A compass needle is 4lo4rb; cddp (c sm2wub9 (3(hylel c(not always balanced parallel to the Earth’s surface, but one end may dip downwa(2d w(4eu49 c;prmby3l bdh (lso (cclrd. Explain.

Draw the magnetic field lines armn1b 9*a 1(nl mlntk3iound a straight section of wire carrying a current horib(mi1nk9a*1l t lnm3 nzontally to the left.

In what direction are the magnetic field lines surrounding a st/t-f,l b8pxpno t96dx+mql/ wraight wire carrying a current that is moving directlydq n p pblwlfot9/8+t ,6/xmx- away from you?

A horseshoe magnet is held vertically with the north pole o /faqe//k bt c6: hwqac+t/g,bn the left and south pole on the right. A wire passing between th:tb,tbge qc 6+h/w cak/f/ q/ae 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 those made 9gvs f84 5iy:j(ztg uhof iron? (Try it and see.) Why is this sovgs i5f8(:zjh 4uy9gt?

Two iron bars attract each otherbsbwp)c )n b6bm1c84;v gmc(m no matter which ends are placed close together. Are both magnets? Explain.b ))mccn;w8 bbs gvm pb41cm(6

The magnetic field due to cu8b6ppxd(m( lrh8t zq /:q(0mx/* tb+rmqpt wvrrent in wires in your home can affect a compass. Discuss the effect in terms of currents, including hm/ppx tqm 8 0/(r(+q p6bztqlxt8wdrm *(:vbif they are ac or dc.

If a negatively charged particle enters a region of unif ,+t bfxa7y0sgorm magnetic field which is perpendicular to the particle’s velocity, will the kinetic energy of the particle increase, decrease, or stay the same? Explain your answer. (Neglect gravity and assume there is no elec7g,ts+ xyfb0a tric field.)

In(Fig. Below), charged parer(hiimh:g , -;-ubr cticles 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 direction of the magnetic force due to the ,ei rigu;br--:(h chm magnetic field produced by the wire.

Three particles, a, b, and c1k);iqmzu.bewq 3( la, enter a magnetic field as shown in Fig. 20–46. What can yml 3)bk q 1wa.;(ziequou say about the charge on each particle?

A positively charged particle in a nonuniform magnetic field o;zp fci;h(l: follows the trajectory shown i;z(p:h l i;cofn
(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 rod? What must y:wi8-+a/a s5svb yw*buinxg *ou consider to ans i v:-a*/wgsb+ 5uibyx*w na8swer these questions?

Explain why a strong magnet held near a CRT television screen (Sectioo : ml re-0kzvrwkn2+)n 17–10) causes the picture to become distorted. Also, explain why the picture sometimes goes completek:n mrrz-e)+w0vl 2ok ly 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 lq8*-qsg ;ap pzxjyfpo91 r2 -the third is not. How would you determine which two are the magn a;r qs*fgo28 p-q zlyjp9x-1pets without using any additional objects?

Can you set a resting electron into motion with a magnetic fio0s p+zo 0osj vw0p 2v/nlrb9v3nd3/ geld? With an electric fip2l9j s3dzn o+0rn/0sowbvgv0 3 vo/peld? Explain.

A charged particle is moving in a circle under the influence of a uniform my/c- avein +(yagnetic field. If an electric field that points in the same direction as the magnetic field is turned on, describe the path theciae /+(- nyyv charged particle will take.

The force on a particle in a magnetic fientf l0it,3 n*af*h3jk ld is the idea behind electromagnetic pumping. It is used to pump metallic fluids (such as sodium) and to pump blood in artificial heart machines. The basic design is shown in(Fig. Below). An electric field is applied perpendicular to a blood vessel an*0t3ln tnff k j3h,a*id 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 directed toward a horizontal wire carrying a currer.7xna:,ey1sho 3l9lk;nm7yd 8 y id7o7 yvkdnt from left to7,yyv1 9rk7 n;o3:ds 7edxk8lahi d .ynlym7o right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or mag;u -jmhf4aw1h .xena (netic fields that surround a moving electric charge.awnemf(uh4j1a; .xh -

A charged particle moves in a straight line through a particular w 3qjwdz+4bs -region of space. Could there be a nonzero md-w3bzj+ s q4wagnetic field in this region? If so, give two possible situations.

