A compass needle is not always balanced parallel to the Earth8zqlu;r*lm /p 4bg-y c(v pbl9’s surface, but one end may dip downward. Explz;vb(rq49u g mlylpb8*lp-/ cain.

Draw the magnetic field lines aro9n+r9b-a3;cxs hzya e5)nhjjund a straight section of wire carrying a current horizy3r 9n5;h+ja bs)ezhnxaj9- contally to the left.

In what direction are the magnetic field lines surrounding a sxlpt 065s-o g-mqlqa -traight wire carrying a current t a ts xql0-5--6lqpmgohat is moving directly away from you?

A horseshoe magnet is held 1hbc2twd4ilf7josu, .ph 2g4 vertically with the north pole on the left and south pole on the right. A wire passing between thhod4w hj27pu1,slcf .t 2 bgi4e 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 maxm(19mtf* n2b k yn(zode of iron? (Try it and see.) Whf (mobn2*9z xk1 (nmyty is this so?

Two iron bars attract each other no matter which ends are placed close togethetdr hz1 b1n6-er. Are both magn znt 61eb-dhr1ets? Explain.

The magnetic field due to current in wires in your home caf ,ytj)co.mw8 j *3gzye3a s7pn affect a compass. Discuss the effect in terms of currents, including if they are ac or jj7e3*pyfo g3c,8.ms yzta w )dc.

If a negatively charged particle enters a regi3dk) a2ojecnheh+5 yqklg .9rfra 88-on of uniform magnetic field which is perpendicular to the particle’s velocity, nag8)r83h- cde 9 k q5 efr.alhyjk+2owill the 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 oa w9wo;phmtv0 *zfc*2 f a current-carrying wire. For each charged particle, the arrow indicates the direct*com 0;z wva2thw f*p9ion 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, enter a magnetic fiee3 t b-ucosy *c4+u)ykld as shown in Fig. 20–46. What cku* toye3) sbyu4c +-can you say about the charge on each particle?

A positively charged particle in a nonuniform magnetic field followsm5 xszdnuk7 t+coide,:;8j8d the trajectory ,o c;e+nd u:z8xsd m8tjdi7k5shown in
(Fig. Below). Indicate the direction of the magnetic field everywhere in space, assuming the path is always in the plane of the page, and indicate the relative magnitudes of the field in each region.

Can an iron rod attract a magnet? Can a magnet attract :dfoz a 171gjqan iron rod? What must you consider to answer the:qj1a 7 zodfg1se questions?

Explain why a strong m x 18y 42ta-p3thuwmrgagnet 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 thea8mxw14tr p-uhg3y2t 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 ia +ncj 2v3d)i56 degtsio;6 jdhwo8/o ron rods, two of which are magnetized but the third is not. How would y dcs2adi6; jnv wt +odi8e5h3 o)g6/joou determine which two are the magnets without using any additional objects?

Can you set a resting electron into motion pbp,koub221 /s5 sqxhwith a magnetic field? With an electric field?psup21/xq 5bk h,sbo2 Explain.

A charged particle is moving in a circle under the influence of a uniform magn;4*ex3svw h) 3luwio aetic field. If an electric field that points in the same direction as the magnetic field is turned on, dew34vo 3l*a;)s hxuwiescribe the path the charged particle will take.

The force on a particle in a magnetic field is the idea xxs4eb hmrv zti o;:3* ,p/0epbshz1- behind electromagnetic puhes/ :e,vs1o -ptzxxri*0mb; zbp 34hmping. 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 horizont yyyps7 fpr2rai .t(4*al wire carrying a current from left to right ryspai7p.ytr2y(4 *f
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic f1 ;5ru.v84 qqqxvif8jy9yslmields that surround a moving electric charge.qy8yl 8x1j mu95; .srivf q4vq

A charged particle moves in a straight line through a particular region of ck.q 8tu3t+w tspace. Could there be a ntctq8 k 3.+uwtonzero magnetic field in this region? If so, give two possible situations.

If a moving charged particle is deflected sideways in some region of space, can r.71tba z+ jbbiua2h:we conclude, for certa t b+2arj.hz bi7:b1uain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is a uniform magnetic fis (:afjjsbm*-p 5v3xf eld $\vec{B}$. 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 space are 0/bu-zdel2ce v6qvurvs* (o+ 2)wz bg being deflected by an electbuw0qbcszrz )e-eu / 2ovdv+vg 6l*( 2ric field or by a magnetic field (or by both)?

