A compass needle is not alwgu.sb*7q1a, zk gxw:c ays balanced parallel to the Earth’s surface, but one end mw :zasqu7kg1 ., *bxgcay dip downward. Explain.

Draw the magnetic field lines around a straight section of wireloy:)t jl4o6ram7 ejs1gj + 7v carrying a current horizontally t+7jmrygv t)4al e1:6j j so7loo the left.

In what direction are mk 6n*d pat gcz38h) qpk27up.mi ne;:9fj.tathe magnetic field lines surrounding a straight wire carrying a current that is moving direct :8*73ki2pmqnj m eft;tpnkgua 6h..a 9dcp)z ly away from you?

A horseshoe magnet is held vertically witq j( 0qm2 oj-gvahk0n4h the north pole on the left and south pole on the right. A wire passing between the poles, equidistant from them, carries a current directly -q0 (avj40n kgjm ho2qaway from you. In what direction is the force on the wire?

Will a magnet attract any metallic object, or only those made obam1 lgg6a, o-7 j7dxdf iron? (Try it and see.) Why is this -1aobm 7 76g ldxj,agdso?

Two iron bars attract/kb*4i9zro wy each other no matter which ends are placed close together. Arwio k9* z4ryb/e both magnets? Explain.

The magnetic field due to current in wires in youm5f *8rvp/h vgr home can affect a compass. Discuss the effect in terms of currents, inc fm8v* 5h/vpgrluding if they are ac or dc.

If a negatively charged particle enters a region of uniform magneticn8p wqzfx8 8)z field which is perpendicular to the particle’s velocity, will thwx8)z 8p8nqzfe kinetic energy of the particle increase, decrease, or stay the same? Explain your answer. (Neglect gravity and assume there is no electric field.)

In(Fig. Below), charged particles move in the vicinity of a cur2c (icp.fwo:a rent-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 direcpo .c2 :wcaf(ition of the magnetic force due to the magnetic field produced by the wire.

Three particles, a, b, and c, enter a magnetic field as shown in Fijkfed *yb/2)d g. 20–46. What can you say about the cb*ekj2d)/y dfharge on each particle?

A positively charged p.)ly zx/vie:z article in a nonuniform magnetic field follows the trajectory.e :lvx/)zyzi 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? C ybwebrv0-i:*,xv o; *pm:my can a magnet attract an iron rod? What must you consider mpb;,v*iry- y0mvoc xbe:w*:to answer these questions?

Explain why a strong l*h7k;v ihep( x::f6uaj3 hd wmagnet held 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 to your TV by trying this.][/But don’t risk damage to your TV by trying this.vk wil(;jhuh3 :fde7h pa :x*6]

Suppose you have three iron rods, two of which are magnetized but the third is m/3e/diaiw .:9jdhab nm:3idd / ./a9hwbieajot. How would you determine which two are the magnets without using any additional objects?

Can you set a resting electron into mot*3wwpo-e9l 9z ar)j:mpsug4b ion with a magnetic field? With an electric field? Expla*e lapj4- w)9bswupo :mz9 3grin.

A charged particle is moving in a circle under the influence of pl s8+,r-maas a uniform magnetic field. If an electric field that points in the same direction as the magnetic field is turned on, describe the path the charg arml+ s,a-ps8ed particle will take.

The force on a particle in a mag3z,q gcg57ti fnetic field is the idea behind electromagnetic pumpingt7gq5gf , ic3z. 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 same direction?

A beam of electrons is directed toward a ho6f0 9(dpui/ cl r)cmgmrizontal wire carrying a current from le i0m6/clu gd(rmcp9f) ft to right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields that surround a moving electric char,ba6f 7+v1xujh+4 nvq )vlj:i ehopd:ge.o 7 6hxjavdbnp,4+ v:u1evqj+):ih fl

A charged particle moves in a straight line through a p 1+rz tm1c9nloarticular region of space. Coul1mzr o+1c9 ltnd there be a nonzero magnetic field in this region? If so, give two possible situations.

If a moving charged particle is deflected a t1s z ibvg;n,0:jv8ssideways in some region of space, can we conclude, for certain, i0n j81vb sv:,zt;sgathat $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is a uniform ma1p-r it,/hvnke31/9dgwszk ,-jtial gnetic 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 m pk.3qn8n 5xkmoving electrons in a certain region of space are being deflected by an electric mq5xpkn 8n3k .field or by a magnetic field (or by both)?

