A compass needle is not alwayses2 i c4g398k6pbuzvbva( f8d balanced parallel to the Earth’s surface, but one end ivkf2z698u( b4d8a e c3psbgvmay dip downward. Explain.

Draw the magnetic field lines around a straight section ofmcv 62m8asx9 m6pb 3ji wire carrying a current horizontally to the lef xa6m2mmsvj96 i 3bcp8t.

In what direction are the magnetic field lines surrounding a straight wire4u(om3f-0qz3f v kfo o carrying a cur uo3oz-fom4 0kv (q3ffrent that is moving directly away from you?

A horseshoe magnet is held vertically with the north pole on the left and sc5 +13mnezue1d96 a o,raldibouth pole on the right. A wire passing between the poles, equidistant from them, carries a current directly away from you. In whaed1udz e l1 6oca5n +bmrai93,t direction is the force on the wire?

Will a magnet attract any metallic oeh :2m8vb d7gw-zsqw.bject, or only those made of iron? (Try it and see.) q bv8mzhg:2 ww-d.7seWhy is this so?

Two iron bars attract each other no matter which ends are placed close tog6tlbun*k(gr nv*n2 u*mbi( 7hyda 9+qether. Are bo7ium(k6uyhn(bn2d** aqvg*9r+ b l ntth magnets? Explain.

The magnetic field due to current in wires in your home can affect a 7jbs 40an b9vbcompass. Discuss the effect in terms of currents, including if they a js7 9b4nabvb0re ac or dc.

If a negatively charged particle enters a region of uf 86j;irul v+dniform magnetic field which is perpendicular to the particle’s velocity, will the kinetic energy of the r8juil6+fd ; vparticle 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 vicinitycww)jq6b8p0y of a current-carrying wire. For each charged particle, the arrow0c)jybwq pw 86 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 magnetic field produced by the wire.

Three particles, a, b, and c, enter a magnetic field as shown in 1z-0,2wsp.o-8 c/cl w si3h g-nci jczwdw 3riFig. 20–46. What can you say about the charge on each pa ici z- wn ow hs, i123wp-cwsz/38rgcc.ljd-0rticle?

A positively charged particle in gs*5 mgybml;. a nonuniform magnetic field follows the trajectory shown in sg5 g l*yb;mm.
(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 attra3wkhh8r:b9 9xnde )*3 mwizzqct a magnet? Can a magnet attract an iron rod? What must you consider to a)e kw:39 wi9*hmbrh nx3qz8z dnswer these questions?

Explain why a strong magnet held:bf(dbi;l n qubchc,1z1 07p r near a CRT television screen (Section 17–10) causes the picture to become distorted. Also, explain why the picture sometimes goes completely black wherd7 bc 1ihbq0f:l;p(nb ucrz1, e 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 ar52 7iz0ndmb sie magnetized but the third is notn02sibi7 z m5d. How would you determine which two are the magnets without using any additional objects?

Can you set a resting electron into motion with a magnetic fielllx/ 41 qt4-te3cxe qf qpl;j*d? With an electric field? Eq/tlet x l 4l -xcpf4q1*;j3eqxplain.

A charged particle is moving in a circle under theo4an/k l( pk0b.swd mm;0lfm1 influence of a uniform magnetic field. If an electric (f.d/l0aomn1b4 p;wlmm k0sk field that points in the same direction as the magnetic field is turned on, describe the path the charged particle will take.

The force on a particle in a magnetic f.fmgrd+ sk850 xy;ztfx d-b/ field 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 and to a magnetic field. Explain how ions are caused to move. Do positive and negative ions feelfmgf;+ f/dyxrzsk0dt5.b x-8 a force in the same direction?

A beam of electrons is directed toward a horizontal wire carry 3zda-w-u( n+inuz. cyg-vp tt+sb/p9ing a current from le-szc+9 gdnzp(uin .3p /tbvy tuw +-a-ft to right
(Fig. Below). In what direction is the beam deflected?

Describe electric and/or magnetic fields that surroun jde:3ys ibc,7d a moving electric charge.ijc:7e y, dbs3

A charged particle moves in;- vs xayq vdk0mi1t5) a straight line through a particular region of space. Could there be a nonzero magnetic field in this region? -)t0vay 5ms;qkxdi 1v If so, give two possible situations.

If a moving charged particle is defrofe j41 j;4y, g1hi7 pbulh/tlected sideways in some region of space, can we conclo ,u1yhlgrh4 p 47jj /if;1tebude, for certain, that $\vec{B} \neq or \ne 0$ in that region? Explain.

