A compass needle is not always brq0o:hcf:voal57qz z71o y o (alanced parallel to the Earth’s surface, but one end may dip d0oq:l ooca1:r7h 7vfoqz5(z yownward. Explain.

Draw the magnetic field lines around a stxl +of3 d7onq3raight section of wire carrying a current horizontally to the left.l+odnq3 o37f x

In what direction are the magnetic fieltgn oe)fk(hb 9g0*moso -7u*xd lines surrounding a straight wire carrying a current u 0hgto-(se *o)xn*kfb omg79 that is moving directly away from you?

A horseshoe magnet is held vertically with the north pole on the left and sv)svnc k9ye +8x, m(kn/o bqiu kf84s1outh pole on the right. A wire passing between the poles, equidistant from them, carries a current directly away from you. In what direction is t4xk/k( ycbo ,ks 8nnq+v8u9i msvf1) ehe force on the wire?

Will a magnet attract any metallic objecpk1ou(w.y86 6 mm46 atodhd8vij.t1 itajd +nt, or only those made of iron? (Try it and see.) Why is p1t+d iud1 6ynd6i.k.twtvo o(mh86ja4m8aj this so?

Two iron bars attract each other no ma waul. rz c1*n(gg 3ft3p2igr*tter which ends are placed close together. Are both magnets? Explain. 3r(t zar 3*ig*uf2ngcplgw1.

The magnetic field du3ha)vdpc,5 ixp1mmv4e6mw k(i2 f 4a fe to current in wires in your home can affect a compass. Discuss4xivphcam e3md4w( i m,fvp5a f)2k 61 the effect in terms of currents, including if they are ac or dc.

If a negatively charged o+vnliu 73 5qybn.3piparticle enters a region of uniform magnetic field which is perpendicular to the particle’s velocity, will the kinetic energy of the particle increase, decrease, or stay the same? E+3iy 3il5n uv7pn.o bqxplain your answer. (Neglect gravity and assume there is no electric field.)

In(Fig. Below), chargedf4gb nfs f d+1f(44emm particles 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. For each of the particles, indicate the directionfm 44 fb1+(esf4fndmg of the magnetic force due to the magnetic field produced by the wire.

Three particles, a, b, an4mhe( kmrxaq ke8m/2a k4ndpdcs;3/ 6d c, enter a magnetic field as shown in Fig. 20–46. What can you say about the char/arkeac m(8 6k/ 42de q4s; 3mndxkphmge on each particle?

A positively charged particle in a nonuniform magnetic field follows ths 4bgavnuu35uv)-t+u e trajectory v4g5 ub)un3us +u-vta 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 att61cyv 6f hf*yoract an iron rod? What must you consider to answohy6c y1v* f6fer these questions?

Explain why a strong magnet held 1f+ ,cbil6g.gy(5(h pwc tb p6xgiyh:near a CRT television screen (Section 17–10) causes the picture to become distorted. Also, explain why the picture sometimes goes completely black where the field is the strongest. [But don’t risk damage t(iy l6 b+6xp tgy.g(wgh c1icb:pf,5h o 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 the third ishid) ay-)bv)am c+8wo not. How would you determine whichodmab8) a)-i+wv)yhc two are the magnets without using any additional objects?

Can you set a resting electron into motion with a magnetic fielk3s ce- 3xgltsf-up /0lja tf;*ovr)( d? With an electric - (3 fpk sov f03uec)s*/xlrta;jgt-lfield? Explain.

A charged particle is moving in a cirrk sst t 76fbq) g;ic0m i ne8r;eu6li117i(dwcle under the influence of a uniform magnetic field. If an electric field that points in the same direction as the magnetic field is turned on, describegn8u7r6t ibki6mrc1;es;eq7si l i0f1 wt )d( the path the charged particle will take.

The force on a particle in a magnetic field is the idea behind electromagneti-csoww x/e;y4 jhk (oqyof 3;gl) 0dx8qp28rhc pumping. It is used to pump metallic fluids (such as sodium) and to pump blood in artificial heart machinesqf-2eyx/xwo3q8 ;; o(wj0hp y4 sld)c okhrg8. 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 i( z*l.f9b8z-wbv cke) yjv6jzs directed toward a horizontal wire carrying a current from left to right j6b.)9fzzzvv yk*8lej bwc -(
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields that surround a moving jpq aqm7+gn:aof/7l 5vgl:e.electric charge.:g 7q :a.jllem5q/gvaf +n po7

A charged particle moves in a straigh(b mry,(m-boc e(/n8n ze0vr8s4ryb vt line through a particular region of space. Could there be a nonzero magnetic field in this region? If so, give two possible v v( -snyz e/ob8ce8y mrrb4m((,n b0rsituations.