How can you make a compass without using iron or other ferromagnetic material?mjua37i+8x; 9m;owwj y ,bi bk

Two long wires carrying equal currents I are aq:1 ibd) 1buxrg.o3surhu i+ qkc;;g7t right angles to each other, but don’t quite touch. Describe the magnetic force one exerts on the othe b b)dk gqur;gu73:co;iuis .h+q xr11r.

A horizontal current-carrying wire, free to move in Earth’( sy.v-w2-usu w3fh vjs gravitational field, is suspended directly above a second, parallel, current-carrying.vs(y-v-wf uw 3su hj2 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 of iron cri8x3 q89e+gmoddymi5)a i8 ?

An unmagnetized nail will not attract an unmagnetized paper7wz7oim 3 j 8z zfa(,wif(b: b0aby3xr clip. However, if one endj zm(z7b,3 rf ia387bybfizww0xo:a( of the nail is in contact with a magnet, the other end will attract a paper clip. Explain.

Two ions have the same mass, but one is singly ionizq)/e29rdt m 0fp9nc es5wbfj8cu 1dd:ed and the other is doubly ionized. How will their positions on the film of a mass spectromet1w5nd q:u29dcfbd s m/9p f80rjce)et er (Fig. Below) differ?

What would be the effect on B inside a long sorc qsgw0o8ju68/ishb5q8 w*c,.l pvalenoid if
(a) the diameter of all the loops was doubled,
(b) the spacing between loops was doubled,
(c) the solenoid’s length was doubled along with a doubling in the total number of loops?

A type of magnetic switch similar to a sojap /7qgl b-r l0g37ttpsv :7jlenoid 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 re lp-0jbgs7vrj: 7q t ptlg73a/lay to close an electrical switch. A relay is used when you need to switch on a circuit carrying a very large current but you do not want that large current flowing through the main switch. For example, the starter switch of a car is connected to a relay so that the large current needed for the starter doesn’t pass to the dashboard switch.

  (a) What is the magnitude of the force per qo fruz2 eet:ljw qip* 27/8w1meter of length on a straight wire carrying an 8.40-A cu iqeo*j 22f:1/wlz7q 8rewtpurrent 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 zo7llc 23 (rt+a+zonzthe magnetic force on a 160-m length of straight wire stretched between two towers clz +ooct z+237(anrzlarrying a 150-A current. The Earth’s magnetic field of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  Calculate the magnitude of the magnetic force on a 160-m length of sozx ba mxq;u-ig* ;c)34i1rvssrt/.itraight wire stretched betweeuzbix3s.so1v;amqi ;/ xcig )* 4-trrn two towers carrying a 150-A current. The Earth’s magnetic field of $ 5.0\times10^{-5 }\;T$ makes an angle of 65$^{\circ}\,$ with the wire.    N

  How much current is flowi 6wy3. 1wmum(icz11as yv8huvng in a wire 4.80 m long if the maximum force on it is 0.750 N when placed in a u31s6c h1 y1uawzumv8.mwv(yiniform 0.0800-T field?    A

  A 1.5-m length of wire carrying 4.5 A of current is oriented horizontally. x7qb c8)w ph(:uc4se;h/vjtnAt that point on the Earth’s surface, the dip angle of the Earth’s magnetic field makes an angle ofqvxu;: 47esnpht)/w c cj(bh8 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 maximum9b7 fbv0cyqa3 40unaq of 1.28 N when placed between the pole faces of4qu vy0 n0bacfab973q a magnet. If the pole faces are 55.5 cm in diameter, what is the approximate strength of the magnetic field?    T

  The magnetic force per meter on a wire is measured to be only 35bjcc*,ut(9z n .z*ugu4ho0r 9z ekp9s% of its maximum possible value. Sketch the relationship of the wire and the field if the force had been a maximum, and sketch the relationship as it actually is, calculating ucs.k9 9goucz 94r*u* e jbz(,htpz 0nthe angle between the wire and the magnetic field.    $^{\circ}\,$