How can you make a compass without using iron or other feb 25acx wm,v*srromagnetic material?

Two long wires carrying equal currents I are at right angle. -3(khh(: cwpo3kt 9opk tvuls to each other, but don’t qukt3 :hlt9 khvpp3o c-.(ouwk (ite touch. Describe the magnetic force one exerts on the other.

A horizontal current-carrying wire, fr+ ff4 oxqnlli;*;xozu m4ew7r2i/*n eee to move in Earth’s gravitational field, is suspended directly above a secon4*+*oxe7eil ;n mfqi wr/;z u 4nxof2ld, 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 + 2/k z(wsjuhpattract an unmagnetized piece of iron?

An unmagnetized nail will not attract an unmnza*l.dai i4 )agnetized paper clip. However, if one end of the nail is in contact with a magnet, the other end will attract a paper clipda.z)a4 in*li . Explain.

Two ions have the same mass, but one i ic;dg8-m:klh ca4pc9s singly ionized and the other is doubly ionized. H4cih8cl k:;dcmp- ga9ow will their positions on the film of a mass spectrometer (Fig. Below) differ?

What would be the effect on B in+dw8 ox7lw.cw :fkcv*side a long solenoid if
(a) the diameter of all the loops was doubled,
(b) the spacing between loops was doubled,
(c) the solenoid’s length was doubled along with a doubling in the total number of loops?

A type of magnetic switch similar to a solenoid is a ;38wwxmtw jw23s gdx y07- k(ehokif9 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 current but you do not want that large current flowing through the main switch. For example, the starter switch of a caj fdw wi(s h2 kg-7x3k0xwmywt o;e839r 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 memo kjtqha59d 2f8 /mu1ter of length on a straight wire carrying an 8.40-A current wm/ht5f8umj k dq 92ao1hen 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 magnitudehupapj q :vdltz083 e :::orq6 of the magnetic force on a 160-m length of straight wire stretched between two towers carrying a 150-A current. vr:z6a ueoq8tqhj 0l3pd: ::p 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 b+9b fg8gz 2 hbgwn6/c160-m length of straight wire stretched between two towers carrying a 15b6+/ggbbchwz f98ng 20-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 flo:kvpc2 aw a,v-psw8 (cby -/egwing in a wire 4.80 m long if the maximum force on it is 0.750 N when placed in a unifowv: ,8c ky-p cs-ape/avg(wb2rm 0.0800-T field?    A

  A 1.5-m length of wiwv,4j-r 5e5x ;isi6heqx ncgd3 vmh48re carrying 4.5 A of current is oriented horizontally. At that point on the Earth’s surface, the dip angle of the Earth’s magneticwv8d54;nhxvig 6q je- m4xr e 5hi,s3c field makes an angle of 38 $^{\circ}\,$ to the wire. Estimate the magnitude of the magnetic force on the wire due to the Earth’s magnetic field of $ 5.5\times10^{ -5}\;T$ at this point.    $ \times10^{-4 }\;N$

  The force on a wire carrying 8.75 w*t/j3u pf5an A is a maximum of 1.28 N when placed between the pole faces of a magnet. If the pole faces are 55.5 cm in diameter, what is the approximate strength of the magnetic field? wn *u/t5p fja3   T

  The magnetic force per meter on a wire is measured kr-au2- 8yiu8nirn 8 ito be only 35% of its maximum possible value. Sketch the relationship of the wire and the field if the fork i-8ru88- ya2riun nice 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:m 76lji ;nxz -vo h:.tbj-zbs 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 “floo*w70j+ub bocat” horizontally in air because of the force du b*jwcuob7 +0oe 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 clc6 p.bb ,tyj+harge $q\,=\,+2e$ 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 dire-w )*kv) zzbswjzxas;8: yxn-ction 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 nexyiquc))ngr (z 71f(ggative charge for each diagram shown in (Fin) ( ) (yigzuxqg1rc7fg. 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 direction of/vw+bmr2z7x utourlki- e(8 + $\vec{B}$ 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 verticals ,uputg9vs -ywnb(sd ,i/5b4ly upward 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) *n ca.;jf.amhproton enters a 0.20-T field, in a plane perpendicular to the field. Whaam ;.f*c.jn hat is the radius of its path?    m

  An electron experiences the greatest force as iraha x2 ,ojf2e-( )o 0m7lkbdgg6 4x,m/uukrmt travels $2.9 \times10^{6 }\;m/s$ in a magnetic field when it is moving northward. The force is upward and of magnitude $7.2 \times10^{-13 }\;N$. What are the magnitude and direction of the magnetic field?    T ----待选择----EastWest 

