A compass needle is not always balanced paral rojbdckal9l: 5*aogy 7 6;ta 2;b/.2gpiynfplel to the Earth’s surface, but one end may dip down2g p. ka b6pl;9*yoo 7jl5c2ga: fai/brnytd;ward. Explain.

Draw the magnetic field lines around a straight secti6th w:q ti:4uz2iv2qjon of wire carrying a current horizontally to the lz q46wi tuhjvq2 i:t2:eft.

In what direction are the mag;b1o b4x)ipia6hth co/u ;)g-oruo8z netic field lines surrounding a straight wire carrying a current that is moving directuig6caobr b) oozt/ ; i1)h;48hupx- oly away from you?

A horseshoe magnet is held vertically with the north pole on thl;. xhp9m*8h dj9hu ;ad:tg rxe left and south pole on the right. A wire passing beh9h;g;d9:puhjx*l a .dx m8 trtween the 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 qq49p4fnf2pcpq c7 63zq ix;btj8 6aymetallic object, or only those made of iron? (Try it and s 8xpqq6p f4qqcn 279p 3 at6;ybfc4zijee.) Why is this so?

Two iron bars attract each other no matter which ends are placed clorbro7; i,7uy a lltf.2se together.ufa2;r,.li 7 7obr lyt Are both magnets? Explain.

The magnetic field due to current in wires in your home can affl7) re2wjcz/ vect a compass. Discuss the effect in z 7w/ vljcre2)terms of currents, including if they are ac or dc.

If a negatively charged particle enters a region of uniform magneticv;hcd)8y h8gkx88 ch0zuo 6oc field which is perpendicular to the particle’s velocity, will the kinetic energy of the particle 8dvcco0o gh8hx;zk6u8) c 8y hincrease, decrease, or stay the same? Explain your answer. (Neglect gravity and assume there is no electric field.)

In(Fig. Below), charged particles move in t0398+3nd kanj9n3fpjmwdn 9za k )fi ehe vicinity of a current-carrying wire. For each charged particle, the arrow indicates amf3jwne0adn9 9 dp)k3nf k983 nzi +jthe 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 wire.

Three particles, a, b, and c, entt 5 w.cu3oi(oter a magnetic field as shown in Fig. 20–46. What.ti3c5 oou(t w can you say about the charge on each particle?

A positively charged particle in a nonuniform magnetisuccvq .73h2,dgfsz qmu:3t9 c field follows the trajectory shown it:c2 s9sqqc g7hudz3u,f.v m3 n
(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 attrac 7 :hmnvf5mc7ly8grvmq9k). vt a magnet? Can a magnet attract an iron rod? What must you consider to answer these qucmvn7:l 5fgk v)v8ymm 7 qrh9.estions?

Explain why a strong magnet held nearxn (h)wpcmca/wf*) ,x 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 to your TV by trying this.][/But don’t risk ,ac()nxhwxpf*w/c m) damage to your TV by trying this.]

Suppose you have three iron rods, two of which are magnetiz f 9fs*ky:ez:ged but the third is not. How woue9*: fszgfy k:ld you determine which two are the magnets without using any additional objects?

Can you set a resting electron into motion with a magnetic fi*iljq4 a 2kze0eld? With an electric fieql a*z 0e2ij4kld? Explain.

A charged particle is moving in a circle under the influence of a uniform ma94zda(. sweqkayv d6 x3 f,b6xgnetic field. If an electric field that pointswqdf,9az4dv.6 ybs e(x6k xa3 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 elec ;k 5gxd4j ,emz0;wwactromagnetic 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 are caused to move. Do positive and negative ions feel a force in the smc;agxe45w jdzkw; ,0 ame direction?

A beam of electrons is dire1x g) n, hmgz0gyr,lj3cted toward a horizontal wire carrying a current from left to hgggmy0xl3nj, , )r1zright
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields that surround a moving elei y 4 dm ze hsfv:isj 8liv3p5bx45i0;zpe2w/0ctric charge.3 i4e4p h2;f0 : pdsez/jwvbizxilms8i5 y0v5

A charged particle moves in a straigqvl27ky e(ae 0sgm2l /ht line through a particular region of space. Could there be a nonzero magnetic field in this regione m0k272g/ laq(l svey? If so, give two possible situations.

