A compass needle is no +qk)skqt kj -1/va0l gx(b5yot always balanced parallel to the Earth’s surface, but one end may dip downwa)j/ okv0gks+ql a( t15bxqky- rd. Explain.

Draw the magnetic field lines d6 ,yjql87zhaaround a straight section of wire carrying a current 7zdy, 6jhlqa8horizontally to the left.

In what direction are the magnetic field lines surroufnrvl: 9cr3)e+kqjq 6 nding a straight wire carrying a current that is moving directly away from yo6rflq+nkr: cje )93qv u?

A horseshoe magnet is held vertically with 1+2h8c ik+r( nt i/bcoq4qahqp( d s1vqas.u4the north pole on the left and south pole on the right. A wire passing between the .cqnqt k1ip q++di4ho4av/(a 81shc2sbqru( poles, equidistant from them, carries a current directly away from you. In what direction is the force on the wire?

Will a magnet attract any metallic object, or only ya:tjafi 5v+v+ sd51fthose made of iron? (Try it and see.) Why i 15f aitjfd :a+y5vs+vs this so?

Two iron bars attract each other no mah)1wxq9hr bpm9g w*i1 tter which ends are placed close together.w*mxh w) 9ipq9ghr11 b Are both magnets? Explain.

The magnetic field due to current in wires in your home can affect a compass. fa(amsa; l 84sp, p.gxDiscuss the effecpfsa , (lgp aax;48.smt in terms of currents, including if they are ac or dc.

If a negatively charged gacvx27mv9 . jrp3vth *aq6sp 9*dt0d particle enters a region of uniform magnetic field which is perpendicular to the particle’s velocity, will the kinetic energy of the particle increase, decreqd7stm r9 9vp6 3v.tv *pjg *h02caxadase, 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 7ihc)l ; y/(obu. t8ijcs8kdlof 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 particles, indicate the direction of the magnetic force due to the magnetic field produced by the wirc)s8u .kio y/lbt7(c i;8hd jle.

Three particles, a, b, and c, enter a magnetic fmpa; 6l )5w8dvyz*r anield as shown in Fig. 20–46. What can you say about the charge on each particl;a m*wn8p5dv6 zrl)y ae?

A positively charged particle in a nonuniform magnetic field followafi03-7b ygd*,e3qhtkf/j tbs the traject3gki, *3dh -fqtb yej /07bftaory shown in
(Fig. Below). Indicate the direction of the magnetic field everywhere in space, assuming the path is always in the plane of the page, and indicate the relative magnitudes of the field in each region.

Can an iron rod attract a magnet? Can a magnet attract an iron -,xam5o1y9 an8c qnyt rod? What must you consider to answer these qu8 yn5toq9ym ,axa c-1nestions?

Explain why a strong magnet h;/,g5q 3zbk2*h g;x mzh qragq,sv-lneld near a CRT television screen (Section 17–10) causes the picture to become distorted. Also, explain why the picture so;s kvx rzl2 g nah;bmqgqh*q53z ,g/-,metimes goes completely black where the field is the strongest. [But don’t risk damage to your TV by trying this.][/But don’t risk damage to your TV by trying this.]

Suppose you have three iron rods, two of which are magnetized but thtff; ;u(f tfe,e third is not. How would you determine which two are the mat,(f; ;ufeff tgnets without using any additional objects?

Can you set a resting electron into motion with a magnetic fi1k n4b-:xdgf tknb b20ohve11eld? With an electric field? Expk0o ng1e1bkvb2 f14b th:-ndxlain.

A charged particle is moving in a circle under th2sfz; bw:a xr-)tu*yv e influence of a uniform magnetic field. If an electric fiel bz-2 rva :xtswf)uy*;d 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 electrot/ nur( y *4dyp9;lbus x;xx+zmagnetic pumping. It i/xs zrux*ty9lb;x d(;+py n u4s 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 are caused to move. Do positive and negative ions feel a force in the same direction?

A beam of electrons is direct+q. 7m,kt1va;w1ai7b jdqoh yed toward a horizontal wire carrying a current from left ta,.kah+y717 twojb1miqd; vqo right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fi+md8r6lg1 c( /a5sjuoz0p, im*li uzdelds that surround a moving electric charge.u8o0zdm di1a5c( p*lmiur j/,6 lg+ sz

A charged particle movei2q2l irj2 2g ;ut.yhds in a straight line through a particular region of space. Could there be a .r y j22d2ihtlu2;qi gnonzero magnetic field in this region? If so, give two possible situations.