If a moving charged particle is deflez5x + hi3 o4sptvr9wp(cted sideways in some region of space, can we conclude, for certaipz3hps+r(w9 5tvo ix4 n, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is a unitara3.auw v5h4e 4 bj1form 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 electrons in a certain region of spacl 4cadz,9 fzn r.*u.(vpms8uoe are being deflected by an electric field or by a u.8 co9 z4m,u*f(ldr. snzpav magnetic field (or by both)?

How can you make a compass withyrn7fw m*0*oyout using iron or other ferromagnetic material?

Two long wires carrying equal currents I are at right anhk*a x/z0jdk: gles to each other, but don’t quite touch. Describe the magnetic force one exerxa jzkdhk *0/:ts on the other.

A horizontal current-carrying wire, free to move in Earth’s w5ky g*p ;7dgfgravitational field, ipw 7d;5yf *ggks suspended 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 attract an unmagnetized piece ol-ccle8*xvz7 u m8fz0 f iron?

An unmagnetized nail iyq3f *l vk (+ppcs;(c)v o11qv( zl3kxcp m.qwill not attract an unmagnetized paper clip. However, if one end of the nail is in contact with a magnet, the other end wilcpp1)zvs;*3q p3cvqi kol( mqlf+cxy v.1 k((l attract a paper clip. Explain.

Two ions have the same mass, but one is singly ion1eq 4f,7;nk n twh;wnkized and the other is doubly ionized. How will their positions on the film of a mass spectrometer (Fig. Below) differ? ;, qkw;n7ften1nwk h4

What would be the effect on B invfc1 in2jn7u t-j ,f,xside 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 simqw+*e1kclepap4:e5g,lha *htij 0 ,yilar to a solenoid is a relay . A relay is an electromagnet (the iron rod inside the coil does not move) which, when activated, attracts a piece of iron on a pivot. Design a relay to close an electrical sw aaq: h0l w*gjteiyl,1c+,ep4k pe5*hitch. 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 ifm( wc3q-jb(xjsar2.gdshv 018 an)e force per meter of length on a straight wire carrying an 8.40-A ir38wv h0f q(axs amgn-j(c2bs. d1j)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 of straight. coqv 7 lfj9p3ir4.um3mt( pz wire stretched between two towers carrying a 150-A current. The Earth’s magnetic field vocm.3(zfmqpirtp4lj3 . 97u of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  Calculate the magnitude of theiuje 9i) qz2i- magnetic force on a 160-m length of straight wire stretched between two towers carrying a 150-A current. The Earth’s mag )i2-ei9zqji unetic field of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  How much current is flowing in a wato d-y c(lm(f;89gd mbhr.-uq+fhk- ire 4.80 m long if the maximum force on it is 0.750 N when placed in a um;c-gd h(lodt +y(fbm.q u-9r8a- hkfniform 0.0800-T field?    A

  A 1.5-m length of wire carrying 4.5 7s3 c 2pyn;lfi:+:7ouly krqa( g*wct A of current is oriented horizontally. At that point on the Earth’s sur gcyu kawt*2c37rlif:yol7s (;q +pn:face, 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 - t z8ghkenmht);xv**carrying 8.75 A is a maximum of 1.28 N when placed between the pole faces of a magnet. If the pole faces are 55.5 cm in diameter, what is the approximate strength of th; h*xg-zhnmtk8)* tvee magnetic field?    T

  The magnetic force per meter on a wire is measut4 0r,cscpa9 pqidvb232c hm9red 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, and3a ,c0 pct 9q2vh2bcipdsr94m 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 maxi)gpz3zk(0e kbtddyv1oj 0tc -t5pz 9y7 4w4 eemum 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 jusp2rnb ()gehg*p./ 6b up7zjlu t “float” horizontally in air because of the force duenru.)bjelbg 6u h2g*ppz/ 7(p 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 cha (sz+j np/, o3w7bvzzsrge $q\,=\,+2e$ 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 elec/+d nq5h8uwdw/ftofu) j1n (mtron 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 negat7.: rd dkj.1n3zgr f/+jedsnlo:0sea ive charge for each diagram shown in (F n7sn:/zo j10:e.d.3r fdljsagkrde +ig. Below), where $\vec{v}$ (green) is the velocity of the charge and $\vec{B}$ (blue) is the direction of the magnetic field. ($\otimes $ means the vector points inward. $\ odot $ means it points outward, toward you.)