If a moving charged pa wwx;hfgu:g 6.rticle is deflected sideways in some region of space, can we conclude, for certgfhx;: wuw.6gain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular regiony4o:uy) oe :p1xk;chb of space 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 moving electrons in a certain regionnhtw)( w 5/yuj of space are being deflected by an electric field or bywnt5( hj )wuy/ a magnetic field (or by both)?

How can you make a compass wit0*dswjde g 32ay +dm,ahout using iron or other ferromagnetic material?

Two long wires carrying equal currents I are at right angles to eagmfq-4rtm6,uhc xg8 pju1: x7ch other, but don’t quite touch. Describe the magnetic force one exerts on the othercp 1mx,qmx:-gh8f 47r6ujt ug.

A horizontal current-carrying wire, free to move :0elw gjca b63,fet;liaf /k9 in Earth’s gravitational field, is suspended directly above a sec jba,;c6e9a3l: 0/i gflefwktond, 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 o*l-t11pt1 r hyiddo2kdjb r16 f iron?

An unmagnetized nail will not attoo0 0 gyp)a4/+u fstdcract an unmagnetized paper clip. However, if one end of the nail is in contact with a magnet, the other end will attract a paper clip. ) +4co0tpaus yg0 df/oExplain.

Two ions have the same mass, but one is singly ionized and the other is dou(s +b sn0uz8snbly ionized. How will their positions on the film of a mas(s8snn0z ubs+ s spectrometer (Fig. Below) differ?

What would be the effect on B inside a long sol7q bf99fupuokeg (k +gw61te 4enoid 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 8ewj 5of2d1i fa 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 switch. A relay is used when you need to switch on a circuit carrying a very large currej8f5f1do wei 2nt 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 q y6kz4/(w z+dtpxbm5b5lf7hof length on a straight wire carrying an 8.40-A current when perpendicular to a 0.90-T uniforxzdt6wm(p + qk/475 zbb 5hyflm 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 g-,3m unqj o4:ran,lx force on a 160-m length of straight wire stretched between two towers carrying a 150-A current. The Earth,nm4j nru-o g,qa 3x:l’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 ofja5w. rh s68bur+)qj d straight wire stretched between two towers carrying a 150-A current. ja . wr8hq6)ur5d sb+jThe 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 the maximum2zmdg/i e 6gbhq k120j force on it is 0.70 eh/j1 qbdmk2z6ggi2 50 N when placed in a uniform 0.0800-T field?    A

  A 1.5-m length of wire carrying 4.5 A of current is oriented horizontally. //xrp4zl,lbsj0u ) ks At that point on the Earth’s surface, the dip angle of the Earth’s magnetic field mak/ jls 4pxu)0/klbzsr,es 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 carryings 8rrkxdwzyv3 l ,i5bx)77yd/ 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 v7zbskr5lx) xy i7w8 yrd,/3dapproximate strength of the magnetic field?    T

  The magnetic force per meter on a wire isj.h 80c zfkji( measured to be only 35% of its maximum pojc(8 fz hi0j.kssible 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 and the magnetic field.    $^{\circ}\,$

  The force on a wire is a maximum of)t)) f+i nor2vvcv*ij $ 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 1.0e6hzf: pr4/wq2y ;g sf0-mm-diameter copper wire could just “float” horizontally in 4 szyf:gep/wrh;f2q6 air because 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 chargezcz62hd5o /u l $q\,=\,+2e$ 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 magnitlo 6 - daajaml)8.t,pvude and 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 force on a negative charge for each diagram shown in hf+dri,;if - l(Fig. Bel,i-li;rf f+ dhow), where $\vec{v}$ (green) is the velocity of the charge and $\vec{B}$ (blue) is the direction of the magnetic field. ($\otimes $ means the vector points inward. $\ odot $ means it points outward, toward you.)