If a moving charged particle is deflected sideways in some region x7oqmx +is0p41uua y :of space, can we co1u:axsm0 xy up oq74i+nclude, for certain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of s1z,s)-nuq dhrl*; s.1qogc8q is,8w 8dranvcpace there is a uniform magnetic field $\vec{B}$. Outside this region, B = 0 Can you inject an electron from outside into the field perpendicularly so that it will move in a closed circular path in the field? What if the electron is injected near the center?

How could you tell whether movinmx44,imooz 7cfod k2;,i kvt d6,u:udg electrons in a certain region of space are being deflected by an electric field or by a magnetic field (or by bozx;d fkc 6vmdu2,,ii7tk,o4md: ou4 oth)?

How can you make a compass without u ym bu5v 4m+,ujw+jf5hsing iron or other ferromagnetic material?

Two long wires carrying equal currents I arep fjl- 82b exy9lxsn35 at right angles to each other, but don’t -expy35 b892jfslnx lquite touch. Describe the magnetic force one exerts on the other.

A horizontal current-carrying wire, free to move in Earth’s gravitationalbt;1e*57lsb4,vo0 zn arwkq y field, is susz bk*a0s ot1y 74lvn; rw,qeb5pended 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 magnet attra3hua jh;8e 7 qqc *f/w bc04wwsiyst-3ct an unmagnetized piece of iron?

An unmagnetized nail will not attract an unmagnetized paper clip. Hbjp7h-z 4 6mbuowever, if one end of the nail is in contact with a magnet, the other end will attract a paper clip. Explain467phbmz b-ju .

Two ions have the sa ;d*3sjx4 ldqwme mass, but one is singly ionized and the other is doubly ionized. How will their d43l d *wsjxq;positions on the film of a mass spectrometer (Fig. Below) differ?

What would be the effect on B inside a long solenoid if nls3s8(4l*kh0s 9 +gxevnhqp / refdu8p;ev0
(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 sw zc.hmuu91cr; 4jd9glitch similar to a solenoid is a relay . A relay is an electromagnet (the iron rod inside the coil does not move) which, when activated, attracts a piece of iron on a pivot. Design arhm;c gj ud.9c9uz 41l 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 th ;;(+u hfrlbbbn0 pps7e force per meter of length on a straight wire carryb;f+0 (b n;r7sbhplup ing an 8.40-A current when perpendicular to a 0.90-T uniform magnetic field?    N/m
(b) What if the angle between the wire and field is 45.0$^{\circ}\,$?    N/m

  Calculate the magnitude of the magnetic force on a 160-m leng 4jbi*uaunex*jh 2,e +b:rm5z th of straight wire stretched ,: e iu+nh2 j ue*54mzjrxbba*between two towers carrying a 150-A current. The Earth’s magnetic field of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  Calculate the magnitude of the magnetic force on a 160-m length of strqjb 0f1;n+mtiaight wire stretched between two towers carrying a 150-A current. The Eari;m f b+t0qnj1th’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 the maximum forcexlyt ;i *8o1cy on it is 0.7508 c1yxl*yiot; N when placed in a uniform 0.0800-T field?    A

  A 1.5-m length of wire carryi45rk7cx tuj* wng 4.5 A of current is oriented horizontally. At that point on the Earth’s surface, the dip angle of the Earth’s magnetic field maktc5 j *4ru7kxwes 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 ifazk/wdcxam;72.zu0 /c n2c qs a maximum of 1.28 N when placed between the pole faces of a magnet. If the pole f ;27c/uz.zf/aqaxc2 nc0kwd maces are 55.5 cm in diameter, what is the approximate strength of the magnetic field?    T

  The magnetic force per meter on a wire is meawvk y9:k ;hk)2mm5qcel7 c7i rsured 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 r77 5vk hkqc lymwciek; 92m:r)elationship as it actually is, calculating the angle between the wire and the magnetic field.    $^{\circ}\,$

  The force on a wire is a maximum of x:d+s*2jfq n2chi r u*h0ksm3 $ 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 j0/ s.o6ka gjuzust “float” horizontally in air bec/gu ak0zo6s.jause of the force 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 chargev* nc)6sr0k mikgqp;0p5m0gh76q r mm $q\,=\,+2e$ 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*b 5bwwd( p0hu direction 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 fzrrh7 g0q v,m..6wk guorce on a negative charge for each diagram shown in (Fig. B.w g,zmr rv70g.hq6ukelow), 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 direct(yinb-:cpv0uac ..ma ion 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 speed of n1n5)wxd3 j qj$1.7 \times10^{6 }\;m/s$ 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 gmdl+ owqu84h t(y;9kenters a 0.20-T field, in a plane perpendicular to the fo+qwly84m9gtu( h; k dield. What is the radius of its path?    m