Determine the directior)+ladtmm st.d ) h9l(n 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 o3 c4br7f hul1of $1.7 \times10^{6 }\;m/s$ 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 field r1 b*-3nwhr;ylj sk5onpj 43e, in a plane perpendicular to the field. What is the radius of its pat- sly*b31jepkr rnh4;w3 o5 jnh?    m

  An electron experiences the greatest force as it tt dtr0zho, o/)ravels $2.9 \times10^{6 }\;m/s$ 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 beamt8d20 yz jdo;f.da1pvw /igo7 of electrons that go undeflected when passing through perpendicular electric and magnetic fielptyzg2;0a81vid do d/o. f7wj ds 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 iqennr qe29i. *aj0,fis $6.6 \times10^{-27 }\;kg$ 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 pl c;pbmz8t )rl.jk2f c4i8 mz+article of charge q moving with constant speed v to make z+ ltm.p ;)kcr f82limjz8b4c 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 move5y(,pt en v+e5 hlcl(ks in a circular path of radius r in a uniform magnetic field B. Show that its mollk5nh,ee ((5+vyp ct mentum is p = qBr .

A particle of mass m and charge q moves i b;-cp)ubb/hx9w q76 rl-g;quqh2e isn a circular path in a magnetic field B. Show that its qbb7c 9pw-i)ebhquhq l2-s;gu; x6/r kinetic energy is proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momentum of the par,iy+*-h /m 1nfwqvp ol- s+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 -,6li 7mb x lk0v3gytjtwdvg2g8 fi 09perpendicular to the Earth’s magnetic dt6y-l b3gki t0gw08jfv 7xvmgil9,2field 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 magnitude-rqbp tpe( :ivd+x:k , $0.40\times10^{-4}\mathrm{~Т}$ 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 spey-1 eci ,ns/vped $\nu=2.0\times10^5\mathrm{~m/s}$ 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. wrwgj1.4/quac,cz4 tHow strong is the magnetic field 6.0 cm away from it? Compare to the Earth’s ucgw,qj wz.4a/cr 4t1 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 prod0,w5 /4/io7zg -1zssf*t gtan qxc+2j wfpmgouce a magnetic field no larger than that of the Ear n 7tx m ,1wgggfq-pa4* f/zz2siw5s0tjcoo/+th $(0.55\times10^{-4}\mathrm{~Т})$ 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 2ijnv0h mcwhh98 wc*y4bp8-(pd w, oji0,a chof the page toward you. Indicate, with appropriatihmci nhww0 -yw bpcd2 ch*o, 849,8j(ah0p vje 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(0t4m ug,svnmezt mm) 7(+kk 6wl8znr upward 24-A current exerts an attractive force per +w8gt,l46n vu (ztmsn e 0)7kmz(m rmkunit 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 between p,2 ,e a7kbzij,re b(mtwo parallel wires 35 m long and 6.0 cm apart, each carrying 25mikep(reab , bj, z2,7 A in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic field is being carried out 1.bj2f-(wl gk .7v8 julb00 m from an electric cable. What is the maximum allowable current in the cablgl-v 2wjfbuk. jb(87 le if the experiment is to be accurate to $\pm1.0\%?$    A

  A power line carries a current of 95 A along the tops of 8.5ye:+4 ker6cld-m-high poles. What is the magnitude of the magnetic field produced by this wire at the ground? How does thiy eec6k4rd+l :s 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 car9fqqu: oc:ut bc,+ cwps/ 1bs4ry 25-A currents in the same direction. Determine the magnetic field at point P, 12.0 cm from one wire and 5.0 cm from the other(Fig +uco/4 bcpcqf,u:wqtbs9 :1s. Below).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is x at7-6n0ks4fy y,dktt:paat 0 l2 0raplaced 18 cm due south from a straight vertical wire carrying a 35-A current downward. In what direction does the compass needle point at this location? Assume the horizontal componenka tr0a:2t0tt xaknpy7 60s4,l -aydf t 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 thsb). zpj(llg) hufv 02e net magnetic field 20.0 cm due west of thelf) (lv) bj2u0 zgph.s wire if the Earth’s field there points north but downward, 37$^{\circ}\,$ below the horizontal, and has magnitude $5.0\times10^{-5}\mathrm{~Т}?$
   $ \times10^{-5 }\;T$
$\theta$ =    $^{\circ}\,$ below the horizontal