Determine the direction ofdxs+0m/ud q,u i, bt1o $\vec{B}$ 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 wt. z/2,l9 ynnb8y 6s(fpb mcpkith a speed of $1.7 \times10^{6 }\;m/s$ into a uniform magnetic field of 0.350 T that is directed horizontally away from the observer. Describe the electron’s path in this field.    $ \times10^{-5 }\;m$

  A 5.0-MeV (kinetic energy)yw b/mt8 :;s3nh xca) 5rfs9n (x:dulm proton enters a 0.20-T field, in a plane perpendicular to the field. What is the radius of its:();539 xnrx mh: /8faybstl scnm udw path?    m

  An electron experiences the greatest force as it traveo2 umx db* vj;x47ftf6ls $2.9 \times10^{6 }\;m/s$ 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 or yf 0u(fy*,okeloq;,8v1tqvmp3 1w beam of electrons that go undeflected when passing through perv1o omt,qqo 0pfv 81yfky*3 w(el,r;upendicular 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 wyoy jf cn)0. ,v87poawhose mass is $6.6 \times10^{-27 }\;kg$ is accelerated by a voltage of 2100 V.
(a) What will be its radius of curvature if it moves in a plane perpendicular to a uniform 0.340-T field?    m
(b) What is its period of revolution?    $ \times10^{ -7}\;s$

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

Show that the time T required for a particle of charge q moving with conso u i2p646: xv,qdu9 xd1wxdektant speed v to make one cid, k91uxvdwp2iq6d uo:6xx4e rcular revolution in a uniform magnetic field $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge m *4;he:cqvsejl69ssq moves in a circular path of radius r in a uniform magnetic field B. Show that its momj evs94s6:h cq*; mselentum is p = qBr .

A particle of mass m and charcd3)urn c*w z0 s/zqg,5i2yoxge q moves in a circular path in a magnetic field B. Sqzy *wz c,grs 0c35ou)x/d n2ihow that its kinetic energy is proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momentum e5*suu1 ni j+x zsg1n2of 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 mb )lw,qlcttvgf2,1:+q1r ofy/s perpendicular to the Earth’s magnetic field ofqcwf1: )gqt1olybl , t +rf,v2 $5.00\times10^{-5}\mathrm{~T}$, 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 h16c zcg2)fd8sjpw vmv,2v u )pas 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 sppzvb 4w)y 73k3vc;r1ni5gmhweed $\nu=2.0\times10^5\mathrm{~m/s}$ 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 curr,zs)o-f2/moga zsjas*; 4kiu ent. How strong is the magnetic field 6.0oa;kza/fg2*zs- uisj,o )s4 m 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 l7/wb t02dbu l( pf:bu5rjoki5 arger than that of the Earub utk5(r2d7 f p5wj ob0l/i:bth $(0.55\times10^{-4}\mathrm{~Т})$ at a distance of 25 cm, what is the maximum current the wire can carry?    A

In (Fig. Below), a long straight wire carr+upk04 jsxtz,) h9k:9bkzjuries current I out of the page toward you. Iu k px49r ,9+:kj0tbhs)zuzk jndicate, 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 24mbwjp*bl2 a8 5-A current exerts an attractive force per un5*28albbwpm jit 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 two ps)e:hy2x,2zxny ivf 4arallel wires 35 m long and 6.0 cm apart, each carrying 25 A in ty2:ihxen zsv ,)xf2 4yhe same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s ma;mzvp7 *d1jy agnetic field is being carried out 1.00 m from an electric c; 1 y7zjpmad*vable. What is the maximum allowable current in the cable if the experiment is to be accurate to $\pm1.0\%?$    A

  A power line carries a current of 95e/ b/9-owhog x A along the tops of 8.5-m-high poles. What is the magno bw-xgo 9/eh/itude of the magnetic 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 paralle4g-zlcy1,g zyt; m/ey+ o7+is7c ofkel wires 13.0 cm apart carry 25-A currents in the same direction. Deter 4y ;-1 c moy7ziots+f/ke,y+zegcl7 gmine the magnetic field at point P, 12.0 cm from one wire and 5.0 cm from the other(Fig. Below).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18 cm due south from a straight vertical 4lz8b osd yo/jo)cn 3 3.jml*ewire carrying a 35-cz.b8 eyn 4o3d*)mo3ls l oj/jA current downward. In what direction does the compass needle point at this location? Assume the horizontal component of the Earth’s field at this point is $0.45\times10^{-4}\mathrm{~T}$ and the magnetic declination is 0$^{\circ}\,$.    $^{\circ}\,$ N of W

  A long horizontal wire carries 22.0 A of current due north.q h7i,cnr:(jif6+bsa n do( /k What is the net magnetic field 20.0 cm due west of the wire if the Earth’s field there points north but downwar:6in+a ( 7o ,bnhi(dckjrf/qsd, 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 po4ksdq*f+ .phk int 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 midway between two long straig6mj*va:+n ts(k *ks echt wires 2.0 cm apart in terms of the current I in one when the other carries 15 A. Assume these currents are (ne*s*k+sjtc: a6vkm
(a) in the same direction,
(b) in opposite directions.

