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习题练习:Electromagnetic Waves

 作者: admin 发布日期: 2025-06-18 10:16   总分: 66分  得分: _____________

答题人: 游客未登录  开始时间: 25年06月18日 10:16  切换到: 整卷模式

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1#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
The electric field in an EM wave traveling north oscillates in an east–wnxjbm23x; lbij0 g e up6:0og4est plane. Describe the direction of the magnetici xxe4 0joj bu206mpg3ng :l;b field vector in this wave.
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2#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Is sound an electromagnetic wave? If not, wfrn( kbjn4w75hat kind of wave is it?
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3#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Can EM waves travel through a perfect vacs+ 0j7(zzsk fecrj+i :ij+ hw:qv gu)*uum? Can sound waves?
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4#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
When you flip a light sw)v0()kw qc;im /ekg xiitch on, does the light go on immediately? Explain.
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5#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Are the wavelengths of radio and television signals longer or shorter than thosem+0yq /hz3aqei:3zd ;hz u;ke detectable by the human edh;u:kyqi em0a e ; z/+qh3zz3ye?
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6#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
When you connect two loudspeakers to r msr fiv q/zm9l38z e46lrk(lmrf9 0.the output of a stereo amplifier, should you be sure the lead-in wires are equal in length so that there will not be a time lag between speakrqzfl6(r9m z3e/fr 90. srm8 l4v ilkmers? Explain.
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7#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
In the electromagnetic spectrum, myh9+; ( qgrsc4bq2q 4x xe4edwhat type of EM wave would have a wavelength of+ qhdq4c s qe42b94xeymx (rg; $10^3km$ 1 km? 1 m? 1 cm? 1 mm? $1\mu m$
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8#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Can radio waves have the same frequgz78h9 jk3qi : bw:e dnv.5onfencies as sound waves (20 Hz–20,000 Hz)?
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9#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Can two radio or TV stations broadcast on the same carrgfov+sf-w 7 0y 94ofipier frequency? Explain.
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10#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
If a radio transmitter has a vertical antenna,z)dxi-pb3 r28yzfp tzvht it49 3w*e+ should a receiver’s antenna (rod type) be ver2-9i ifzpz tex3d8)+yhzvtr43*w ptb tical or horizontal to obtain best reception?
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11#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
The carrier frequencies of FM broadcasts 3.xv40fw qmai are much higher than for AM broadcasts. On the basis of what you 4w0qx3fia.m vlearned about diffraction in Chapter 11, explain why AM signals can be detected more readily than FM signals behind low hills or buildings.
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12#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
Discuss how cordless telephones make use oitbggfk dv ,7z4 tf(8k8e +(dsf EM waves. What about cell phones?
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13#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
A lost person may signal by flashing ifq5v/v1qih jk5j g5h13g5mu a flashlight on and off using Morse code. This is actually a modulated EM wave. Ishqhg515mv ji5v15qg/if j3 uk it AM or FM? What is the frequency of the carrier, approximately?
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14#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  At a given instant, a j( kyah6t,9wu ntlz- ,1.8-A current flows in the wires connected to a parallel-plate capacitor. What is the rate at which the elect ukh, 6( 9-tjalwztyn,ric field is changing between the plates if the square plates are 1.60 $cm$ on a side?    $\times10^{14}\mathrm{V/m}\,\cdot \mathrm{s}$

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15#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A 1200$-nF$ capacitor with circular parallel plates 2.0 $cm$ in diameter is accumulating charge at the rate of 35 $mC/s$ at some instant in time. What will be the magnitude of the induced magnetic field 10.0 $cm$ radially outward from the center of the plates?    $\times10^{-8}\mathrm{~T}$
What will be the magnitude of the field after the capacitor is fully charged?   