  An electron experiences the g4yp pa sp+o gq3(+jh6qreatest force as it travels $2.9 \times10^{6 }\;m/s$ in a magnetic field when it is moving northward. The force is upward and of magnitude $7.2 \times10^{-13 }\;N$. What are the magnitude and direction of the magnetic field?    T ----待选择----EastWest 

  What is the velocity of a beam of electrons thatgrv7:i yl+xh:sr *r 2d go undeflected when passing throvyx:rlhri:s*72 r dg +ugh perpendicular electric 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 atom whose b2/fe t i,;sx2 euyd*qmass 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 cha oaw. rg-0s8 zo3iy/jo 1tcy8trge q moving with constant speed v to makioz .ow/88yy0c3stg - oja1rte one circular revolution in a uniform magnetic field $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge q moves in a circular path of radius r in a uniform magneti;(9dpbfhs3qla: wz6x c field B. Show t3q 6bdpzxas h9 fl;(w:hat its momentum is p = qBr .

A particle of mass m and charge q moves in a circular path in a/emwx 3jpmix27bdv 174 ljpr 6 magnetic field B. Show that its kinetic enew1 bjxp 23vj6/xp7edm7l ri 4mrgy is proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momentum 0 r6rfjenyqq 81zcn2/kep 3 p3dr- ss1of 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 Eart4bdhz *nh/r) yna9 um;h’s magnetic fid)h/rmh9 * y4nza ;bnueld 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 equator has +q:f ww5vdyw10qpn9v 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:qkjvelq+jsk:d39,6lwl( x )tp o1 ( 5qnls pr 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 to start a stalled vehicle carries a 65-A current. Howp nc2+dqf. x)w strong is the magnetic field 6.0 cm away from it? Compare to the Earth’s magneti.qnw dfx+2 pc)c 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 a 8sx-atigm41b / nc xtq7ibp2*0,evllarger than that of theb74tx l *,-tep/g nva s8aiqc mi21b0x Earth $(0.55\times10^{-4}\mathrm{~Т})$ at a distance of 25 cm, what is the maximum current the wire can carry?    A

In (Fig. Below), a long straight wire carries current I ou x6 gz8rqdjr 5qusjrh(n n3905t of the page toward you. sgqx r86z3(h95q0 djn rn rju5Indicate, 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 i8 kghscd)--tw1 nfx*w(m /jewire carrying an upward 24-A current exerts an attractive force per uni-t8g/1m*cfe)h idx wkj-s (n wt length of $8.8\times10^{-4}\mathrm{~N/m}$ on a second parallel wire 7.0 cm away. What current (magnitude and direction) flows in the second wire?    A  ----待选择----upwarddownward 

  Determine the magnitude and direction of the force b b4phe4r.bt35eb s +c4w4omgeetween two parallel wires 35 m long and 6.0 cm apart, each carrying ewrec s+4bt p 4ho4 bgb.em43525 A in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic field is being carried out 1.00 m fro0 (5k pikar+qw i*u5xom an electric cable. What is the maximum allowable current in the cable if tk k*5 (iao iquw5rxp0+he experiment is to be accurate to $\pm1.0\%?$    A

  A power line carries a current of 95 A along the topwih2x.vx j 5; oory+cvsf64/es 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 fieldfirs x2+vx6hce o45; .vwyoj/ 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 dircj0u5onnh 54 dection. Determine the magnetic field at point P, 12.0 cm from one wire and 5.0 cm from th5jnd45uhc 0 noe other(Fig. Below).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18 cm due south from az)m h(a9c v)q hgif-8q straight vertical wire carrying a 35-A current downward. In what direction does the compass needle a ihcf qz9qm))vg8h -(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 nojq-vnv0rj: . yjcn 2t:9yifo-rth. What is the net magnetic field 20.0 cm duo n q:i j.9jc:0vfyty-j-2vnre 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 p*i:/lmo.f ,pbd;kv agiven point in space at a rate of $1.5\times10^9\mathrm{~protons/s~}.$ What magnetic field do they produce 2.0 m from the beam?    $ \times10^{ -17}\;T$