  The force on a wire is plpao dsk:4qfo /5;m; a maximum 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” wzpk q5h4;3c*v,esee ds;ehamqscsh8, )/8 x horizontally in air because of the force due to the Ep hdkh/3h m5scs;sve;, *wes eaq4) ,ez8cxq 8arth’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 che;7d xy 2x7tx/psjd w(arge $q\,=\,+2e$ 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 electrotbhz tu1s.nt+ osf0;9 lsdd4.n 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 oxh4a1 j4l e2-jr tyrk4n a negative charge for each diagram shown in (File 44ryj2-4 1jthx karg. 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 directi r *p 8gjfjdqg(nd0-s8v3.zxbon 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 w2h mq7mx2nfd5rray*8w zf9u9 ith 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) j:s9 vg7 tia+vr ;-9s8jcl ndgiw;m.k) ud.fk proton enters a 0.20-T field, in a plane perpendicular sjgk- i9rdaktf:j.)d c g muvi987n; s+lw.;v to the field. What is the radius of its path?    m

  An electron experiences the greatest force as itseap1.5,(+tkhcri xfud k w03 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 velocityzh)qxh 653o:k pe dkk* of a beam of electrons that go undeflected when passing through perpendicular electric and magnetic fields of magnitude5hdk*k hq p):x6ze 3ko $8.8 \times10^{3 }\;V/m$ 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 mas/ca /;x.hv mf4:rjihqs 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 movimyr7j0 x :vnr*ng with constant speed v to make one circular revolution inn:vj rxr*0 ym7 a uniform magnetic field $\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge q moves in a circular path of radius r in a uniform magnhs9gj1w w b7gfb0/gb8etic field B. S81 hw/bgfgg7w0sb9b jhow that its momentum is p = qBr .

A particle of mass m and charge q moves in a circul:.qccp3secjw 886k4iw e y2n xar path in a magnetic field B. Show that its kinetic energy6k c4 ww cxqjpec3 syi:.8e8n2 is proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angularopuwfc5w3+fs*j42eh e bw *b0 momentum of the particle in Problem 21 is $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves with a speed of 160 m/s perpendicu6 60my zv4bh0 p8dfmsblar to the Earth’s magnetic d6m 64vys bzbm0p08fhfield 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 eq9dj-ix *gheow 4(z 6czuator 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 withxs:+-t*kjaaa xi 4,c5he ua i7 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. Howff5qt;v;* mk -wqg3 fn strong is the magnetic field 6.0 cm away from it? Compare ;*w5gkqt ;fm 3nvf-fq to the Earth’s magnetic field. $B_{cable}$   $ \times10^{-4 }\;T$ the field of the cable is about    times that of the Earth.

  If an electric wire is allowed to produce a magnetic field no larger thansi 1cnz sy6w06g )xj*s6 rq-ev that of the Ec6 z *1x ew0ys66qrv )gjnis-sarth $(0.55\times10^{-4}\mathrm{~Т})$ at a distance of 25 cm, what is the maximum current the wire can carry?    A

In (Fig. Below), a long straight wire carries cf7q) -to;/wze2gbivppk*9w uurrent I out of the page toward you. Indicate, with appropriate arro -izk)7boquv; *w e9tp/2gpw fws, 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 carryi4/hb obdp+9l- p3-x/ di hsvmrng an upward 24-A current exerts an attractive force per univ-34s9 xhp+l/i hd mrd-bb/opt 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*a+-p ,2k3ld imdmb vd1(yjtg force between two parallel wires 35 m long and 6.0 cm apart, each carrying 25 A in the same directioda,v l3dmibk g* -1+jt p(dm2yn.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s ma c n+wymg-pe jps;i;31gnetic field is being carried out 1.00 m from an electric cable. What is the maximum allcisny ;e3wp1g+pm- ; jowable 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 of 8-4xi;dgz k qe/agny g-xm.6+-,xfkp t .5-m-high poles. What is the magnitude of the maad 6gq- ;zkxp-+4mxkng , eyit/- fgx.gnetic field produced by this wire at the ground? How does this compare with the Earth’s field of about $\frac{1}{2}G$?    $ \times10^{-6 }\;T$ The field of the cable is about    % that of the Earth.(retain two decimal places)

