic fields can be us1fq femyuo72uiolc 40( ;h) lu*lzqv9 ed 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 a beam of protons traveling at $ 1.0\times10^{7 }\,m/s;$ be bent?    $^{\circ}\,$

  The magnetic field B at the center of a circulu t b2s m-tjj4:.9wkgopnw 5*/ngs6cpar coil of wire carrying a current6-m4p *j/.k tbswwcn g2n95jt:sg po u I (as 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:ty(1tjhsini;b dir 1 60 g ivf2dv;*b 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 u8c kb9coxz :l(e:8fny k+m(w of magnetic fields produced by overhead power lines. You estimate that the two wires are each about 30 m above the ground and are about 3 m apart. The local power company tells you that the lines operate at 10 kV and provide a maximum of 40 MW to the local area. Estimate the maximum magnetic field you might experience wal+wy:8zfk ce(8: mb(ol9ku n xcking 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 fieldnj l/l-/g nq0pc**nkb would make a beam of electrons, traveling to the right at a jb0 */ql*lkpg nc/n- nspeed 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 9lurb1 (t5z3r6zd;a a md 3zut0.010 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 u;zld5 zaut ar3tr(69 dm13zband 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 taf lxs,,csje49c p8 t0o produce a 0.30-T magnetic field at its cepca8,l ,0sfx c49se tjnter. 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 1atof e-dz 05ekm: ( h(tpk2ml0.50 mm, carry the same current but in opposite dil2mo ( ae :1ztftk-ekhmp05d(rections. They are suspended 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 uniform m27 k opg 60-ed(cmebhfagnetic 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$