If a moving charged particle is deflected sx8m5tuxn*hytkf g*1 aby* 9* xideways in some region of space, can we conclude, forgtxfth 5y1 y**k8x9*bxn m* ua certain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there tjaxzra, cza5ry2 3)6 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 region of 8*a w:tif;fvxf 4+)0s8fyvw r cegw) ospace are being deflected by an electric field or byywwi4 f)8)x fsv e0ct;fvg fwro+ 8*:a a magnetic field (or by both)?

How can you make a compass wit6.jw:dgqxs 5 n5kfhg7hout using iron or other ferromagnetic material?

Two long wires carrying equal currentsngc j5b;c xw4a*(1vlo I are at right angles to each other, but don’t quite touch. Describe the ; 1lxanjw*gb c5o4(c vmagnetic force one exerts on the other.

A horizontal current-carrying wire, frey 6u*ekrom3e+gj, 1d oe to move in Earth’s gravitational field, is suspended directly above a sec r3* ogjd1um+6,okyeeond, 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 :te5 w7gl; tnpvbvh7gemd(95f iron?

An unmagnetized nail wi)atu2umd5 69- 7 d6r9qxn;zccjwpzr a ll not attract an unmagnetized paper clip. However, if one end of nxdpmud6c)56tw jr9297z-aczq u;ra the nail is in contact with a magnet, the other end will attract a paper clip. Explain.

Two ions have the same mass, but o.tpb4k+gglo5g/ s 8g6. dvkayne is singly ionized and the other is doubly ionized. How will their positions on the film of a mass specvto6.glysk .kp+gdba 8g54/gtrometer (Fig. Below) differ?

What would be the effect on B inside a )mx-bb-mq 4u lu0 nzt*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 sim*mtgwdf+a n( .r-mhz0ilar 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 switch. A relay is used when you need to switch on a circuit carrying a very lamha(tr0wd-*mz g n. +frge current but you do not want that large current flowing through the main switch. For example, the starter switch of a car is connected to a relay so that the large current needed for the starter doesn’t pass to the dashboard switch.

  (a) What is the magnitude of the forc wna0j gj-e6q-e per meter of length on a straight wire carrying an 8.46gjqejawn - 0-0-A current when perpendicular to a 0.90-T uniform magnetic field?    N/m
(b) What if the angle between the wire and field is 45.0$^{\circ}\,$?    N/m

  Calculate the magnitude of the magnetic force on a 160-m length of st-fn6- xroz(y. yifd-eraight wire stretched betwee --fi6z-yry(do.efn xn 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 ofv- o8dz62jn;sye m-mp straight wire stretched between two tomzpj- -onde2v m68;ys wers carrying a 150-A current. The Earth’s magnetic field of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  How much current is flowing in .w 0:g:al ixkmc5ww k;2ks:qxa wire 4.80 m long if the maximum force on it is 0.750 N when pla2iax .:kk;5lq0: sxw wkw gc:mced in a uniform 0.0800-T field?    A

  A 1.5-m length of wire carryizmw:w.; jprzp,;s;m:p c9 shjng 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 makes a;mw9hp :j;pw.psr mcs;,zj :zn angle of 38 $^{\circ}\,$ to the wire. Estimate the magnitude of the magnetic force on the wire due to the Earth’s magnetic field of $ 5.5\times10^{ -5}\;T$ at this point.    $ \times10^{-4 }\;N$

  The force on a wire carrying 8.75 A is a maximum of 1.28 N when placed between t ij n1z;e06luxhe pole faces of a magnet. If the pole faces are 55.5 cm in diameter, what is the app0 xenlj1i6 ;uzroximate strength of the magnetic field?    T

  The magnetic force per meter on a wire is measured to be only 35% oz5q9( wha dh 8ujikc+0f its maximum possible value. Sketch the relationship of the wire and the field if the force had been a maxh(h0uca8 5+dwkzi j 9qimum, 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 m1e7 (t xzd6ql ; hfx: fclic-j3-keu/5estf2vaximum of $ 6.50\times10^{-2 }\;N$ when placed between the pole faces of a magnet. The current flows horizontally to the right and the magnetic field is vertical. The wire is observed to “jump” toward the observer when the current is turned on.
(a) What type of magnetic pole is the top pole face?  ----待选择----North PoleSouth pole 
(b) If the pole faces have a diameter of 10.0 cm, estimate the current in the wire if the field is 0.16 T. $\approx$   A(retain one decimal places)
(c) If the wire is tipped so that it makes an angle of 10.0° with the horizontal, what force will it now feel?    N