  A long pair of wires conducts 2na9::p)7 qpa o:gj3 *bpetu kg5.0 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 c au eojb)k9:p7:pg a3t nqpg*:m 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 thfd7zlu;kek-8:le.dul m qu83my- - p he plane of the two wires shown in (Fig. Below), parallel and just tklqfp e lzl:;.-7 kedm 8huy3 8d--uumo 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 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 ,j3 ,zdk u0uoz23$^{\circ}\,$ 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 1/ 9yri mqtah ad5goecz21x8./q4op t same plane as a straight wire, as shown in (Fig. Below). There is a current of 2.5 A in both wires. Determine the magnitude and direction of the net forciqa.qty g12p /8z m1o9e/h5 oc4xdtare 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, mad/vls mf+*dun 1e of 2.5-mm-diameter copper wire and parallel to the first, is kept in suspension magneticallymud n1vf*/l+s 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 i 3/ tqxa4qs8lthat they are perpendicular to each other. At their closest, they are 20.0 cm apart (Fig. Below). What is the magnitude of the magnetic fiel3ixsq8q4t/ l ad 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 (k wc+jsy n e4mei icp-sg+,0,15 cm apart. Wire A carries 2.0 A current. Wire B’s current is 4.0 A in the (me+ck pgisye ,ij4-0 c w+ns,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. (Looking along t)azt.lt) e+(xl mnz*9 jzb;ke hem, they are at three corners of an equilateral triangle.) The current in each wire is 8.00 A, but its directionx*)m.ee(a kjlt lzb;z+n )z9t in wire M is opposite to that in wires N and P (Fig. Below). Determine the magnetic force per unit length on each wire due to the other two.
$\frac{F_\text{M net y}}{l_\mathrm{M}}$ =    $ \times10^{ -4}\;N/m$ =    $^{\circ}\,$
$F_{N\,net}$ =    $ \times10^{-4 }\;N/m$ $\theta$ =    $^{\circ}\,$
$F_{P\,net}$ =    $ \times10^{ -4}\;N/m$ $\theta$ =    $^{\circ}\,$

  In (Fig. Below), determine the magnitude and direction of the magnetic fieldekuicjn. c92re3e; g (/(epbq at the midpoint of the side of the triangle between wire M and wire 9e .ei 2ckeun;qr3e/(g p bc(jN.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a distance d apart, carry equal cur sh43jo1 ppc6*d( zg64vhvc jsrents I in the same direction. One wire is at x = 0jjccs4vgop6sp vhd3h(z* 461 , the other is at x = d, (Fig. Below). Determine $\vec{B}$ along the x axis between the wires as a function of x.

  A thin 12-cm-long solenoid has a total of 420 turns of wire and carrie3x30knktz1x)f xk1hf s a current of 2.0 A. Calculate the field inside near tzk0) xk1 f3xk3 1xfhnthe center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm l2op..99 wr30kbjhqm q bf*sfin diameter is to produce a field of 0.385 T at its center. How much current should the solenoid carry if it has 975 turns of thwf.mb.9*br 029hq3lkq o sf pje wire?    A

  A 550-turn solenoid is 15 cm long. The current in it is 33 A. A 3.0-cm-long str t *8ot:yt3 0l ds/miiz) jorr/4imm(cque/ :naight wire cuts through the center o)03/tqeimdylt8c:/(m*onrz 4i soi ut mj:r/f the solenoid, along a diameter. This wire carries a 22-A current downward (and is connected by other wires that don’t concern us). What is the force on this wire assuming the solenoid’s field points due east?    N

You have 1.0 kg of copper and want to make a practical soleys1 w;fos-3no noid that produces the greatest possible magnetic field for a given voltage. Should you make your copper wire long and thin, short and fat, or son3 wy1fs -os;omething else? Consider other variables, such as solenoid diameter, length, and so on.