In a particular region of space there is a uniform magnetic fiee1v ;*o.wdefbt4:n x rld $\vec{B}$. 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 elet5cp6j0mji 6j ctrons in a certain region of space are being deflected by an electric field or by a mm 5ij jp6c0j6tagnetic field (or by both)?

How can you make a compass without using iron or other ferromagna afad3 *bc40ryq n9f4etic material?

Two long wires carrying equal currents mjct3( 1u9thdbf5 wtvi0oc40ngq4 m1 I are at right angles to each other, but don’t quite touch. Describe the magnetic force one exerts on thcdcn 1u vq54ihmt t(9030ow 4 jfgtm1be other.

A horizontal current-carrying wy yyqhkv/46z h8p61m7buv i6tire, free to move in Earth’s gravitational field, is suspended direct8 / vpykyyhi 7qu66tvzh16b4mly above a second, parallel, current-carrying wire.
(a) In what direction is the current in the lower wire?
(b) Can the upper wire be held in stable equilibrium due to the magnetic force of the lower wire? Explain.

Why will either pole of a :8zfnj 0qfheu2 7cye 8magnet attract an unmagnetized piece of iron?

An unmagnetized nail will not a-t ss6d) kxr*httract an unmagnetized paper clip. However, if one end of the nail is in contact with a magnet, the other endxkrss *t h)-d6 will attract a paper clip. Explain.

Two ions have the same mass, but one is singly ionized co-gcy dh pe0+pn+4h6and the other is doubly ionized. H 6c+pc+dh0o-ey ghp n4ow will their positions on the film of a mass spectrometer (Fig. Below) differ?

What would be the effect on B inside a long solenw (z:dj. mhso0)4sb)vhfbpa*oid 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 simisz+ict 3dxg. :lar 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 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 th s.+i3td zcgx:e starter doesn’t pass to the dashboard switch.

  (a) What is the magnitude of the force per meter of length 5chw hl4m 8z*ion a straight wire carrying an 8.40-A current wh*m hw54hz8 iclen 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 ofjciz *o619ne61ftlywj bb 6 ;e the magnetic force on a 160-m length of straight wire stretched between two towers carrying a 150-A current. The9ze wtofjby16j*li6 cne;6b 1 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 straiaxysysu7 / j 34w33fisght wire stretched betfsyi4wu3jyss / 37a x3ween 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 flowing in a wire 4.80 m long if the maximum force on it is vt0- rbyl/1,tp5*o 0bdzodgzk4m g v+0.750 N when placed in a unifor b14/o prt-tvd mgodz yv,*b0kzg5 +l0m 0.0800-T field?    A

  A 1.5-m length of wire carrying 4.5 A of current is cjtep.pd7)dreyt7i0 m re3-jn51wc8 oriented horizontally. At that point on the Earth’s surface, the dip angle- )ep0c73 w875pydcm .rt ejd rtjien1 of the Earth’s magnetic field makes an angle of 38 $^{\circ}\,$ to the wire. Estimate the magnitude of the magnetic force on the wire due to the Earth’s magnetic field of $ 5.5\times10^{ -5}\;T$ at this point.    $ \times10^{-4 }\;N$

  The force on a wire carrying 8.75 A is a maxim/ 065 whvrqi f8zin lwam0w;p5um of 1.28 N when placed between the pole faces of a magnet. If the pole faces are 55.5 cm in diam m5 iv;ai5 f8nzwl0whp6/qw 0reter, what is the approximate strength of the magnetic field?    T

  The magnetic force per meter on a wire is measured to be only 35% of its maximumzqzjz:l0y , 3u possible value. Sketch the relationship of the wire and the field if the force had bzu ,y 03zlzqj:een 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 2+b 7.rofkjz9tctr b: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 1.0-:8a,wkdyvzxm ev7hu+ *uh5i0-mm-diameter copper wire could just “float” horizontally in air because of zim kud7x 8:hh,-5 avwu*evy+the force due to the Earth’s magnetic field $\vec{B}$, which is horizontal, perpendicular to the wire, and of magnitude $5.0 \times10^{ -5}\;T$. What current would the wire carry?    A Does the answer seem feasible? Explain briefly.