Determine the magnetic field midwa8rri:2g6ngtnu p ; lx0y between two long straight wires 2.0 cm apart in terms of the current I in one when the other carit2n:n6rr8p 0lug; gxries 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 instrument.o fc )0pudd5i1o; .cpd If the insulated wires are of negligible diameter but are 2.8 mm apart, what is the mup p.;df io 1cd5dco)0agnetic 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), par6g7aa 9r2x24 paziz4covo5b lallel and just to the right. If it carries 25.0 A upward, what force per meter of length dog x zp274vo oab4l2 i6cr9za5aes 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 poip/san 7h5n r(bxgiyz * 3hu3/*ot.jo rnts 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 s mfa5 u5wgv+wv, cq7(tame plane as a straight wire, as shown in (Fig. Below). There is a current of 2.5v(cfa,w m gv +755tqwu 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 A. A second wire,.h , vfvkz-3u7cvm( lo made of 2.5-mm-diameter copper wire and parallel to.vlm vkz,-och v( u7f3 the first, is kept in suspension magnetically 15 cm below (Fig. Below).
(a) Determine the magnitude and direction of the current in the lower wire.    A the current is to the  ----待选择----leftright 
(b) Is the lower wire in stable equilibrium?  ----待选择----not in stable equilibrium in stable equilibrium 
(c) Repeat parts (a) and (b) if the second wire is suspended 15 cm above the first due to the latter’s field.

  Two long wires are oriented w gy/6jy m,6kosc29 qfso that they are perpendicular to each other. At their closest, they are 20.0 cm apart (Fig. Bkg2w cqfsmo6yy,/9 6jelow). 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 ao:)d d 5ab +hu5q7iierpart. Wire A carries 2.0 A current. Wire B’s current is 4.0 A in the same dire +ia57 )d:hqedi5ubr oction.
(a) Determine the magnetic field magnitude due to wire A at the position of wire B. $\approx$    $ \times10^{-6 }\;T$(retain one decimal places)
(b) Determine the magnetic field due to wire B at the position of wire A. $\approx$    $ \times10^{-6 }\;T$(retain one decimal places)
(c) Are these two magnetic fields equal and opposite? Why or why not?
(d) Determine the force on wire A due to wire B, and the force on wire B due to wire A. Are these two forces equal and opposite? Why or why not? $\approx$    $ \times10^{-5 }\;N/m$(retain one decimal places)

  Three long parallel wires are 3.8 cm from one another. (Looking along themg;x4vkcdp p 3-, 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 length on each wire due to the other gpc43xpvkd- ;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), deteg2fzos*0 .e0rd :c82 lfanevrrmine the magnitude and direction of the magnetic field at the midpoint of the side of the triangle between wire M andfdgz0lanec*. r80v: 2 eo2frs wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a distance d apart, carry equal currens0407kp lxq 2dlcu: ;aa1cnrqts I in the same direction. One wire is at x = 0, the other is at x =r17 cula0lps2nqd:x0qa4 c k; 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 tu2ir7 8 c xua7e8+e 1njehcm;pkrns of wire and carries a current of 2.0 A. Calculate h ijem1 7an cxrpcu828ek+e;7 the field inside near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameter is to produce a kd it i7kd7(o:pttu p) ml46(; p7dtizfield of 0.385 T at its center. How much current shoup7ditk mltdku :i pot;7)p ti(6d7z4(ld the solenoid carry if it has 975 turns of the wire?    A

  A 550-turn solenoid is 15 cm long. The current in it is 33 A. A 3.0-cm-long .w8lx 9zxof7dg 8 moqum433ed straight wire cuts through the center of the solenoid, along a diameter. This wire carries a 22-A current downwamfoxgz8eoq 7d48d9 x3mw.l 3 urd (and is connected by other wires that don’t concern us). What is the force on this wire assuming the solenoid’s field points due east?    N

You have 1.0 kg of copper and wa odsv+z+:m vni2:++qi b y*wdlnt 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?2s+nb +id:+odw vlvi mzq+* y: Consider other variables, such as solenoid diameter, length, and so on.