  Two long thin parallel wires 13.0 cm apart carry 2p zic5n) ohf-95-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. Below5i-n h)9focp z).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18 cn7apzar/x r9j3g) ,zjm due south from a straight vertical wire carrying a 35-A current downward. In73x/ jjz)z g,apna r9r 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 cur -xefl0ij;tmm 8*, wdarent due north. What is the net magnetic field 20.0 cm due west of the wire if the Earth’s field there points north bul-mfi8m;wxjt a d *e0,t 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 space at a ra(bs:d8ucur 2p;0.fl sku8mrcte 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 gra-;h z-/ 9*p;gxaps7ez tdj p0y5natwo long straight wires 2.0 cm apart in tep-ya7ta9*s-z5j; d ra/g0xn ;pzphge rms 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 de pgx( 912kxb5v5zni A of dc current to, and from, an instrument. If the insulated wires are of negligible diameter but are 2.8 mm apart, what is the magnetic field 10.00 cm from their midpoint, in their plane (Fig. Below)? Compare tox1(xgvbpz5di 92n5k e the magnetic field of the Earth.
   $ \times10^{-6 }\;T$ The field of the wires is about    % that of the Earth.(retain two decimal places)

  A third wire is placed in the plane of the two wires shown in (Fig. Belowavfhkxl)(6p) ;c 5 hoq), 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 o(xfakp hlv5 h;c)q)6 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 pointgl9n1pw u1o( rs 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 ,ruvr0 ;u5lre in (Fig. Below). There is a currentur0r,;leu 5 rv 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 c al-nsbsy;h-v,p qojk3:+ v f1arries 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 magne k1oa bp,j+fvnshv ql-y-:3 s;tically 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 orienkr5o:w.2 n/ci7 ziorx ted so that 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 midwarc o5ii.:rx 72 wozn/ky between them if the top one carries a current of 20.0 A and the bottom one carries 5.0 A?    $ \times10^{-5 }\;T$

  Two long straight parallel wires are 15 cm apart. Wi (m9 vzobm*i6wre A carries 2.0 A current. Wire B’s current is 4.0 A in the samemvzmo(w6 9* ib 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. +hv dfcu26tlwx3c0 n. (Looking along them, they are at three corners of an equilateral triangle.) The current in each wire is 8.00 A, but its direction in wire M is opposite to that in wires N and P (Fig. Below). Determine the magnetic force per unit length ou2 dl+t wx v0ch6nc.3fn 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 magnitudc/p- t:lk9o ror;p*qqe and direction of the magnetic field at the midpoint of the side of the triangle between ; *ctlproqr p/qk:o-9 wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a distanw7pzvca7*5 s nh)o iel.8or2;gg,apcce d apart, carry equal currents I in the same direction. One wire is at x = 0, thhp gzc, ec 2 o;a7pg7vwisl5naro )8*.e 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 carries a spr*/ abgktg 1e5:3*fxze+vxiloz/,current of 2.0 A. Calculate thez/ glr*/e*,+f31 esxkatpo zi 5:vbgx field inside near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameter is to produce ayih.d 2,m ic u)1d byix.j31(5o2rdze ihg (au field of 0.385 T at its center. How 1 u2i j35d,d yuhira(2 oe(mx1.ycdbzii )g.hmuch current should the solenoid carry if it has 975 turns of the wire?    A

  A 550-turn solenoid is 15 cm long. The current i8qj .i(u(q455rp 0vcpm brv ts laao+0n 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 the force on this wire assuming the soleja io tp(85rq mpa+4buv.l0 vqs c0(5rnoid’s field points due east?    N

You have 1.0 kg of copper and want to make a practical9 im+vsl(51k ukz p0d0 gaq3ql solenoid that produces the greatest possible magnetic field for a given voltage. Should you make your copper wire long and thin, short and fat, or something else? Consider other v m 3k0luqi5s(dplz9 +1k aqg0variables, such as solenoid diameter, length, and so on.

A toroid is a solenoid in e7teim/ )v1/pmddwz/ the shape of a circle (Fig. Below). Use Ampère’s law along the circular pat 1/t w mev7/edpidm/z)h, shown dashed in (Fig. Below a), to determine that the magnetic field
(a) inside the toroid is $B=\mu_0NI/2\pi r$ where N is the total number of turns, and
(b) outside the toroid is B = 0 .
(c) Is the field inside a toroid uniform like a solenoid’s? If not, how does it vary?