  Suppose a straight 1.00-mm-diameter copper wire could just “float” horizontld/oc f 1l37+8 iwbqsially in air because of the fi1 f +i378bsco /qwldlorce 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 chaq*pdh +hb: ecf8mu;ao3s y0)4 obre fzzt-h(+rge $q\,=\,+2e$ 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 forf*nc t +n9g270gqtriwce 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 each0(9 tvw97ogyzuhs 8xu34m9y/ ki2nk efrp +nn diagram shown in (Fig. Below3yz t8v9io4nrx(nkyhmn9u se9k7w2 /g 0f pu+), 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 of szlx5y9-a,/su u .lbl $\vec{B}$ 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 u hhli.,ywlvrnb i;o9pv2hqdb8 3/ k56 pward with 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) proton enters a 0.20-T field, in a plane perpendip *2+n zrz6*..* wmbb ohebv,vce0yczcular to the field. +*cnbo,z2zbveyrp *.w .0mhz * 6ebvcWhat is the radius of its path?    m

  An electron experiences thef:fb4 ttnl1b +-nq(qg greatest force as it travels $2.9 \times10^{6 }\;m/s$ in a magnetic field when it is moving northward. The force is upward and of magnitude $7.2 \times10^{-13 }\;N$. What are the magnitude and direction of the magnetic field?    T ----待选择----EastWest 

  What is the velocity of a beam of electyrjvidn2a;/ 1/-cl; vbpng/e rons that go undeflected when passing through perpendi/v/; e-g /lcjibna12y; dpnrvcular 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 whosk ,ewj1nuev,a k/c(x0e 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 requicm4 q9m 7xvi5e4bz.f .u: xjilred for a particle of charge q moving with constant speed v to make one ciz..xj4m cv f:i9ubl45 7iqxem rcular revolution in a uniform magnetic field $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge q movesknoehspp/ 2 t) (*6wzw in a circular path of radius r in a uniform magnetic field B. Show that its momentum is p = qBrh p6)s2pwz/(kt w no*e .

A particle of mass m and charge q .dn1 id 9zn 2+erapqn/moves in a circular path in a magnetic field B. Show that its kinetic energy isnidpz2a rq+1 e/.9nd n proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momentum of the particle in Probl yq k:*ly9j4iyem 21 is $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves p4rc6uxnc.p. with a speed of 160 m/s perpendicular to the Earth’s magnetic fin.cc xr.pu46 peld 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 et t;mv.7rir)kbcr 8yc2c. e6magnetic field at the equator has magnitude $0.40\times10^{-4}\mathrm{~Т}$ and a northerly direction at all points. Estimate the speed a singly ionized uranium ion $(m=238\mathrm{u},q=e)$ would need to circle the Earth 5.0 km above the equator. Can you ignore gravity? $F_B$    $ \times10^{ 8}\;m/s$ $\frac{F_B}{F_g}$    $ \times10^{8 }\;$

  A proton moving withg, ivimg44aw 7 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. 3f mkh4/c/soa How strong is the magnetic field 6.0 cm away from it? Compare 3/aohskcm4 / fto 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)/ dshj9(2*lus*lwn umro4 ad to produce a magnetic field no larger than that of the4uo2lm(n/h) j**surs9dd w la 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 curre ujco-hb*h*3v1 j.lw bnt I out of the page toward you. Indicate, l*.o c-bhbhj1w j*v3u 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 car g e8vymrlwhxw-b2 +0-rying an upward 24-A current exerts an attractive force per unit length ofx8w-yv r+bg-e0hw2 ml $8.8\times10^{-4}\mathrm{~N/m}$ 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 s:u;+utr+ xws*x9svm parallel wires 35 m long and 6.0 cm apart, each carrying 25 A in th;m9wsxssx :+r+tuuv *e same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s mag/ 6h1adru3s8ko5ax5db0 vhel netic field is being carried out 1.00 m from an electric cable. What is the maximum allowab1 /laode6aruh v0db58h3 x k5sle current in the cable if the experiment is to be accurate to $\pm1.0\%?$    A