  A straight stream of protons passes a given point in spax/t 6y-z4 jsp4ugk r+dce 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 f 8/bop8 y/bi*ut6hl3nnv qh,f wgm:)bield midway between two long straight wires 2.0 cm apart in terms n8 : o hhfq)gt8pib3y,n6/bulmw/*b v of the current I in one when the other 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 i a w++wvtj9vknk8y 4f/nstrument. If the insulated wires are of negligible diameter but are 2.8 mm apart, what is the magnetic field 10.00 cm from their midpoint, in their plane (Fig. Below)? Compare to the v849k+ v+/knt jfwa wymagnetic 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 ofvg ysfvp 6(37knfiz-9 the two wires shown in (Fig. Below), parallel and just to the right. If it carries 25.0 A upward, what force per meter of length does it exert on each of the other two wires? Assume it is 2.8 mm from thzfs 6gy7-vpnik 3fv9(e 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 poizkzespjmb *5j-lem8 iw07 :38dmcm6gnts 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 straight wire, as shown i3y(n m x7r0hhin (Fig. Below). There is a current oiy3 m70 xh(nrhf 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 n-sl5r 0, r xgfxwb f;h2gv31ycurrent of 48 A. A second wire, made of 2.5-mm-diameter copper wire and parallel to the first, is kept in sus3r y5x,rf hw nl-2g0vbg1f;xs pension magnetically 15 cm below (Fig. Below).
(a) Determine the magnitude and direction of the current in the lower wire.    A the current is to the  ----待选择----leftright 
(b) Is the lower wire in stable equilibrium?  ----待选择----not in stable equilibrium in stable equilibrium 
(c) Repeat parts (a) and (b) if the second wire is suspended 15 cm above the first due to the latter’s field.

  Two long wires are oriented so that they are perpendicular to e77njj3ymf 27rjm jmf8ach other. At their closest, they are 20.0 cm apart (Fig. Below). What is the magnitude of the magnetic field at a point midway between them if the top one cjr27jmjm jm ffy7n7 38arries a current of 20.0 A and the bottom one carries 5.0 A?    $ \times10^{-5 }\;T$

  Two long straight parallel wirlj pm /f*nj.hmp+d j)*es are 15 cm apart. Wire A carries 2.0 A current. Wire B’s current is 4.* pnph.fmjl /j*mj+)d 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 are 3.8 cm from one another. (Lck+lz ( df n*y6vzz:d(ooking 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 magneti+z6fzy: dl(n (dk*zcvc force per unit length on each wire due to the other two.
$\frac{F_\text{M net y}}{l_\mathrm{M}}$ =    $ \times10^{ -4}\;N/m$ =    $^{\circ}\,$
$F_{N\,net}$ =    $ \times10^{-4 }\;N/m$ $\theta$ =    $^{\circ}\,$
$F_{P\,net}$ =    $ \times10^{ -4}\;N/m$ $\theta$ =    $^{\circ}\,$

  In (Fig. Below), determine the magnitude and direction of the+ubpgg1: x;v jr h5r,c.gx 8tk magnetic field at the midpoint of the side of the triagrcgx;:bhku 1 j5tx g,.vpr8+ngle 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 currenta a g.z:,diw 2(2onadks I in the same direction. One wire is at x = 0, the other is at x = d, (Fig. Below). Den22iw:,d(zk . oaag datermine $\vec{B}$ 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 carrie(s;u/h)+x4cpqh omly p nu9367jqqk egf r54f s a current of 2oq(+ycn uxf6p)sfqq 54hh/ g7 ;3kmeu4 rjpl9.0 A. Calculate the field inside near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid o,m hpiq k5:n;1.25 cm in diameter is to produce a field of 0.385 T at its center. How much current should the solenoid carry if it hapon :ki5h;m ,qs 975 turns of the wire?    A

  A 550-turn solenoid is ma)xi pyl16x8fu75a :y, ybln15 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 connected byf:pax,yy)8lm6xi y nu57lba1 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 wantkdk ax2w (p7 :hmt958s)zwy ixjg.+ kq to make a practical solenoid that produces the greatest possible magnetic field for a given voltage. Should you mamx iqj8z:)+xks k .tkd5 h7yp2g(waw9ke 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 law u 6jcxa:l,h )ralong the circular path, shown dashed in (Fig. Below a), to 6c)xau :j,rh ldetermine 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 tx py1s ml4m.c1he conductors of a coaxial cable (Fig. Below) is 11l.4mxysm cp$B=\mu_0I/2\pi r$ if r is greater than the radius of the inner wire and less than the radius of the outer cylindrical braid.
(b) Show that B = 0 outside the coaxial cable.