A toroid is a soleno0lf sbl vw:+pta06 oa2id in the shape of a circle (Fig. Below). Use Ampère’s law along the circular po0+: a lw2lt vfs6pab0ath, shown dashed in (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 magnetic field between the conductors)w9tt j/qtu ot; 5bf6jdt4f -s of a coaxiatfqs5bt ;6-doj4wtf tu /)j9tl cable (Fig. Below) is $B=\mu_0I/2\pi r$ if r is greater than the radius of the inner wire and less than the radius of the outer cylindrical braid.
(b) Show that B = 0 outside the coaxial cable.

  A single square loop of wire 22.0 cm on a side2cti9*ut p*pq is placed with its face parallel to the magnetic field between the pole pieces o9pic*tpqt *2uf 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 for acu+3tpmrv 4q: $53.0 -\mu A$ 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% ovebwmw4q.tqw .rjvba)ys(- aw2e c : oco*i-/f-r the years, what current will give full-scale deflect- qwo:cfq.b( wi)tw -.vys-r ambe4 2cjw *o/aion if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drol 6rfhjwhy3hhcf jz1*s/ y.0+ps by 12%, by what factor does the output torque change hfzw/y 13sjhjh.+rf6l 0h*yc ?

Show that the magnetic dipole moment M of an electron orbiting thjog5 kxfd/m*8 ex(fs) e proton nucleus of a hydrogen atom is related to xfo85)md fe (k xg*j/sthe orbital angular momentum L of the electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in5 q9y7djm19xap b1;doxs uyu 7 diameter and containing nine loops lies flat on the ground. The Earth’s xo17bu;yp5d yx1as7d9 jqu m 9magnetic 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-l+ur: 1ro t9c tr3e xz-*)pcfdT magnetic field. What value of electric field could make their paths straight? In what direction -xlu t*rfrpc: z1od 9+e3r)tcmust it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atog*u5dk 2;rj eoms have radii of curvature equal to 21.0, 21.6, 21.9, 22.2, and 22.8 cm. The largest radius corresponds to an atomic mass of 76 u. What are the auog52*;ejkr dtomic masses of the other isotopes?

  Suppose the electric field be. .zd tyfrzmizi 0g5f7 gr3.o:tween the electric plates in the mass spectrometer of (Fg.f z0f. otyr7 z:3r.mzigdi5ig. Below) is $2.48\times10^4\mathrm{~V/m}$ and the magnetic fields $B=B^{\prime}=0.68\mathrm{~Т}.$ The source contains carbon isotopes of mass numbers 12, 13, and 14 from a long-dead piece of a tree. (To estimate atomic masses, multiply by $1.67\times10^{-27}\mathrm{~kg.}$)
How far apart are the lines formed by the singly charged ions of each type on the photographic film?
$2r_{13}$ - $2r_{12}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)
$2r_{14}$ - $2r_{13}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)
What if the ions were doubly charged?
$2r_{13}$ - $2r_{12}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)
$2r_{14}$ - $2r_{13}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)

A mass spectrometer is being used to monitor air pollutants. It is difficult, yf;3u r x.lox ..s5nwqhowever, to separate molecules withln;sw5fr.y ux 3 xq..o nearly equal mass such as CO (28.0106 u) and $N_2(28.0134u)$. How large a radius of curvature must a spectrometer have if these two molecules are to be separated on the film by 0.50 mm?

One form of mass spectrometer acceleratesy3;auuj6p hq.f.oln5 ions by a voltage V before they enter a magnetic field B. The ions are assumed to start from rest. Show that the my;3q .5o nalp fuj.6uhass of an ion is $m=qB^2R^2/2V,$ where R is the radius of the ions’ path in the magnetic field and q is their charge.

  A long thin solenoid has 430 loops of wire per meter, and a 25-A current flows tg,upa rz 63k(nhrough the wire. If the permeability of t( 3n 6r,ugakpzhe iron is $3000\mu_0$ what is the total field B inside the solenoid?    T

  An iron-core solenoid is 38 cm long and 1.8 cm in diameter, and hasipl ) t/)j6q g-, ksocy.e7spm 640 turns of wire. The magnetic field inside the solenoid ) spskm) 76- yjteogpl/.q,ciis 2.2 T when 48 A flows in the wire. What is the permeability $\mu$ at this high field strength?    $\times10^{-5}\mathrm{T}\bullet\mathrm{m/A}$

  Protons with momentum zv+42yu pk8fc.wo l3n$4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ are magnetically steered clockwise in a circular path 2.0 km in diameter at Fermi National Accelerator Laboratory in Illinois. Determine the magnitude and direction of the field in the magnets surrounding the beam pipe.    T

  A proton and an electron have the same kinetic energy upon xkw(t;j9u s ) rg/ilwp*l/ j2l4oa4tg entering a region of constant magnetic field. What is the ratio of the radii of their cijl24tts(* go/x); lkiw 4 au/w9rplgjrcular paths?   