  A power line carries a current of 95 A along the tops 2 8tw tempw g,tz.+e,0xz-uktof 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 8 0ktextwg,+ 2t, - zupmwtez.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 o9vq 9*w,4s :tuw wjvlcarry 25-A currents in the same direction. Determine the magnetic field at point P, 12.0 cm from one wire sw:*,jw4w99 q tlvuo vand 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 p 3o coro;fh*:wire carrying a 35-A current downward. ;c ho:rop3* ofIn 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 c7 qky/hsi 02eyurrent due north. What is the net magnetic field 20.0 cm due west 07h/2 y ekqysiof 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 protonks 3y04f2e jnls passes a given point in space at a rate of $1.5\times10^9\mathrm{~protons/s~}.$ What magnetic field do they produce 2.0 m from the beam?    $ \times10^{ -17}\;T$

Determine the magnetic field midw u9(q bc*2 )p.s+ew.k0etcaatpdpqz 3ay between two long straight wires 2.0 cm apart in terms of the current I in one when the other carries 15 A. Assume theupp epkqe 9.t(t)aq0c3zcs w2a.+ *bd se currents are
(a) in the same direction,
(b) in opposite directions.

  A long pair of wires co;p p+ 3yhw:l u+.nwociv( vn-znducts 25.0 A of dc current to, and from, an instrument. If the insula3znov. ;u(w-cv++ yn : lhippwted 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 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 (p1g/ hbzour/5vvao a r30u i2v,;hl 9zFig. Below), parallel and just to the right. If it carries 25.0 A upward, what force per meter of length does it exezl1h iv roo;v a,u35rgbz9 a/ 2u0/hpvrt 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 poi;b/q2: /p:erti rvy m(pr gi6unts 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 show nhm0+e5oi hxs7p6r)t n in (Fig. Below)se n6mhi5)o+ph7 xt r0. There is a current of 2.5 A in both wires. Determine the magnitude and direction of the net force on the loop.    $ \times10^{ -6}\;N$  ----待选择----away from wiretowards wire 

  A long horizontal wire carries )jpait b- y 8fbh(eu(s-:z0hx a current of 48 A. A second wire, made of 2.5-mm-diameter copper wire and parallel to the first, is kept in suspension ubf-bs hhxi8:ypet( j)az(0- 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 thatz-in0o0 md e4t they are perpendicular to each other. At their closest, they are 20.0 cm apart (Fig. Below). What is the magnitude of the magnetic field at a point midway between them if the top one carries a current of 20.0 A and the t-4zi enmo00d bottom one carries 5.0 A?    $ \times10^{-5 }\;T$

  Two long straight parallel wires are 15 cm apart. Wire A carri y.a (hr;2ahxzes 2.0 A current. Wire ha;a(y rh2 .xzB’s current is 4.0 A in the same direction.
(a) Determine the magnetic field magnitude due to wire A at the position of wire B. $\approx$    $ \times10^{-6 }\;T$(retain one decimal places)
(b) Determine the magnetic field due to wire B at the position of wire A. $\approx$    $ \times10^{-6 }\;T$(retain one decimal places)
(c) Are these two magnetic fields equal and opposite? Why or why not?
(d) Determine the force on wire A due to wire B, and the force on wire B due to wire A. Are these two forces equal and opposite? Why or why not? $\approx$    $ \times10^{-5 }\;N/m$(retain one decimal places)

  Three long parallel wi3*+loto)jb 8s4opa ekres are 3.8 cm from one another. (Looking along them, they are at three corners of an equilateral triangle.) The current in eol4j8b* o3)pta soek +ach wire is 8.00 A, but its direction in wire M is opposite to that in wires N and P (Fig. Below). Determine the magnetic force per unit length on each wire due to the other two.
$\frac{F_\text{M net y}}{l_\mathrm{M}}$ =    $ \times10^{ -4}\;N/m$ =    $^{\circ}\,$
$F_{N\,net}$ =    $ \times10^{-4 }\;N/m$ $\theta$ =    $^{\circ}\,$
$F_{P\,net}$ =    $ \times10^{ -4}\;N/m$ $\theta$ =    $^{\circ}\,$

  In (Fig. Below), determine the magnitude ad wk -5dhhtdk0fg,o)7 nd direction of the magnetic field at the midpohk kt -5hwd)f7,ddog 0int of the side of the triangle between wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wiresbu3 b;l 1yofr .ke v46ks4uz*s, a distance d apart, carry equal currents I in the same direction. One wire is at x = 0, the other is at x = d, (o* lfk ;b6.4ev13s ubrysz4ukFig. Below). Determine $\vec{B}$ along the x axis between the wires as a function of x.