A toroid is a solenoid in the shape ru-;p.nu.cor of a circle (Fig. Below). Use Ampère’s law along the circu.up.-r;r n ocular path, 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 that9d h xfp5bm49kt2sxv+ the magnetic field between the conductors of a b fmkx429sdp+59 xhvtcoaxial 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 side is placed with i- )+ 4tuu*kl +vp(tn7/vvnf dyx v2tlmkdj++jts face parallel to the magnetic field between2 +dlfynvjj utvmptdx t7 +u/vvn)l-*+( 4k+k the pole pieces of a large magnet. When 6.30 A flows in the coil, the torque on it is $0.325\cdot N$. What is the magnetic field strength?    T

  A galvanometer needle5v mad2w(.b(f5 z77w zsw75zgyx nhzqdx0 5y p 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 galvanometer weakens by 25% over the yearlxt0lt )07j3i:zf e* m c,bngqs, what current will give full-scec*l)7:3ti j n0 mflbg tx,q0zale deflection if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by r qgz.nm 69hc(what factor does the output torque chz6hcnmq 9.g (range?

Show that the magnetic dipole moment M of an electron orbiting the proton nucleuxzh209qj rqi- s of a hydrogen atom is ri0 9jz2xqh- qrelated to the orbital angular momentum L of the electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter and containing nine:yzf9 oq+e) mn y2rlh*8;(jo l pmje;r loops lies flat on the ground. The Earth’s magnetic field at this location has ma9);+ze o2yo:mjl m*rflp h ner;qjy(8gnitude $5.50\times10^{-5}\mathrm{~Т}$ 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 magnetic field. What 3t2 yh1r9;n2xsyty. jqi6kuyyx0d5uvalue of electric field could make their paths straight? In what yj59t 10x uhi3;nd22k . qytyxsury 6ydirection must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium a keazrj ozz:)i7pk2j (b-8(bk toms have radii of curvature equal to 21.0, 21.6, 21.9, 22.2, and 22.8 cm. The largest b-zzjzbk8j2 o a7)(k:k( riperadius 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 mass lo :hwcij(i80spectrometer of (:08i lj(ocw hiFig. 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 u+.g rlowpw 06th/( k4m qc4lpzsed to monitor air pollutants. It is difficult, however, to separate molecules with nl hrp4o(wqw4pm .k/tz+ lcg60early 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 accelerates i zdg5rzx n)g49ons by a voltage V before they enter a magne)g9d xz5r4nzg tic field B. The ions are assumed to start from rest. Show that the mass of an ion is $m=qB^2R^2/2V,$ where R is the radius of the ions’ path in the magnetic field and q is their charge.

  A long thin solenoid has 430 loops oaa 8iho:ixf 4327jyv ef wire per meter, and a 25-A current flows through the wire. If the permeability of the irioa:fiyv8x 2 h7ja 43eon 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 3;l9q 3 ggct4hsm5 haaw0n5cg in diameter, and has 640 turns of wire. The magnetic field inside the solenoid is 2.2 T when 48 A flows gl5ac0n tgs 49mqw3a;gh 5hc3in the wire. What is the permeability $\mu$ at this high field strength?    $\times10^{-5}\mathrm{T}\bullet\mathrm{m/A}$

  Protons with momentum 8ydj4; qn2m8l9 xq ysi$4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 enteriny(2(cb gqclf-uy *n3uq 3bcx.g a region of constant magnetic field. What is the ratio of the radii of their ci3cq(bylgyqcnb c(* x3 uf2-u .rcular paths?   

  The power cable for an electric trolley (Fig. Belyy9*cj0ad )qu1dqg 3 0ve1e 4zx;zrmdow) carries a horizontal current of 330 A td1udy zz1eve0 ;q3ac *rg9) j4qmydx0oward 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 hajds/7j.yrw 1l )w+ wt5 gvop9is 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 field points almost horizontally to)jn3s ih..t- 3 mshrnd the north and has .3r .n)-h ntim 3dhssjmagnitude $B=0.50\times10^{-4}\mathrm{~T.}$ 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, whtxq,:gca 1r ,zose 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. /.os o t1ziqv1Below). A large current moves in a closed loop composed of fixed rails, a power supply, and a very light, almost frictionless bar touching the rails. A magnetic field is perpendicular to the plane of the circuit. If the bar has a length L = 22cm, a mass of 1.5 g, and is placed in a field of 1.7 T, what constant current flow is needed to accelerate the bar from rest to 28m/s in a distance of 1.0 m? In what direction must the magnetiqz11osit/v.o c 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 i/(jk .c xbcd9elf7djd5i a +p0n 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 fcx5j/j pk70efi d9dc(bd a+.l low in the suspended wire.    A