  A single square loop of wire 22.0 cm on a side is plaplmby my7qdpy)6w8c0m2ij :-ced with its face parallel to the magnetic field between the pole pwpjm2d) i:867byp0y c ym-lmqieces 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 needled b5h:6 y0ynd/7y6rkd dnxif+ deflects full scale for a $53.0 -\mu A$ current. What current will give full-scale deflection if the magnetic field weakens to 0.860 of its original value?    $\mu A$

  If the restoring spring of a galvanometmf* yhj6u12h wer weakens by 25% over the years, what current will give full-scale deflection if it originally u*6y1 hhmjwf2 required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by what factor does the xne(gvq+ 2 )ajoutput torque chan+v(xg en qja)2ge?

Show that the magnetic dipole moment M of an electrfc 1:gu t6tyw w1.ihk:on orbiting the proton nucleus of a h hkf6wt:.yit 11uc gw:ydrogen atom is related to the orbital angular momentum L of the electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter and containib v 81u5d3te957yv giohz g+kong nine loops lies flat on the ground. The Earth’s magnetic field at this locatio ouv hezk58ig+9gt v1yod37 5bn 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 z8bi:.vw;)f2od pcge radius 5.10 cm in a 0.566-T magnetic field. What value of electr ;wd8)v2 ogpiebc:z.fic field could make their paths straight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atoms have radii nno gw 1chh7z4e 8b3q8of 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 h zh834cn8ogn 7qbew1 u. What are the atomic masses of the other isotopes?

  Suppose the electric field+mb;oks 34qzq v8mm*+x4 hokn between the electric plates in the mass spectrometer of* 8ok;q+q 4zksohmb4vxnm+m 3 (Fig. Below) is $2.48\times10^4\mathrm{~V/m}$ and the magnetic fields $B=B^{\prime}=0.68\mathrm{~Т}.$ The source contains carbon isotopes of mass numbers 12, 13, and 14 from a long-dead piece of a tree. (To estimate atomic masses, multiply by $1.67\times10^{-27}\mathrm{~kg.}$)
How far apart are the lines formed by the singly charged ions of each type on the photographic film?
$2r_{13}$ - $2r_{12}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)
$2r_{14}$ - $2r_{13}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)
What if the ions were doubly charged?
$2r_{13}$ - $2r_{12}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)
$2r_{14}$ - $2r_{13}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)

A mass spectrometer is being used to m s) y9t1pv;:+wv yjjrionitor air pollutants. It is difficult, however, to separate molecules with nearly equal mass such as C:;yr+1j jvw9v iy) stpO (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 ac oq* j hh 6 1gqtas(/fapg6g4h +xig/1bcuo4n-celerates ions by a voltage V before they enter a magnetic field B. The ions are assumed to start from rest. Show that the mass of ao ctig61sj64*n41 h -/uqxpaoha(+ g/qghfbgn 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 flowsfwd.9 rfzyn+k+v* ;iu through the wire. If the permeability v9 zr nfiuy+kd+w;*.fof the iron is $3000\mu_0$ what is the total field B inside the solenoid?    T

  An iron-core solenoid iekhjdah)bdrb(qb7kuc. .:pl+6 5 w5 rs 38 cm long and 1.8 cm in diameter, and has 640 turns of wire. The magnetic . h.6rwuh jdbde5a7qb rk)5(bklpc:+field inside the 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 momentujn4o nvb2 7ow.bz9+cp xg,)od m $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 entering a region h1rr(iqk/g6f of constant magnetic field. What is the ratio of the radii of theirf6ir/g 1k( qrh circular paths?   