  A thin 12-cm-long solenoid hagcra*w y .buy6u ga4.i-s)d9r ,ud(h ps a total of 420 turns of wire and carries a current of 2.0 A. Calculate the field inside near the gra.y4 *i,69uuw- u(cga.) r byspddh center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameter is to protq/6wk)n 5v,vh s;/eulhtmj -*fa/ as duce a field of 0.385 T at its center. How muchlkeft ; n,- jv/*uw5s)h/am6 /aqhstv current should the solenoid carry if it has 975 turns of the wire?    A

  A 550-turn solenoid is 15 cm long. T7p, 4 zo6wx yvwynb2h:he current in it is 33 A. A 3.0-cm-long straight wire cuts through the center of the solenoid, along a diameter. This wire carries a 22-A current downward (and is connected by other wires that don’t concern us). What is the47yw6p2bhwo ,yvxnz : 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 solenoiwi s 7 tb1ac:ai15/ajt b,+jrtd that produces the greatest possible magnetic fj51b+7: aattcb1riwij a, s/t ield for a given voltage. Should you make your copper wire long and thin, short and fat, or something else? Consider other variables, such as solenoid diameter, length, and so on.

A toroid is a solenoid in the shape of a circle (Fig. Below). Use Am88q8mjhtb2lg mdoih:u968 ulrms;9 j père’s law along the circular path, shown dashed in (Fig. Below a), to determine that qbmj8ij9l dru lm688og9 8u2:h htm ;sthe 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 magn/tp85wnu vhvtkh93 4wetic field between the conductors of a cowpth38vvkt 9 w/uh4n5axial 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 x2b1cix0y 4ei.vgc0 md7i2 qf; :ujaqplaced with its face parallel to the magnetic field between the pole pieces of a large magnet. When 6.30 A flows in:mf;xc yj10vie2b c2aqg.xqi74d u i0 the coil, the torque on it is $0.325\cdot N$. What is the magnetic field strength?    T

  A galvanometer needle hp/ky/pb0wbewv3 q48 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 galvanfvh+ d-ggy5n .wsw*f 6ometer weakens by 25% over the years, what current will give full-scale deflection if it originally 6*.wfvd h ygg-n+ f5wsrequired $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by what factor does the output to+2 2k zuix/yxxrque ch2x /i+xyu zxk2ange?

Show that the magnetic dipole moment M of an elect6o3qt)f gzg:n;j g 3uzron orbiting the proton nucleus of a hydrogen atom is related to the orbital angular momentum L of the)fg3q zz6jg3g ton:u; electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter and containing nine loops lies flat ohy52 4 kgzmix -yz9v.ln the ground. The Earth’s magnetic field at this location has magni5mkgyyv2. 4 lxiz9-zhtude $5.50\times10^{-5}\mathrm{~Т}$ 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 i:0s z)xq+vzp psf *g drgyp)66n a 0.566-T magnetic field. What value of electric field could mz x6gg)rpzvy :*fp+ 6ssq pd)0ake their paths straight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atoms have radii of cu10hhb 5+ az 47j vn2oqrx7splurvature equal to 21.0, 21.6, 21.9, 22.2, and hpv247rjb5lonx01qha 7u+ zs 22.8 cm. The largest radius corresponds to an atomic mass of 76 u. What are the atomic masses of the other isotopes?

  Suppose the electric field between the electric plates in the mass spectr)0jj/yp q 2ocyometer ofj yjy0qpc /)2o (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 monipg h1-)(oykb mtor air pollutants. It is difficult, however, to separate molecules with ny-mogkh( )1p bearly 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 ions by a volp ysgs 989qsdlmtsg:-+) mm(dtage V before they enter a magn9s-)p+g(s:dmg syd q8smt l9m etic field B. The ions are assumed to start from rest. Show that the mass of an ion is $m=qB^2R^2/2V,$ where R is the radius of the ions’ path in the magnetic field and q is their charge.

  A long thin solenoid h wl2 ,lhk,3 wlmxe(q l2plil3*as 430 loops of wire per meter, and a 25-A current flows through the wire. If the permeability of t l23xle3*wmli2,l hq wl, kl(phe 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 diamx2uzt*y n ,k)seter, and has 640 turns of wire. The magnetic field inside the solenoid is 2.2 T when 48 A flows in t2xzk* uy)s,n the wire. What is the permeability $\mu$ at this high field strength?    $\times10^{-5}\mathrm{T}\bullet\mathrm{m/A}$

  Protons with momentum tlkl7e 629a 8jsreb .y$4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 enterings1w s w13ivob9 a region of constant magnetic field. What is the ratio os11w93bs ivw of the radii of their circular paths?   