  The power cable for an electric trolleq;m8f gv y1/kj+lpum 8iin.m2y (Fig. Below) carries a horizontal current of 330 A toward the east. The Earth’s magnetic fiei8.28lig 1 q;ujf/ my+ kpvmmnld 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 o( ;pej vu q pn9;-lba-:)hl4it qo5jyhn an airplane which has acquired a net charge of $1550\mu C$ and moves with a speed of 120 m/s perpendicular to the Earth’s magnetic field of $5.0\times10^{-5}\mathrm{~T}$.    $ \times10^{-6 }\;N$

  Near the equator, the Earth’s magnetic w( 7y s/ki2e/zexz lkq6z-s8dfield points almost horizontally to the north and has magnitudel(ies 6/8 7yq zez-s/ dw2kzkx $B=0.50\times10^{-4}\mathrm{~T.}$ 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,9 :*nfa ;f a s:c+-5fey3r;ojyd msxkt 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 (Fig. Below). z vqepvthdt(1 r+;p39 A large current moves in a closed loop composed of fixed rails, aepqvz+(h;t 31tp9vrd 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 1.00k( c fpou1b-xqa*01 rj-mm-diameter copper wire and is suspended in air due to the two magnetic forces from the bottom two wires. Thecp *0 1auf(xob1kqr-j 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;k 3axoe 5euoeqc1 h;9 a horizontal plane act as rails to support a light metal rod of maoq;uxo h ;1ea3e k5ec9ss 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 tj +rn1 *6riy wh)6-vseebq ol2*nss4ghe center of a T6*wys2 e6jh*4-l)nbr g q 1o i+sevnrsV 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 elementarxyh.d mx87:3-x x2b eaujvh ,ida7 (wzy 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 hollxx a8e3dd7j,x auh7 yiw m-z(bx:hv .2ow 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 ti c9/lcl-ipd (he corners of a square of side l, carry equal curre-i/ (pcl ild9cnts $I_0$ 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 crbm;i b*ya3es3 d,0suseful in particle accelerators for “beam steering”; that is, the magnetic fields can be used to chad*yrbbac3 ;iem,s0s 3nge 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 circular coipsf5u:3 hl vx1pre.si.nr*- jl of wire carrying a current I (as in Fig. Below:r jp -*sh13rn seivl fp..ux5) 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 aboxoir8wsi (h1z(r6e dfez5. sa5p4 g+zut 1G($ 1\times10^{ 4}\;T$) Imagine a simple model in which the Earth’s field is produced by a single current loop around the equator. Roughly estimate the current this loop would carry. [Hint: Use the formula given in Problem 80.]    $ \times10^{ 9}\;A$

  You want to get an idea of the magnitude of magnetic fields produced by ove0:: fzv ztlh3m(, lwli (zvur:zvle-.rhead 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 walking under these power lines, and comparelzev(vz,z z.t(3:w-l:mv: fhu r0 ill 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 matr ayjf9.6u( jgnetic field would make a beam of electrons, traveling to the right at a speedj(afyjr9u6 t. 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 fr7 ki+t:zhmq1ma,f+ .010 T, perpendicular to the plane of the spiral, as shown in (F, 1qrthk+fm+ z 7fmi:aig. Below). In two successive loops, at points P and Q, the radii are 10.0 mm and 8.5 mm, respectively. Calculate the change in the kinetic energy of the proton as it travels from P to Q.    $ \times10^{-20 }\;J$

  A 32-cm-long solenoid, 1.8 cm 0 6n5orjmhg :r tzg/1cin diameter, is to produce a 0.30-T magnetic field at its center. If the maximum current is 5.7 A, how many turns must the soleno61t :/gnmj0zo crr5h gid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, each of diameter 0.50 mm, carry the same 4cb j* bhb s0d78q 9u4orjjx;k6og4nt current but in opposite directions. They are suspended by 0.50-m-long strings as shown in (Fig. Below). If the suspension strings make an an ut qo b40 7og8 4r9sb*jhcx4djk6nbj;gle of 3.0$^{\circ}\,$ with the vertical, what is the current in the wires?    A

  An electron enters a uniform magn:+mb (iw mrtn4e,f 5gnetic 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$