  Alpha particles of c8u 7pcipffese)(6v w *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 direction of the force on an96 bwle g8x+;xu z7bbh 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 4rg2xd* mpc z0charge for each diagram shown in (Fig. Below), where 2 x4* cpdgmrz0$\vec{v}$ (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 ofuv5s7pb6uh9 a $\vec{B}$ 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 t6gw7g9ruzl 1:o gxf4upward 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 perpendoi( sjw+ +utj6pn()gricular to the tj+n(iro(jw+ )p 6ug sfield. What is the radius of its path?    m

  An electron experiences the greatest force as it .mo i,c*usc1ytravels $2.9 \times10^{6 }\;m/s$ 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-k3yxk;f tktp 0* *lyt electrons that go undeflected when passing through perpendiculayk*k;0y3 t ptf-* ltkxr 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 whho2 wjw-g t)m ,usb vnx3/en;7ose mass is $6.6 \times10^{-27 }\;kg$ is accelerated by a voltage of 2100 V.
(a) What will be its radius of curvature if it moves in a plane perpendicular to a uniform 0.340-T field?    m
(b) What is its period of revolution?    $ \times10^{ -7}\;s$

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

Show that the time T required for a particle of charge q movingnm /tp0kbc,7i with constant speed v to make one cimkpbti7 c/,0n rcular revolution in 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 unifoj0))k))6wxqkenh / chozs- berm magnetic field B. Sh)z/ b0s oehwxk6-c)kq)hnej) ow that its momentum is p = qBr .

A particle of mass m an,j) 0:fxypy5u f4oc-qk8 u.gd;rzgxkd charge q moves in a circular path in a magnetic field B. Show that its kinetic energy k:.p5- yf ygocuz;uqfg) kx4j0x,8r dis proportional to $r^2$, the square of the radius of curvature of its path.

Show that the angular momentum of the particle(y+8ooyoe11 ( dgzq xi in Problem 21 is $L=qBr^2$ about the center of the circle.

  A 3.40-g bullet moves with a speed xnr(vx.ee . s5of 160 m/s perpendicular to the Earth’s magnetic field v.xe5(r s.xn eof $5.00\times10^{-5}\mathrm{~T}$, If the bullet possesses a net charge of $13.5\times10^{-9}\mathrm{~C},$ by what distance will it be deflected from its path due to the Earth’s magnetic field after it has traveled 1.00 km?    $ \times10^{-7 }\;m$

  Suppose the Earth’s magnetic field at the equator has mae2cs;av,4l-f q iub53q.zfj agnitude $0.40\times10^{-4}\mathrm{~Т}$ 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 speebrc jb6or -*/cd $\nu=2.0\times10^5\mathrm{~m/s}$ 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 x(ed;s* on6mwku0u j9xow0h7 vrt;8 lstart a stalled vehicle carries a 65-A current. How strong 9*txmr 0k0o uv6 (;lxhj wseu8;ndo7w is 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 larger than 1gbrvqewoz)o/ bf g3.90 , p5wcff:qmthat of the p.9cg)wr5 mv fowqb1b qf3/,g :foze 0Earth $(0.55\times10^{-4}\mathrm{~Т})$ at a distance of 25 cm, what is the maximum current the wire can carry?    A

In (Fig. Below), a long straq0z) e(gck7myight wire carries current I out of the page toward you. Indicate, with appropriate arrows, the direction of 7ze( )gcqmy0k$\vec{\mathbf{B}}$ at each of the points C, D, and E in the plane of the page.

  A vertical straight wire carrying -)3w+umosq inm qw g2+an upward 24-A current exerts an attractive force per unit 2+nwq+o mwsiu3m-g) qlength 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 parallel wt9hp ez13p3pxu kbx-,o k; 9muires 35 m long and 3p91bpkumez ;h p- u9 x3x,okt6.0 cm apart, each carrying 25 A in the same direction.    N  ----待选择----attractiverepulsive 

  An experiment on the Earth’0n g:keehp79 ls magnetic field is being carried out 1.00 m from an electkhe ep0g9:7 nlric cable. What is the maximum allowable current in the cable if the experiment is to be accurate to $\pm1.0\%?$    A

  A power line carries a current of 95 A along the tops of 8.5-m-high poles. Wga5m2ol v-2ol hat is the magnitude of o 5v2-olgma2l the magnetic field produced by this wire at the ground? How does this compare with the Earth’s field of about $\frac{1}{2}G$?    $ \times10^{-6 }\;T$ The field of the cable is about    % that of the Earth.(retain two decimal places)