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16#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  If the magnetic field in a traveling EM wave has a peak magn( h0o.bkrd,jv/f hu4*wiwvm q2lg50fitude of 17.5 $nT$ at a given point, what is the peak magnitude of the electric field?    V/m

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17#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  In an EM wave traveling west, the B field oscillates vertically and has a frequekbr 7+d+; qj2q9u)vhx j4jclnncy of 80 9;jdjj) l cx2 +nk4qqr+hv7bu.0 $kHz$ and an rms strength of $6.75\times10^{-9}\mathrm{~T}$. What are the frequency and rms strength of the electric field, and what is its direction? (Fig. Below)
frequency    kHz
$E_{rms}$ =    V/m
direction  



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18#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  What is the frequency of a microwave wvtz6 98jz0u(hg 0ztxiovj5-x hose wavelength is 1.60 $cm$?    $ \times10^{10}\mathrm{Hz}$

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19#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  What is the wavelength of e+gpxi9yu*vb ck 4+b end(w;0 a $29.75\times10^9-Hz$ radar signal?    $ \times10^{-2}\mathrm{m}$

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20#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  An EM wave has frequev. y mz 2f5;cty6xlha1ncy $9.66\times10^{14}\mathrm{~Hz}.$ What is its wavelength, and how would we classify it?    nm

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21#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  An EM wave has a wavelength of lp)v h31pw5gs650 $nm$. What is its frequency, and how would we classify it?    $ \times10^{14}\mathrm{Hz}$  

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22#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  How long does it take light to dk :g fi9-lat4 0znf0creach us from the Sun, $1.50\times10^8\mathrm{~km}$ away?    min

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23#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A widely used “short-wave” radio broadcast band is referred to as the 49-m ba fd)n oa,x. mtv03r0mqnd. What is the frequency of0ra ,xn tfmo.)m vdq30 a 49-m radio signal?    $ \times10^{6}\mathrm{Hz}$

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24#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Our nearest star (other than the Sur 9(e4+ nyzeghn) is 4.2 light-years away. That is, it takes 4.2 years for the light it emh9rnegz( 4e+yits to reach Earth. How far away is it in meters?    $\times10^{16}\mathrm{m}$

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25#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A light-year is a measure of distance (not time). How manv-zv0 sslkx/6+2lox a v7pie6 fl7yj)y meters does light travelxyll+f0v 7vejk2/zo)-p l a7 6s6v xsi in a year?    $ \times10^{15}\mathrm{m}$

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26#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  How long would it take a message sent as radio waves from Eart6 oze-.j;d zjyh to reach Mars
(a) when nearest Earth,    s
(b) when farthest from Earth?    s

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27#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A student wants to scale down Michelson’s light-speed experiment tlr53q mlrsh, x9;nh2mo a size that will fit in one room. A six-sided mirror is available, and the stationary mirror q m 95n;3hxrsllm,2 rhcan be mounted 12 m from the rotating mirror. If the arrangement is otherwise as shown in (Fig. Below), at what minimum rate must the mirror rotate?    $\times10^6\text{ revolutions/s}$


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28#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Who will hear the voice of a singer first — a person in the zvfu 7q37i9 ,lwto, o9*rp kw ef5qk0zbalcony 50.0 m away from the stage (Fig. Below), o r7 vw7,lq0zo kt3ou95*z,p9fe wifq kr a person 3000 $km$ away at home whose ear is next to the radio? How much sooner? Assume that the microphone is a few centimeters from the singer and the temperature is 20$^{\circ}\,C$.
 
   s



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29#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Pulsed lasers used in science and medicine produce very short2 j xgewc f.-fpz0)ng; bursts of electromagnetic energy. If the lasefz;)fwg p0n -cxg. e2jr light wavelength is 1062 $nm$ (this corresponds to a Neodymium-YAG laser), and the pulse lasts for 32 picoseconds, how many wavelengths are found within the laser pulse? How short would the pulse need to be to fit only one wavelength?
N =    wavelengths
$\Delta t'$ =    fs

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30#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  The $\vec E$ field in an EM wave in free space has a peak of $21.8mV/m.$ What is the average rate at which this wave carries energy across unit area per unit time?    $\times10^{-7}\mathrm{~W/m^2}$

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31#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  The magnetic field in a travelin2bs ) 35o48,cyhq mvpwfv3qgv g EM wave has an rms strength of 28.5$nT$. How long does it take to deliver 235 J of energy to $1.00cm^2$ of a wall that it hits perpendicularly?    days