  What is the velocity of a beam of electrons that go undef 5vl / bo-(ty(5.kmr0 bdqgppolected when passing through perpendicular electric a0 vq-b.yg5op /mkto (pdr(bl 5nd magnetic fields of magnitude $8.8 \times10^{3 }\;V/m$ and $3.5 \times10^{-3 }\;T$, respectively? What is the radius of the electron orbit if the electric field is turned off? $F_E$    $ \times10^{6 }\;m/s$ $F_{max}$   $ \times10^{ -3}\;m$

  A doubly charged helium atom whose mass is0m;:eg:2cc -mggjx1 x1n whdl $6.6 \times10^{-27 }\;kg$ 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 p8nx7/v*k ad- t( ,rtapf no)fxarticle of charge q moving with constant speed v to make one circular revolution in a uniform magnetic field fptxr-tk)*a8no,vx7/d f( na$\vec{B}(\perp\vec{v})$ is
$T\,=\,\frac{2\pi m}{qB}$.

A particle of charge q moves in a circular path of radius r in a una+p6n22 d2b p8mnlljniform magnetic field B. Show that its momentum is p = n a62n+2bjll 2dn8 ppmqBr .

A particle of mass m andgxxh/h2ph +q1sa-m w9 charge q moves in a circular path in a magnetic field B. Show that its kinetic energy is proportion-x sm/2+a9xhh1 wgqph al to $r^2$, the square of the radius of curvature of its path.

Show that the angular momentum of the particle in P 2xvu;6 8rmymwroblem 21 is $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves with a speed of 160 m/s perpen;gxc1a 9psxj7yu xipa3l60 5gdicular to the Earth’s magnetic field 9x;x5p0igya jxa guc 3p76ls1 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 equgt1xm kp9/ ol qm.ax-t7k/) dh1; ktgxator 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 with j w qlfki+(8d+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 stallgw05 ra b;b qq82vfyj)wmq/lz5qm +-aed vehicle carries a 65-A current. How strong q0;gqj+lq-5qbr )vb2yw5 awmf8/a mzis the magnetic field 6.0 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 la; h:7m5v+f fmlmau 5cu:oghy(rger than that of the Ea+ 5o;v fuyhl mh: g57famc(u:mrth $(0.55\times10^{-4}\mathrm{~Т})$ at a distance of 25 cm, what is the maximum current the wire can carry?    A

In (Fig. Below), a long straight wire carries current I out of theg (j0rrb qhnbvv.i/*, page toward you. Indicate, with appropriate arrows, the direct*qbvv0b h.rirj(,g n/ ion 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 24-A current exerts 0tre dbbz:j9 eh(70kkan attractive fohke(bt9bd e jr 70zk:0rce per unit 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 paralbmd- *9c sz d 8+v45atqykz,xnlel wires 35 m long and 6.0 cm apart, each caz5 +qk4xts9-,bmn8yv ddazc* rrying 25 A in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’s magnetic fieldwduq9r ;6;s +*ucufvfh(f8cx is being carried out 1.00 m from an electric cable. What is the maximum allowable current in the cable if the experiment is x9+; fu;vsf8(ucr* u6qh cfdw to be accurate to $\pm1.0\%?$    A

  A power line carries a 7c6+1wpxr ugl+7 sv kocurrent of 95 A along the tops of 8.5-m-high poles. What is the magnitude of the magnetic field produced by this wire k+xc 7w7p sv1 u6rl+ogat 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 25-A currents in the samebxw 0w61e kdwtw:/eu lc9/ m9z direction. Determine the magnetic field at point P, w919lc wkd/uw60:x twe z/mb e12.0 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 wkf, lg- a)o(e-eqy(ksouth from a straight vertical wire carrying a 35-A current ( awly,k)(fee--oq gkdownward. 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. What is the ntk*7 j ;.q5zsflp jqu-et magnetic field 20.0 cm due west of the wire if the Earth’s field there points nortljtk .;5qf -sqjpz7u*h but downward, 37$^{\circ}\,$ below the horizontal, and has magnitude $5.0\times10^{-5}\mathrm{~Т}?$
   $ \times10^{-5 }\;T$
$\theta$ =    $^{\circ}\,$ below the horizontal

  A straight stream of protons passes a given pof h6,gw+ne 5c( fds9tye*) 3 jhigg-jrint 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 straight wires 2.0 cms20reccl 7el . apart in tel .sc0ec7 er2lrms of the current I in one when the other carries 15 A. Assume these currents are
(a) in the same direction,
(b) in opposite directions.