  Two long thin parallel wires 13.0 cm atoxi 2 gkq1;fa5ef)/3/lw.k: zxn plz part carry 25-A currents in the same direction. Determine the magn5xi zn :pfatq2lzf.kxw1ke/ /lo; )g 3etic field at point P, 12.0 cm from one wire and 5.0 cm from the other(Fig. Below).
$B_{net}$=    $ \times10^{-4 }\;T$@90$^{\circ}\,$

  A horizontal compass is placed 18 cm due south from a i 5hdc1jw2l2 9 g574xxsc wrd,oklpj1straight vertical wire carrying a 35-A current downwar s9hdw, c1 52wl kr dclxjigxj5214po7d. 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 b cx8ca1e80l.p cnz;ccurrent due north. What is the net magnetic field 20.0 cm due west of the wire if the Earth’s fieldp1el ; a 0ncbccz.c8x8 there points north but downward, 37$^{\circ}\,$ below the horizontal, and has magnitude $5.0\times10^{-5}\mathrm{~Т}?$
   $ \times10^{-5 }\;T$
$\theta$ =    $^{\circ}\,$ below the horizontal

  A straight stream of protons passes a g .(n q jk;vpx) pfyg4ymvg8y5x;w. 5zaiven 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 midway between6x(+p dom(v 12frx8qwr r l,qz two long straight wires 2.0 cm apart in terms 2 mqr+r((q,l x1zf 8dpowx v6rof 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 curren6 7k.jpio;vcis0bx7 nlt .wbki.2 h(nt to, and from, an instrument. If the insulated wires are of negligible diamet7hi ibk(b2l;xnt v.ockj 0 .p6ns7.i wer 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 placigb d jz/y)/k*ed in the plane of the two wires shown in (Fig. Below), parallel and just to the right. If it carries 25.0 A upward, what force per meter of length does it exert on each of the other two wires? Assume it is 2.8 mm from the nearest wire, center toizjgd )*/b /yk center.
$F_{near}$ =    $ \times10^{ -2}\;N/m$  ----待选择----attractrepel 
$F_{far}$ =    $ \times10^{ -2}\;N/m$  ----待选择----attractrepel 

  A compass needle points 24:uyvuc6- gqb3$^{\circ}\,$ 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 lievm e(/9g.ygnsny/xb; ,pg3 ccs in the same plane as a straight wire, as shown in (Fig. Below). cm/9 ;g gync ,y3be(.sngp/vxThere 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 a current of 48 A. A second wire, made of 2.5-m, rfl3qsebn4wg)8g sz;25 pcnm-diameter copper wire and parallel to the first, is kept in suspension magnetic;pl28wn45fgrqc3s g szn )b ,eally 15 cm below (Fig. Below).
(a) Determine the magnitude and direction of the current in the lower wire.    A the current is to the  ----待选择----leftright 
(b) Is the lower wire in stable equilibrium?  ----待选择----not in stable equilibrium in stable equilibrium 
(c) Repeat parts (a) and (b) if the second wire is suspended 15 cm above the first due to the latter’s field.

  Two long wires are oriented so that they arc1 azu 70awwg5di w1o;/nei jkkq;2k4e perpendicular to each other. At the4e5 kwidkojg7k2q0au;wica1;n wz 1/ ir 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 bottom one carries 5.0 A?    $ \times10^{-5 }\;T$

  Two long straight parallel wires are 15 cm apart. Wire A carries 2.gp*y5lr2gjxh4iilf ke7 4ab2t wh7 5-0 A current. Wire B’s curren2l4txhhl2 kbe 45 -p*5g7gw iyjira7 ft 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 wires are 3.8 cm from one anothexpfv,o+-qhx 6 r. (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)h xq-pfox+v6 ,. Determine the magnetic force per unit length on each wire due to the other two.
$\frac{F_\text{M net y}}{l_\mathrm{M}}$ =    $ \times10^{ -4}\;N/m$ =    $^{\circ}\,$
$F_{N\,net}$ =    $ \times10^{-4 }\;N/m$ $\theta$ =    $^{\circ}\,$
$F_{P\,net}$ =    $ \times10^{ -4}\;N/m$ $\theta$ =    $^{\circ}\,$

  In (Fig. Below), determine the magnitude and direction2boyr0q yc s:+ of the magnetic field at the s y:qb2y0c+ romidpoint of the side of the triangle between wire M and wire N.
$B_{net}$   $ \times10^{-4 }\;T$ $\theta_{net}$    $^{\circ}\,$