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32#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  How much energy is tt i/nr6kbee g3n o*6dr,r2l ,co-o2prransported across a $1.00-cm^2$ area per hour by an EM wave whose E field has an rms strength of $38.6mV/m?$    $\times10^{-6}\mathrm{J/h}$

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33#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A spherically spreading Eck* j3xvo-6,7km7kthb-hz 5du0vlzp M wave comes from a 1200-W source. At a distance of 10.0 mkh, k7 xlvzbkc7 tu h-m-0*3o65djvzp, what is the average intensity, and what is the rms value of the electric field?
S =    W/$m^2$
$E_{rms}$ =    V/m

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34#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A 12.8-$mW$ laser puts out a narrow beam 1.75 mm in diameter. What are the average ($rms$) values of E and B in the beam?
$E_{rms}$    $\times10^3\,\mathrm{V/m}$
$B_{rms}$   $\times10^{-6}\,\mathrm{T}$

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35#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Estimate the average powe ;tsmy(y .itxo7tzfv y8(3,lkr output of the Sun, given that about $1350\mathrm{~W/m^2}$ reaches the upper atmosphere of the Earth.    $ \times10^{26}\,\mathrm{W}$

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36#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  If the amplitude of the B field of an EM wave5 oou rxazddr7r6c+38hj-u s 9 is $2.5\times10^{-7}\mathrm{~Т},$
(a) what is the amplitude of the E field?    V/m
(b) What is the average power per unit area of the EM wave? $\overline{I}$ =    $W/m^2$

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37#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A high-energy pulsed laser emits a 1.0-ns-long pulse of average polr)nnml:1 qh * k*1xnawer $2.8\times10^{11}\mathrm{~W}.$ The beam is $2.2\times10^{-3}\mathrm{~m}$ in radius. Determine
(a) the energy delivered in each pulse,    J
(b) the rms value of the electric field. $E_{rms}$    $\times10^9\mathrm{V/m}$

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38#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Estimate the radiation pressure due to a 100-W bulb at x )cc/6nj 0dlukn) z ndkq*+8la distance of 8.0 $cm$ from the center of the bulb. Estimate the force exerted on your fingertip if you place it at this point.
P =    $\times10^{-6}\mathrm{N/m^2}$
F =    $\times10^{-10}\mathrm{N}$

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39#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  What is the range of war 4gcrf38ykci 2jw.7gvelengths for
(a) FM radio (88 $MHz$ to 108 $MHz$)    m to    m
(b) AM radio (535 $kHz$ to 1700 $kHz$)?    m to    m

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40#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Estimate the wavelength for 1.9-GHz cel/ ny f.3ds(r+suoemwxsa,, 569kozjhl phone reception.    m

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41#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Compare 940 on the AM dial to 94 on the FM dial. Which has the longer wavelenggej2d *wf3pg3lz-c u 5th, and by what factor is it largerg3-c2 g* 5ldjw3fzu pe?
 
$\frac{\lambda_1}{\lambda_2}$ =   

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42#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  What are the wavelengths for two TV channelsfot5 a4 ;2sg zwrtlup,8e*pv) that broadcast at 54.0 MHz (Channel 2) and 806 MHz w) , 4l oevztps fr*a8pgt2;u5(Channel 69)?
$\lambda_2$ =    m
$\lambda_{69}$ =    m

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43#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  The variable capacitor in the tuner of an AM radio has a cad 1gu/( jti2jvpacitance of 2800 $pF$ when the radio is tuned to a station at 550 $kHz$. What must the capacitance be for a station near the other end of the dial, 1610 kHz?    $pF$

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44#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  The oscillator of a x/uz+k-2)vizz c jcrwxq23t196.1-$MHz$ FM station has an inductance of $1.8\mathrm{~}\mu\mathrm{H}.$ What value must the capacitance be?    $pF$

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45#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A certain FM radio tuning circuit has a f+ g3urqk2 rtmt ull17ti/j+a;ixed capacitor $C=840\mathrm{~pF}.$ Tuning is done by a variable inductance. What range of values must the inductance have to tune stations from 88 $MHz$ to 108 $MHz$?    $nH$ $\leq$ L $\leq$    $nH$