  The power cable for an electric trolley (Fig. Below) zf;ao jh; fc )--0jkcj:d st3zcarries a horizontal current of 330 A toward the east. The Earth’s majj;0zk htc a-f;:f3)-sdcz jo gnetic field has a strength $5.0\times10^{-5}\mathrm{~T}$ and makes an angle of dip of 22$^{\circ}\,$ at this location. Calculate the magnitude and direction of the magnetic force on a 15-m length of this cable.    N the force on the wire is  ----待选择----southerlynortherly  and   $^{\circ}\,$ above the horizontal .

  Calculate the force on an airplane which has acquired a niv6 29m4a o:rwj wfd4let 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 almo(hv;xj9rn vdz4v0 d(mst horizontally to the nor9hnrdvxv0 z (;d m4(vjth and has magnitude $B=0.50\times10^{-4}\mathrm{~T.}$ What should be the magnitude and direction for the velocity of an electron if its weight is to be exactly balanced by the magnetic force?    $ \times10^{-6 }\;m/s$  ----待选择----eastwest 

  A doubly charged helium atom, whjtok ulg,b.19(0w:/ijm v tp jose 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. Bela7g 86 n3jfbdrow). 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 to3abnjg8f rd7 6 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 wirt iq,9zj*f- e; hxzr+al;po 1pe is 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 th ;qa-rt,1f9 *zzoejxlph ;i +pe two bottom wires is 95 A in each. Calculate the required current flow in the suspended wire.    A

Two stiff parallel wireyd*4;9ue8xw*ebjkg b +/rmfxw) dbh)s a distance l apart in a horizontal plane act as rails to support a light metal rod of mass m (perpendicular to each rail), (Fig. Below). A magnetic y4d; /9e8h*x ugx)mfb b)de br *w+kwjfield $\vec{B}$, 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 maximu fmp; j7-apkcmir4,g+ (gw 7jrm deflection of the electron beam near the center of a TV screen due t gcim;p -4pmkg w,rj j7f+(r7ao 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 oy460yat)9 dqdb v o6pelementary particles such as protons to high speeds. Particles starting at point A with some initiaoo 4qdatb) y9dy6p0 v6l 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 parallel wires, located at the corners orlae6zz xh89cf4v)c-0 4ys j,rjyk. wf a square of side l, carry equaly9 x-rh vws lyje8.zzc ajfc,6)k40r 4 currents $I_0$ perpendicular to the page as shown in (Fig. Below). Determine the magnitude and direction of $\vec{B}$ at the center C of the square.

  Magnetic fields are very useful in particle accelerators for “beam steerin)cpecg( os3b7o76 gcxg”; 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 happens to protons that are not moving with the speed that the magnetic fielg77( 3cc6bxg opces)od 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 c74szbqh4q3ox 89bkc,oi7z ji enter of a circular coil of wire carrying a current I (as in Fig. Be7q8ibk 43s9jqb4zhxc7 ,ozi o low) 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 about 1G(vg( 7pbh)kd zxm)8;jn ;n amy:$ 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 magnetin3 k3sh fu zm;ahw,46dc fields produced by overhead power lines. You estimate that the two wires are each abok3 6h4sn a;dw3u,mfzh ut 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 makh.fyvmanoe):f5)x id-r )4g:k v5ytge a beam of electrons, traveling to the rt:5)yha4ny-o)g)5ff vg kmrixvd e .:ight 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 throug0axr *yvj2oi.6t,j vlh 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, at points P and Q, the radii are 10.0 mm and 8.5 mm, respectively. Calculate the change in the kinetic energy of ttio.,v vaxr 0jj6ly2*he 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-(dvy 304/*eeuhoy6gdjzw, tp T magnetic field at its center. If the maximum current is uo/d3(6e,wh4y ydvz*e jpg t05.7 A, how many turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, eac7vp1*tt 2l lzlh 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 an7vptl*2zll t1 gle of 3.0$^{\circ}\,$ with the vertical, what is the current in the wires?    A

  An electron enters a ujvj d+ r./uoc2niform 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$