  The power cable for an electric trolley (Fig. Below) kdc/ iyc ep8f ysh6z-s6*+x6q carries a horizontal current o-fh6 6+cixs ezp6q /* yd8kcsyf 330 A toward 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 on0.h3 7h 85org-mplwm fcf9sxj 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’sbo) 2qj i y,uj .k+re-;cwrh h4u7k3vz magnetic field points almost horizontally to the north and has .-z7h,2rjvoe w kby3 cj)uki4hur;q +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 iocv0v ak867op)91cif+u atsumfd mh:+ 28h po s $6.6\times10^{-27}\mathrm{~kg},$ 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. Belo g 5h.id7gr 18b4qum*bj5igtcw). A large current moves in a closed loop composed of fixed rails, a power supply, and a very light, almost frictionless bar touching the rails. A magnetic field is perpendicular to the plane of the circuit. If the bar has a length L = 22cm, a masstgr .ggcib5m*7i 8b 4qd j15hu 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 im2o w)wsvs/ (;5pqkv8hytm p *s 1.00-mm-diameter copper wire and is suspended in air due to the two magnetic forces from the bottom two wires. The current flow through the two bottom wires is 95 A in each. Calcuws 5v )(mh*po8ktm2vywp /;sq late the required current flow in the suspended wire.    A

Two stiff parallel wires a distay 7zifawhmt .*/1(xv ance l apart in a horizontal plane act as rails to support a light metal rod of maxvi.(1*ywatahf/m 7 zss 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 maximrkhi; h;hhv.x 7n hy;g/; o4fhum deflection of the electron beam near the center of a TV screen due to the Earyhhxhvr 7o.;hkf4 ;; ghh i/n;th’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 xc h 9yw84q :39rak+(b-3vut4p:eqxqf ft mjzdevice used to accelerate elementary particles such as 4 a qt9 :fb4mr-xc83z 9xwf3 vqhqukpe: (t+jyprotons to high speeds. Particles starting at point A with some initial velocity travel in circular orbits in the magnetic field B. The particles are accelerated to higher speeds each time they pass through the gap between the metal “dees,” where there is an electric field E. (There is no electric field inside the hollow metal dees.) The electric field changes direction each half-cycle, 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 para5 o l: :aiss0iso7/yag6m7/rbk y 4sewllel wires, located at the corners of a square of side l, carry equal cawosekgib m /5::67 4i lr0ay/so 7sysurrents $I_0$ 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 a;93s16eo:2i sww8ok ofvvjuk ccelerators 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. What happenw:9uj v62 es; 3ko8vofks1wois to protons that are not moving with the speed that the magnetic field is designed for? If the field extends over a region 5.0 cm wide and has a magnitude of 0.33 T, by approximately what angle will a beam of protons traveling at $ 1.0\times10^{7 }\,m/s;$ be bent?    $^{\circ}\,$

  The magnetic field B at the center of a circular coil of wire carrying a curren9ss yna 7crmw 3e +d2xhd c,h+6-orpy(t I (as in Fig.a+- d6yo2x3 9(p e+d nsc,y rcwr7hshm 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 th;.gfjqn k*j 3kxx e5p3e 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 the3d zr(53+ 8s saw3kwntop h;qp magnitude of magnetic fields produced by overhead power lines. You estimate that the two wires are3 (3;q5 dzon+wpskhts3r 8w pa each about 30 m above the ground and are about 3 m apart. The local power company tells you that the lines operate at 10 kV and provide a maximum of 40 MW to the local area. Estimate the maximum magnetic field you might experience walking under these power lines, and compare to the Earth’s field. [For an ac current, values are rms, and the magnetic field will be changing.] $B_{net}$ $\approx$    $ \times10^{ -5}\;T$(Round to the nearest integer)

  (a) What value of magnetic field would make a beam j;p2 gnz n1jy:of electrons, traveling to the right at a spejg n1p j;yzn:2ed 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 c;u:dmjn0 f - o6: puzaa5rq/lgas in a magnetic field of 0.010 T, perpendicular to the plane of the spiral, as shown in (Fig. Below). In two successive loops, at points P and Q, the radii are 10.0 mm and 8.5 mm, respectively. Calculate the change in the kinetic energy of the proton as it travels from P tjal6zar cm5 u:ou:0/pnq f;-d o Q.    $ \times10^{-20 }\;J$

  A 32-cm-long solenoid, 1.8 cm in diameter, is to produce a 0.30-T mw uf64 wi0d(eym am)0bagnetic field at its center. If the maximum current is 5.7 A, how many turns wb 6u()d 0m4imayfe0w must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wir ge6kex 2)2 3mzovihcgjqnr2t*gy . ,:es, each of diameter 0.50 mm, carry the same current but in opposite directions. They are suspended by 0.50-m-long strings as shown in (Fig. Below). If the suspension strings make aehg)ivg2rg2ko ne2.* m6x:q cy, j3ztn angle of 3.0$^{\circ}\,$ with the vertical, what is the current in the wires?    A

  An electron enters a uniform mag6h0fn)6:yr (wmeh5 gcyq p( xwnetic 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$