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46#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  An amateur radio operator wisyzn/9 s +x vrg5w9,9ibtiqcc3(7j dkwhes to build a receiver that can tune a range from v7ns9b+9w35kc ,g9twi djryzx q (ic /14.0 $MHz$ to 15.0 $MHz$. A variable capacitor has a minimum capacitance of 82 pF.
(a) What is the required value of the inductance?    $\mu H$
(b) What is the maximum capacitance used on the variable capacitor?    $pF$

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47#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A satellite beams microwave radiatiog4y3-zi 2dt 4x+wvo don with a power of 10 $kW$ toward the Earth’s surface, 550 $km$ away. When the beam strikes Earth, its circular diameter is about 1500 m. Find the rms electric field strength of the beam.    $V/m$

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48#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A 1.60-m-long FM antenna is oriented parallel to the electric fieldqo1x plze75i/z+0px t of an EM wave. How large must the electric fi501 qltz/e7zp+i oxpxeld be to produce a 1.00$-mV (rms)$ voltage between the ends of the antenna? What is the rate of energy transport per square meter?
$E_{rms}$ =    $\times10^{-4}\mathrm{V/m}$
S =    $\times10^{-9}\mathrm{V/m^2}$

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49#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  If the Sun were to disappear or somehow radically change its-urzl5wo3kb tu:6hlg p:/6 to output, how long would it take for us on Earth to learn about it?3u-r6 kt:tlzbo5/ uh6:pgwl o    min

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50#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Light is emitted from an ordinary lightbulb filamez+p91gxq tzq8nt in wave-train bursts about zxt+gp9 qq 8z1$10^{-8}\mathrm{~s}$ in duration. What is the length in space of such wave trains?    m

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51#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  (a) How long did it take for a message sent from Earth to reach t7u l(h i57a*r qgsf;nwhe first astronauts onn57 lu7;r(*hqw gf ais the Moon?    s
(b) How long will it take for a message from Earth to reach the first astronauts who arrive on Mars; assume Mars is at its closest approach to Earth $(78\times10^6\mathrm{~km})?$   min

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52#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A radio voice signal from the Apollo c lth-s7fy6y j9p*ll+p,nlo:.98 hdzcmo,byq rew on the Moon (Fig. Below) was beamed to a listening crowd from a radio speaker. If you were standing 25 m from the loudspeaker, what was the total time lag between when you heard the sound and when the sounhl,lly 6onq 9 9d8c:b+j,z . *p7 ysyolmhtpf-d left the Moon?    s

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53#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Cosmic microwave backgroun t7qrm1zi ts,6c*z ux0d radiation fills all space with an average energy densitysc 7 z6t*t,0uqm1x izr of $4\times10^{-14}\,\mathrm{~J/m}^3.$
(a) Find the rms value of the electric field associated with this radiation.    $V/m$
(b) How far from a 10-kW radio transmitter emitting uniformly in all directions would you find a comparable value?    $km$

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54#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  What are $E_0$ and $B_0$ 2.00 m from a 95-W light source? Assume the bulb emits radiation of a single frequency uniformly in all directions.
$E_0$ =    V/m
$B_0$ =    $\times10^{-7}\mathrm{T}$

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55#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Estimate the rms electric field i xq:/my ri f.7.s7e/tv aaki0on the sunlight that hits Mars, knowing that the Earth receivefmykv.q .si :ara7x/o7i0/tes about $1350\mathrm{~W/m^2}$ and that Mars is 1.52 times farther from the Sun (on average) than is the Earth.    $V/m$

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56#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  At a given instant in tix qk0r2hl eo.,me, a traveling EM wave is noted to have its maximum magnetic field pointing west and its maximum electric field pointing south. In which direction is the wave traveling? If the rateq .,hkxlr 0eo2 of energy flow is $560\mathrm{~W/m^2}$ what are the maximum values for the two fields?
 