(a) Use Ampère’s law to show that the magnetic field b171y zvjti:*wq xv3;oskzpf1 etween the conductors of a coaxial cable (ip3jtvwf;x k71yv z*sz1: qo 1Fig. 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 its fao t5n 5u xx/8hfpyvlq 77)n)npce parallel to the magnetic field between tf pvnn h7yup xqo5t7 l5)/n8x)he 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 needleo qhw01 vd1h:b 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 ta 8t /tdzp9/cdfh/v g1he years, what current will give full-scale deflection if /hcv9/18d/a zpft tdgit originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by what factor does so;ls5 ogc(s(the output torque changsls((o5 gs;oce?

Show that the magnetic dipole moment M of an electmt drpt+m8 -6rron orbiting the proton nucleus of a hydrogen atom is related to the orbital angular momentum L of thpm-6m+dr tr 8te electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter and containing pabsk6;rps4ibx)4cd )p:x9in f-k;qnine loops lies flat on the ground. The Earfr ;psp;):aqxxpkki)s4-6i 4d n b9b cth’s magnetic field at this location has magnitude $5.50\times10^{-5}\mathrm{~Т}$ and points into the Earth at an angle of 56.0$^{\circ}\,$ below a line pointing due north. If a 7.20-A clockwise current passes through the coil,
(a) determine the torque on the coil,   $\times10^{-5}\mathrm{m}•\mathrm{N}$
(b) which edge of the coil rises up: north, east, south, or west?

  Protons move in a circle of riyjenc8 (-f(hia 9d8 dadius 5.10 cm in a 0.566-T magnetic field. What value of e8jadc-yi h ( i(de8nf9lectric field could make their paths straight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germa(b-yc 8f: qjq9(xdlvbjev,w- nium atoms have radii of curvature equal to 21.0, 21.6, 21.9, 22.2, and 22.8 cm. The largest radius corresponds tove8qb(dyj 9q-wl-(c,fx : vjb an atomic mass of 76 u. What are the atomic masses of the other isotopes?

  Suppose the electric field between the elegy3avz6 k5;eeear9s c(4 zla : )4vk+da0tcqzctric plates in the mass spectrometer oda( 5z44av ;vkz y 6: cesa0qg lzt3cer)9k+eaf (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 oj87o ou1ug *pq4 uwi*used to monitor air pollutants. It is difficult, however, to separate molecules with nearly equal mass such as CO (28.010puoi7 g*u8q *oj4w1 ou6 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 voltage V befor f8syr(8/wayo e they enter a magnetic field B. The ions are assumed to start from rest. Show that the mass of an s r8 y8fya/w(oion 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 j(bdi s3 5se5ubm(w)ca 25-A current flows through the wire. If the permeability of the 3e sd bbucji(5)mw(s5iron 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 mn wwze4qa3c2i57( wy6tynwa55 d (ctin diameter, and has 640 turns of wire. The magnetic field inside the solenoid y5 c3iw2 tt6wa5eq(nmww y4 zcd(na75is 2.2 T when 48 A flows in the wire. What is the permeability $\mu$ at this high field strength?    $\times10^{-5}\mathrm{T}\bullet\mathrm{m/A}$

  Protons with momentum gldp: dg k)1ll)/n r)ogl w9)v$4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 energtrpcx k :9d /gm6 4mz5gq6m-lcy upon entering a region of constant magnetic field. What is the ratio of6rk6c tm lm:5g/q -4gxmc9dz p the radii of their circular paths?   

  The power cable for an electric trolley (Fig zus3f e*-7ve50jn prc. Below) carries a horizontal current of 330 vn r- z0*u3cepfjs57e 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 on an airplane k l:h p7,vd+n :z:elcjwhich has acquired a net charge of $1550\mu C$ and moves with a speed of 120 m/s perpendicular to the Earth’s magnetic field of $5.0\times10^{-5}\mathrm{~T}$.    $ \times10^{-6 }\;N$

  Near the equator, the Earth’s magnetic field points almost horizontally to the ,h6 7.ewm5)qw qlrm n:ncnqd6 north and 6qeqrn l ,5:q mnch .)7m6wwdnhas 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 ma 99pj58g7nf* tury;wmg wj1rass 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. Belo s t.3 auqxceduw*u;*9w). 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 d.c;s qeua*39uw*ut x magnetic field point?
   A
the magnetic field must be ----待选择----updown 