Two stiff parallel wires a distance l apart in a horizontal plane qm 35k 2kgdfu7)g9ntw act as rails to support a light metal rod of mass m (perpendicular to each rail), (Fig. Below). A magnetic fm u 2kg3ftq d9ng5wk)7ield $\vec{B}$, directed vertically upward (outward in the diagram), acts throughout. At t = 0, wires connected to the rails are connected to a constant current source and a current I begins to flow through the system. Determine the speed of the rod, which starts from rest at t = 0, as a function of time
(a) assuming no friction between the rod and the rails,
(b) if the coefficient of friction is $\mu_k$.
(c) Does the rod move east or west if the current through it heads north?

  Estimate the approximate maximum deflection of the electron beam near the.bt sa-jf2ufx4dw- 6n fk/h hmyy*9 5i center of a TV screen due to the Eart569wh dhsn/f2 *-f afxyu bti4ykm j-.h’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 elementarh, gui ib932weny ;o,eq hl*/oy 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 elec*/ ebn ooey2uqiw3g;ilhh ,9,tric 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 parallel wires, l)j7d8owj2qt uct* da1ocated at the corners of a square of side l,1cjqt 7t*d jd8 uo)2wa carry 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 acy3q j;: xbfjwb mffj1r mm+ z)60.nn5zcelerators for “beam steering”; that is, the magnetic fields can be used to change the beam’s direction without altering its speed (Fig. j:m6jbfm jqfx.;n0wrm)5fn zb13yz + 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 amq6l )j4f(*uf.fmeidun) x,9b w7zcl circular coil of wire carrying a current I (as in Fig. cff)*)4ji, zf(9d qlmnl uemxuw6 7.b 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 a9c+ uhe r)dc;8fu2dzo. ptk*ybout 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 ide dvz/bdqs*5hefpb4 -p( vrft1r 0 (rm0a of the magnitude 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 walking under these power lines, and compare to the Earth’s field. [For an ac current, tz4 fbqemrs-d5fp(0vd rh/v1br*0p(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 magnetico h/6c wx51ysc field would make a beam of electrons, traveling to the chyw/6 co 51sxright at a speed of $4.8 \times10^{ 6}\;m/s$ go undeflected through a region where there is a uniform electric field of 10,000V/m pointing vertically up?    $ \times10^{ -3}\;T$(retain one decimal places)
(b) What is the direction of the magnetic field if it is known to be perpendicular to the electric field?
(c) What is the frequency of the circular orbit of the electrons if the electric field is turned off?    $ \times10^{7 }\;Hz$

  A proton follows a spiral path u:oe:gh29y zkm ):c(wba zm5uthrough a gas in a magnetic field of 0.010 T, perpendicular to the plane of the spiral, as shown in (Fig. Below). In two successive loops, b y :khmc2m)zw5e (oguzua:9: 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 in diameter, is to produce a 0.30-T magn jye1qbz2b,j 6etic field at its center. If the maximum current bj 1z qe,b2y6jis 5.7 A, how many turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wiresr em :e*kudy1dsvs*.,s0ky q. 0;vmur , 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 an angle s*mu e:*vmkrd;, s0ukry q .edyv1s0 .of 3.0$^{\circ}\,$ with the vertical, what is the current in the wires?    A

  An electron enters a u ,us*cf (jz2ccniform magnetic field B = 0.23 T at a 45$^{\circ}\,$ angle to $\vec{B}$. Determine the radius r and pitch p (distance between loops) of the electron’s helical path assuming its speed is $3.0 \times10^{6 }\;m/s$. See (Fig. Below).
r $\approx$    $ \times10^{-5 }\;m$ (retain one decimal places)
p =    $ \times10^{-4 }\;m$