Let two long parallel wires, a distancei o26vno*qs)-qdj(u sk:qk( ) r,izas d apart, carry equal currents I in the saz)rsjis(k*(ad,2 6 quqkv:q-oin os)me direction. One wire 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 solenoid has a total of 420 turns of wire and carries a cury)vyr35 ;eh ;u/dj gyow;mb,h rent of 2wh;mb)3e,;o dhy5 ygjv/; yru .0 A. Calculate the field inside 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-ar jvdu5l xud /2yx03 T at its center. How much current should the solenoid car ruda2 yxlvj/x d-u350ry if it has 975 turns of the wire?    A

  A 550-turn solenoid is 1qj ;2+aafn3i i5 cm long. The current in it is 33 A. A 3.0-cm-long straight wire cuts through the center of the solenoid, along a diameter. This wire carries a 22-A current doj i32;a +ainfqwnward (and is connected by other wires that don’t concern us). What is the force on this wire assuming the solenoid’s field points due east?    N

You have 1.0 kg of copper and want to make tf64(lb qb8p 1ep4wod ) 1gkxieyqd/+ a practical 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 variables, suo bbp8e64t1dxeqpi4+ ) d(yq1 wk/lf gch as solenoid diameter, length, and so on.

A toroid is a solenoid in the shape of a circle )fe r v7yw+3xhlht-is23i vuw,0s* zm (Fig. Below). Use Ampère’s law along the circular path, shown dashed in (Fig. Below azi*+hmy-e,us v) l0 ws2xhwi3rf vt37), 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 f-fi**ztj sujk-u2 b3 xield between the conductors of a coaxial cable (Fig. xfu*ijuzk- *s23jt -bBelow) 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 w: (ruy-p4zqi7o x1hpjc-rz 09r2o rgj ith its face parallel to the magnetic field between the pole pieces of a large oru-y0iz21rqjr(: c9-h 4zjxop 7g prmagnet. 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 needle deflects fu4vg 3 mi67lv8o,lb swill 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 weakenrb h66xs6zq.f s by 25% over the years, what current will give full-scale deflectbfszh6 q.rx66ion if it originally required $36-\mu A$ ?    $\mu A$

If the current to a motor drops by 1ot zt1:x:bp *j2%, by what factor does the output torque chang *x1bojt::tp ze?

Show that the magnetic dipole moment M of an electron orbiting the proton nuvt: c.if3grqcga.5c ,cleus of a hydrogen atom is related to the orb gi:aqcc..5 cvt3 r,fgital angular momentum L of the electron by
$M=\frac{e}{2m}L.$

  A circular coil 16.0 cm in diameter and containing nine loopm1b*snld gvd0f7 9m4sbq9 p7 zs lies flat on the ground. The Earth’s magnetic field at this location hzs019vfmp l sqgn b7d49 m7db*as 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 radius 5.10 cm in a ;ca 3 )fl9y ;/a(hk6pjptdybc0.566-T magnetic field. What value of electric field could make their paths straight? In what direction musyy3k;)hfbpja/a9 cd;(tc l6 pt it point?    $ \times10^{ 6}\;V/m$

In a mass spectrometer,g bg(-v4xtb c +0svp1qpgg,9d germanium atoms 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 gv9d p +(b p cbs410,qx-vggtgmass of 76 u. What are the atomic masses of the other isotopes?

  Suppose the electric field between the elect9oy3 x *-p9x4pwgqsy vric plates in the mass spectrometer ofxv py*gx p9qwy 9-os34 (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 monitor air pollus ezrmo2yjkh1u6 / q.47 ok4potants. It is difficult, however, to separatomoqu6sh/ kj4o1r7p 2zeyk4.e molecules with nearly 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 spectromeakebk17 t 4o ;zmou0w.ter accelerates ions by a voltage V before they enter a magnetic field B. The ions are assumed to start from rest. Sb 4weo;.t z1omk 07ukahow 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 pk3;w+f ,dl4c*y j6jvuj7q usf er meter, and a 25-A current flows through the wire. If the peq l36s+u*jj yv47;fwdjcu ,fkrmeability of the iron is $3000\mu_0$ what is the total field B inside the solenoid?    T

  An iron-core solenoid is 3t pb +7q*0mkzz8 cm long and 1.8 cm in diameter, and has 640 turns of wire. The magnetic field inside the solenoid is 2.*+pkz t0bqm7 z2 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 momentum5v ixdym (,, q4xpnqr8nfj*/r $4.8\times10^{-16}\mathrm{~kg}\cdot\mathrm{m/s}$ 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 kine dsa*d36dxc.v tic energy upon entering a region of constant magnetic field. What is the ratio of the radii of their circular paths? 6*vsda d3.dxc   