  A long pair of wires conducts 25.0 A of dc current to, and from,sj+fjq(.n.ar df3 s1a an instrument. If the insulated wires are of negligible diameter but are 2.8 mm apars1qa.. j nfdfs3a (+jrt, 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 thev tq4usqkz 9t-l *;(te;lf-xfz v6 i5y plane of the two wires shown in (Fig. Below), parallel and just to the right. If it kt4e9 q6(xlify;*tfulzz;t sq-v -v5 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 poin + kn*4vblv)t3klc wglk/y5a0ts 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 straighy)uh)dopz8 w.t wire, as shown in (Fig. Below). There is a cuy u.8hpdzw) o)rrent 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 a currep5kdv0-j ,a:rzu rrz*nt of 48 A. A second wire, made of 2.5-mm-diameter copper wire and parallel to the first, is kept in suspension mdr ,-zpzvkr: 05a r*ujagnetically 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 osx4a/:il *nb v8d6mwariented 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 midway between them if the top one carries a currend axmvab/8n:iw* ls6 4t of 20.0 A and the bottom one carries 5.0 A?    $ \times10^{-5 }\;T$

  Two long straight parallel wires are 15 cm apart. Wire A car tm3 gi4mtqiin;5y s88ries 2.0 A current. Wire B’s current is 4.0 A g45i n83i8 tm ;msytiqin the same direction.
(a) Determine the magnetic field magnitude due to wire A at the position of wire B. $\approx$    $ \times10^{-6 }\;T$(retain one decimal places)
(b) Determine the magnetic field due to wire B at the position of wire A. $\approx$    $ \times10^{-6 }\;T$(retain one decimal places)
(c) Are these two magnetic fields equal and opposite? Why or why not?
(d) Determine the force on wire A due to wire B, and the force on wire B due to wire A. Are these two forces equal and opposite? Why or why not? $\approx$    $ \times10^{-5 }\;N/m$(retain one decimal places)

  Three long parallel wires are 3.8 cm from one p u ;lg/d6zni3another. (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 u3g/ zl d6ipn;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 t7 jczrd 4k-j*zhe magnitude and direction of the magnetic field at the midpoint of the side of the triangle between- j7zzrkj*4cd wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a disty)-el naw .,wcance d apart, carry equal currents I in the same direction. One wiwa c)wl.eyn,-re is at x = 0, 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 solrnmf 9hj1eg5 :enoid has a total of 420 turns of wire and carries a current of 2.0 A. Calculate the field inside9g1mfjren 5:h near the center.    $ \times10^{-3 }\;T$

  A 30.0-cm-long solenoid 1.25 cm in diameter is to produce a field of 0.385 T at -x);. 2ipgtujm :bt owits center. How much current should the solenoid carry if it has 975 turns of the :g.pm-2o ; )jwtbxuit wire?    A

  A 550-turn solenoid is 1xqw xco-cb+ nc54rv).5 cm long. The current in it is 33 A. A 3.0-cm-long straight wire cuts through the center of thexoc5 c-bq4x w)r n.vc+ 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 cokfx 4ea6)bd9s pper and want to make a practical solenoid that produces the greatest possible magnetic s )4kx9bef6ad field 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 idx7 nge+y 1os:n the shape of a circle (Fig. Below). Use Ampère’s law along the circular path, shown dashed in (Fy 7edsg1:ox+ nig. 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 magneticrze(y7 z- ktszqhre a.fb4 ,09 field between the conductors of a coaxial cable (Fig. Belowf 4syzrt 9zh .ke(-bzeqr70,a) 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 i,w o;mbv5hw+qo++4itts q , ga side is placed with its face parallel to the magnetic field between the pole pieces of a large magnet. When 6.30 A flows in i wvgqhotq+,5ot, +mw4+bs i;the coil, the torque on it is $0.325\cdot N$. What is the magnetic field strength?    T

  A galvanometer needle deflects full scale fc;x(8v335agbysr6)g pcly)xn fvd9x or 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 gm 5qg3ox m*cui2d h9.kalvanometer weakens by 25% over the years, what current will give full-scalmi9 3uo.mq hkx*5 dgc2e deflection if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 12%, by what factor does the output torqlq w+e:letlob6c.9g4 ue chawbq+6c .:e9g 4llelotnge?