$E_0$ =    $V/m$
$B_0$ =    $\times10^{-6}\mathrm{T}$

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57#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Estimate how long an AM antenna would have to b3t re 7jqzyf:5e if it were
(a) $\frac{1}{2}\lambda$    $m$
(b) $ \frac{1}{4}\lambda$ AM radio is roughly 1 $MHz$ (530 $kHz$ to 1.7 $MHz$).    m

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58#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  How large an emf (rms) will be generated in an antenna that consists of a 380fu,kdtx rve9 yt j7w:5;pmx.1 l2x7rh-loop circular coil of wire 7;fx x:xkd5.,m7jt tvw l9rrph2 e1uy 2.2 $cm$ in diameter if the EM wave has a frequency of 810 $kHz$ and is transporting energy at an average rate of $1.0\times10^{-4}\mathrm{~W/m^2}$ at the antenna? [Hint: You can use Eq. 21–5 for a generator, since it could be applied to an observer moving with the coil so that the magnetic field is oscillating with the frequency $f=\omega/2\pi$]    $mV$

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59#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  The average intensity of a par8 xff22 oitmh(ticular TV station’s signal is $1.0\times10^{-13}\mathrm{~W/m^2}$ when it arrives at a 33-cm-diameter satellite TV antenna.
(a) Calculate the total energy received by the antenna during 6.0 hours of viewing this station’s programs. U =    $\times10^{-10}\mathrm{J}$
(b) What are the amplitudes of the E and B fields of the EM wave?
$E_0$ =    $\times10^{-6}$ $V/m$
$B_0$ =    $\times10^{-14}$ T

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60#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  15 km from a radio stat86lzvf+t/8w,kyled: yl *k bgion’s transmitting antenna, the amplitude of the electric de6fk: gyv+by z 8ll*w/tl,8k field is $0.12\mathrm\,{~V/m}.$ What is the average power output of the radio station?    $kW$

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61#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  The variable capacitance of a radio tuner consists of six plf;/s)6bvisu3e/ a3ghuewm 1 bates connected together placed alternately between six other plates, also connected together (Fig. Below). Each plate is separated from its neighbor by 1. eu3hgesmib6f sbu;13w)/a v /1 $mm$ of air. One set of plates can move so that the area of overlap varies from $1.0cm^2$ to $9.0cm^2$.
(a) Are these capacitors connected in series or in parallel?  
(b) Determine the range of capacitance values.    $pF$ $\leq$ C $\leq$    $pF$
(c) What value of inductor is needed if the radio is to tune AM stations from 550 $kHz$ to 1600 $kHz$?    $mH$ $\leq$ C $\leq$    $mH$


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62#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A radio station is alyaig3jf1)m*gxm710 n-j5 ik b 6pzuobp5 m)yolowed to broadcast at an average power not to exceed 25 $kW$. If an electric field amplitude of is considered to be acceptable for receiving the radio transmission, estimate how many kilometers away you might be able to hear this station.    $km$

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63#
 
问答题 ( 1.0 分) 切至整卷模式 搜藏此题  
A point source emits light energy uniformly in all directions at an average r :8o:9ek:jzxhhi wxq5ateh:8qo 5 i:zjx:kxwh9e $P_0$ with a single frequency f. Show that the peak electric field in the wave is given by
$E_0=\sqrt{\frac{\mu_0cP_0}{2\pi r^2}}.$
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64#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Suppose a 50-kW radio station emits EM waves un; dl5fm45lsjm iformly in all directions.
(a) How much energy per second crosses a $ 1.0-m^2$ area 100 m from the transmitting antenna?    W
(b) What is the rms magnitude of the $\vec E$ field at this point, assuming the station is operating at full power?    $V/m$
(c) What is the voltage induced in a 1.0-m-long vertical car antenna at this distance?    V

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65#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Repeat Problem 65 for a distance of 100 km from the n-et 4dfsj4;astation.
(a)    $\mu W$
(b)    V/m
(c)    V

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66#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  What is the maximum power level of the radioty s9 wsy.6dktv8 ;j6ewrt;r8,p- m kp station of Problem 52 so as to avoid electrical breakdown of air at a distance of 1.0 m from the antenna? Assume the antenna is a point source. Air breaks down in an electric fi;88pj kvyd;.6ke r-tps9t wm,wsyt r6eld of about $3\times10^6\mathrm{~V/m}.$ [Hint: See Problem 51.]    $\times10^{11}\mathrm{W}$

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