  In (Fig. Below) the top wire is 1.00-mm-diameter copper wire and is suspendcf7-z (2s cg 8iivkblk:p9 zz9zb *qb0ed in air du p9cziifzk*7b:z -(glz9 08kcb sqv b2e to the two magnetic forces from the bottom two wires. The current flow through the two bottom wires is 95 A in each. Calculate the required current flow in the suspended wire.    A

Two stiff parallel wires a distance l apar5glr5eh.6l sxxvzr 82t in a horizontal plane act as rails to support a light metal rod of mass m (perpendicular to each rail), (Fig. Below). A magnetic fxv.6 5 rhrzl52s e8lgxield $\vec{B}$, 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 deflemf:9b d*tnl1eqe -ub( 58l gxhction of the electron beam near the center of a TV screen due-5(*e u:dm 8xb19elhlgqb tnf to the Earth’s $5.0\times10^{-5}\mathrm{~T}$ field. Assume the CRT screen is 22 cm from the electron gun, where the electrons are accelerated
(a) by 2.0 kV,    mm(Round to the nearest integer)
(b) by 30 kV. Note that in color TV sets, the CRT beam must be directed accurately to within less than 1 mm in order to strike the correct phosphor. Because the Earth’s field is significant here, mu-metal shields are used to reduce the Earth’s field in the CRT.    mm(Round to the nearest integer)

The cyclotron (Fig. Below) is a device used to accegv3 fo0m9ox.u lerate elementary particles such as protons to high speeds. Particles starting at point A with some initial velocity travel in circular orbits in the magnetic field B. The particles are accelerated to higher speeds each time they pass through the gap between the metal “dees,” where there is an electric field E. (There is no electric field inside tux9fg0.3 o omvhe 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 parapz (a wps0y9a e428tpngye8x: (fn s*dllel wires, located at the corners of a square of side l, carry equal currents e:an(89* nt adpxe (82pwsy4gz yp0sf$I_0$ 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 c)m8u 6: bu/v0bhisbqkaie0+ accelerators 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 happens to protons that are not moving with the speed that the magnetic field is designed for? If the field extend0bq0cmu/ukhe)+8b6 sbv :iai s 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 ce(a og8f m lk1ec).cg6ircular coil of wire carrying a current I (as in Fig. Below) cke8g6 c g.ole(1f)amis
$B=\frac{\mu_{0} N I}{2 r},$
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 i f9a-**rkolmls about 1G($ 1\times10^{ 4}\;T$) Imagine a simple model in which the Earth’s field is produced by a single current loop around the equator. Roughly estimate the current this loop would carry. [Hint: Use the formula given in Problem 80.]    $ \times10^{ 9}\;A$

  You want to get an idea of the magnitude of magkh ) e/p8xj00bskc/p p tks5)anetic 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, values are r)khbp/tx 0sp)58 0ksk/ce japms, and the magnetic field will be changing.] $B_{net}$ $\approx$    $ \times10^{ -5}\;T$(Round to the nearest integer)

  (a) What value of magnetic fi cciy9a,:(ih6u qr:ykeld would make a beam of electrons, traveling to the right at a spa h qu6c,(::iycri k9yeed of $4.8 \times10^{ 6}\;m/s$ go undeflected through a region where there is a uniform electric field of 10,000V/m pointing vertically up?    $ \times10^{ -3}\;T$(retain one decimal places)
(b) What is the direction of the magnetic field if it is known to be perpendicular to the electric field?
(c) What is the frequency of the circular orbit of the electrons if the electric field is turned off?    $ \times10^{7 }\;Hz$

  A proton follows a spiral path through a gas in a magnetic field of 0.0egs5om fi, jro*vr 3r)rs v5//10 T, perpendicular to the plane of the spiral, as shown in (Fig. Below). In two successive loops, at points P and Q, the radrv,ssre)g*o i5m5j/3 r/f rvoii 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 ;kdbj a8ssz 7 *1njj8zproduce a 0.30-T magnetic field at its center18j8jk zn7*s;jdzas b. If the maximum current is 5.7 A, how many turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, each of yv9fcl 9o9.ho jfku2 e,sa1 /hdiameter 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 tsce h /ouvaf219yfl.,ok9h 9 jhe suspension strings make an angle of 3.0$^{\circ}\,$ with the vertical, what is the current in the wires?    A

  An electron enters a unifovvzudft, m0pz-7 h7: jrm 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$