Show that the magnetic dipole moment M of an electron orbiting thenl *c7hqu9iw 4 proton nucleus of a hydrogen atom is related to the orbital angular momentum L of 4lihuqc7 9w *nthe electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter and containing nnetr:7 ;in1;b4 +cmv rj .d ow9fiqk3bine loops lies flat on the ground. The Earth’s magnetic field at this location has mag v emr.kn3nb1wf;td;7:49 c+ji o briqnitude $5.50\times10^{-5}\mathrm{~Т}$ 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 valg)yr4p8j0lyy(lus*4ww1 xx) p( hrz gue of electric field could mak 0rxyxs)glj wp(ph)z( 8uy4w *yr1g4l e their paths straight? In what direction must it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer, germanium atomeq drx vi+v.pr05;.i la gt-9ms have radii of curvature equal to 21.0, 21.6, 21.9, 22.2, and 22.8 cm. The largest radius corresponds to an atomic mass of 76 u. What are tr p0xg i .-le9d ;q+5airvvm.the atomic masses of the other isotopes?

  Suppose the electric field between the electric plates in the mass spectromet7j gp(g-8nkrcwqn +;x er of (Fig. Belx8+p- ;qg r wk(7cjnngow) is $2.48\times10^4\mathrm{~V/m}$ and the magnetic fields $B=B^{\prime}=0.68\mathrm{~Т}.$ The source contains carbon isotopes of mass numbers 12, 13, and 14 from a long-dead piece of a tree. (To estimate atomic masses, multiply by $1.67\times10^{-27}\mathrm{~kg.}$)
How far apart are the lines formed by the singly charged ions of each type on the photographic film?
$2r_{13}$ - $2r_{12}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)
$2r_{14}$ - $2r_{13}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)
What if the ions were doubly charged?
$2r_{13}$ - $2r_{12}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)
$2r_{14}$ - $2r_{13}$ $\approx$    $ \times10^{ -3}\;m$(retain one decimal places)

A mass spectrometer is being used to monitor air pol+a4irg9+61z 5 mk lch*favhkz5rxy4c lutants. It is difficult, however, to separate molecules with nearly equa a4xrav5*mzir6fg54h1yc z+hk k9lc +l 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 acceler 8p 8 otncb-hhlt6u539ey vc9xates ions by a voltage V before they enter a magnetic field B. The ions ar88evhlc9 -u 36 yh9topnbxc5te 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 of wire per meter,se zpup8fmg97 pi* ;/d and a 25-A current flows through the wire. If the permeabili p8 d7m/f;s*up pgiez9ty of the iron is $3000\mu_0$ what is the total field B inside the solenoid?    T

  An iron-core solenoid is 38 cm long and 1.8 cm in diameter, and has 640 turns o6cwpzt v 4 +98/eguxjtf wire. The magnet68g+e4pt/c z9vxw u jtic field inside the solenoid is 2.2 T when 48 A flows in the wire. What is the permeability $\mu$ at this high field strength?    $\times10^{-5}\mathrm{T}\bullet\mathrm{m/A}$

  Protons with momentupqnaw;)a) a ak/1dz:q m $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ are magnetically steered clockwise in a circular path 2.0 km in diameter at Fermi National Accelerator Laboratory in Illinois. Determine the magnitude and direction of the field in the magnets surrounding the beam pipe.    T

  A proton and an electron have the same kinetic energy upon e2ch56h xtp:o83k,o /dnv q w8a(rggtdntering a region of conp: vgr /h n58t,3d2(t 6h ocdqxagokw8stant magnetic field. What is the ratio of the radii of their circular paths?   

  The power cable for an e)p( ya7 lttaeq z-n(q)lectric trolley (Fig. Below) carries a horizontal current of 3aytq(7 ( zqptln-)e )a30 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 which has acquired a n*j l1gba1zbg i2o ci3,dw) )mqk ah3w)et 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 nvuzp4x2a8yhm c 32 4eaorth and has magnitude az4y2mp34 2uca e 8vhx$B=0.50\times10^{-4}\mathrm{~T.}$ 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 7wig(sd3nd. n mass is $6.6\times10^{-27}\mathrm{~kg},$ is accelerated by a voltage of 2400 V.
(a) What will be its radius of curvature in a uniform 0.240-T field? $\approx$    m (retain three decimal places)
(b) What is its period of revolution?    $ \times10^{-7 }\;s$