  The power cable for an electric q:g dvr8 avlm,./j3hvtrolley (Fig. Below) carries a horizontal current of 330 A toward the east. The Earth’s 8a.,lj3 hvd vgq/mv :rmagnetic 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 ai*fi2zna hl ee65ut86duo 9 35:lwyf3 rq,p bkgrplane which has acquired a net charge of $1550\mu C$ and moves with a speed of 120 m/s perpendicular to the Earth’s magnetic field of $5.0\times10^{-5}\mathrm{~T}$.    $ \times10^{-6 }\;N$

  Near the equator, the Earth’s magnetic field points ax;s dw(zn;gv1d4+o7r 7 lu jnvlmost horizontally to the north anrn j du;7+vd gzxwv(s1l7;o4nd 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 heliuw7 g ekyrl 41:g(d5o *3qnadxnm atom, whose 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 c pg/ir.,scw5 launcher” is shown in (Fig. Below). 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 asr 5i w/cp.g,c 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-mm-diame 2(0a v;xsdewkter copper wire and is suspended in air due to the two magnetic forces from the bottom two wires. Thed;aw eksx(v02 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 hwev)vup8ebne9r0w, / orizontal plane act as rails to support a light metal rod of mass mwne bw 09,/ rv)ue8vep (perpendicular to each rail), (Fig. Below). A magnetic field $\vec{B}$, directed vertically upward (outward in the diagram), acts throughout. At t = 0, wires connected to the rails are connected to a constant current source and a current I begins to flow through the system. Determine the speed of the rod, which starts from rest at t = 0, as a function of time
(a) assuming no friction between the rod and the rails,
(b) if the coefficient of friction is $\mu_k$.
(c) Does the rod move east or west if the current through it heads north?

  Estimate the approximate maximum deflect8iycz6pw (yu9ion of the electron beam near the center of a TV screen due tyi( 8zy9pc6wuo 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 ul,7-u -06;iy1c9 zxjgcn tezbj yh*dased to accelerate elementary particles such as protons to high speeds. Particles starting at point A with some initial velocity travel in circular orbits in the magnetic figdya7jt ,1 iy-jhuc-6z ;xle 9*zn 0cbeld 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 atmq;*fm pm;:ba the corners of a square of side l, carr m:f;pb*am;mq y equal currents $I_0$ perpendicular to the page as shown in (Fig. Below). Determine the magnitude and direction of $\vec{B}$ at the center C of the square.

  Magnetic fields are very useful in particle accelerators for “beam bk-oy ,,hhaoqst0xi5p3(a5 j 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 with3hha -,0 k(tqbp 5j yoxisa5,o a beam of protons. What happens to protons that are not moving with the speed that the magnetic field is designed for? If the field extends over a region 5.0 cm wide and has a magnitude of 0.33 T, by approximately what angle will a beam of protons traveling at $ 1.0\times10^{7 }\,m/s;$ be bent?    $^{\circ}\,$

  The magnetic field B at the center of a circular coil of wire carrying a currx8+ 6bml: cbi/ cr1khrent I (as in Fig. Belcrbik lb /1xc6:h8r m+ow) 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 magne4qar ggf s3it:d;)5 xetic 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 yp v 7j-zn72m0iw t +iomq:5epmagnitude of magnetic fields produced by overhead power lines. You estimate that the two wires are each about 30 m above the ground and are about 3 m apart. The loc:jemvp+2ni5yw0 i z 7om-7 qptal 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 ; )rgeg,jd4,ruksmm 9would make a beam of electrons, traveling to the right at a spee, ,9 r ugd4jker;)smmgd 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 yc7/u14ez,.l dhy zk uthrough 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, respecy4zld.,7zh1ycku ue/tively. Calculate the change in the kinetic energy of the proton as it travels from P to Q.    $ \times10^{-20 }\;J$

  A 32-cm-long solenoid, 1.8 cm in diameter, is to produce a 0.30-T magne *+sa(k0oz0z1 qt yml1jv8j-ifa5v hhtic field at its center. If the maximum cur0ts 1hfil8 ykv* jzqh0 5-mz1+ (avajorent is 5.7 A, how many turns must the solenoid have?   $ \times10^{4 }\;turns$

  Two long straight aluminum wires, each of diameterdopp .ob9t dq9ll7596cm yt 9b 0.50 mm, carry the same current but in opp979dptpyt qob l6 9dco95.lb mosite directions. They 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 magnetwa o5n16nmg3o ic 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$