  A sort of “projectile launcher” is shown in (Fig. Below). A laawhv/ex( s0 4crge 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 circasxew4c/ (v h0uit. If the bar has a length L = 22cm, a mass of 1.5 g, and is placed in a field of 1.7 T, what constant current flow is needed to accelerate the bar from rest to 28m/s in a distance of 1.0 m? In what direction must the magnetic field point?
   A
the magnetic field must be ----待选择----updown 

  In (Fig. Below) the top wire is 1.00-vw(b.kf e06:hnr7iy ps;.njeur4p.l mm-diameter copper wire and is suspended in air due to the two magnetic forces from the bottom thse4r.pf.(n0.pe:jw; n lv iukb 7ry6wo 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 apart in a horit 2 mo(mgo.6z7omnhd,zontal plane act as rails to support a light metal rod of mass m (perpendicular to each rail) d(z6 omhmt. o2g7om,n, (Fig. Below). A magnetic field $\vec{B}$, directed vertically upward (outward in the diagram), acts throughout. At t = 0, wires connected to the rails are connected to a constant current source and a current I begins to flow through the system. Determine the speed of the rod, which starts from rest at t = 0, as a function of time
(a) assuming no friction between the rod and the rails,
(b) if the coefficient of friction is $\mu_k$.
(c) Does the rod move east or west if the current through it heads north?

  Estimate the approximate maximum def5ggi :z,e-sx2zfz 8d41vihd -cte )c alection of the electron beam near the centerce4fdg id :1exa5vh) st-c gz8z,- 2iz of a TV screen due to the Earth’s $5.0\times10^{-5}\mathrm{~T}$ field. Assume the CRT screen is 22 cm from the electron gun, where the electrons are accelerated
(a) by 2.0 kV,    mm(Round to the nearest integer)
(b) by 30 kV. Note that in color TV sets, the CRT beam must be directed accurately to within less than 1 mm in order to strike the correct phosphor. Because the Earth’s field is significant here, mu-metal shields are used to reduce the Earth’s field in the CRT.    mm(Round to the nearest integer)

The cyclotron (Fig. Below) is a device used to accelerate elementary par7g*q y vb.grmqc 7ph-4f 48llze 7qmq2ticles such as protons to high speeds. Particles starting at point A with some initial velocity travel in circular orbits in the maypv 4mlze78.7 hb2 -l7 m* gcq4qqfqrggnetic 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, j3 g o(ac3ckac b+g-f9located at the corners of a square of side l, carry equal cukg-bgcc( + 3fcj3a9oarrents $I_0$ 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 ver)6 bw+gvgswjr hsx2 zau *197fy useful in particle 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 magnswh )7sv+w2x jb f1za9g6*u gretic field is designed for? If the field extends over a region 5.0 cm wide and has a magnitude of 0.33 T, by approximately what angle will a beam of protons traveling at $ 1.0\times10^{7 }\,m/s;$ be bent?    $^{\circ}\,$

  The magnetic field B at the center of a circular coiv097kk 1xs hhil of wire carrying a current iv71khxk9s0h I (as in Fig. 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 ce0eicp9p. :y3p8fk b88aoe g the magnetic field is about 1G($ 1\times10^{ 4}\;T$) Imagine a simple model in which the Earth’s field is produced by a single current loop around the equator. Roughly estimate the current this loop would carry. [Hint: Use the formula given in Problem 80.]    $ \times10^{ 9}\;A$

  You want to get an idea of the magnitude of magnetic fields produced nx0: facs5 -nvby 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 rms, and the magnetic 0f:v n5- xsncafield will be changing.] $B_{net}$ $\approx$    $ \times10^{ -5}\;T$(Round to the nearest integer)

  (a) What value of magnetic field would make a beam of electrons, t n;2vy yo*kpeqq.j /f:/you 1lraveling to the right at a s2qp; jv.1k:/yq uo* y leof/nypeed 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. qgucowq;b6, j*(v3 ;zab lk0w010 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 kinetikuv 3aw jbw ,;(zo cq;*gqbl60c 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 magnetic f0iq- ;vfoj+ tl59pdfdield at its center. If the maximum current i0;59v ol+ dpqfdj -fits 5.7 A, how many turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, each of diameter gsszlp,7nu3qwd-v)1 0.50 mm, carry the same current but in opposite directions. gz,)l -p1wqu s7v3s dnThey are suspended by 0.50-m-long strings as shown in (Fig. Below). If the suspension strings make an angle of 3.0$^{\circ}\,$ with the vertical, what is the current in the wires?    A

  An electron enters a uniform magnetic field B = 0jvd.p++w +vn tlu4 ea5.23 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$