CHAPTER 24: ELECTROMAGNETIC WAVES

Transcription

1 College Phyi Student Manual Chapter 4 CHAPTER 4: ELECTROMAGNETC WAVES 4. MAXWELL S EQUATONS: ELECTROMAGNETC WAVES PREDCTED AND OSERVED. Veriy that the orret value or the peed o light i obtained when nuerial value or the pereability and perittivity o ree pae ( µ and ε ) are entered into the equation. µ ε We know that µ T / A, and ro Setion 9., we know that - ε.5 F/, o that the equation beoe: ( T ) / A (.54 - F/).99 /. / The unit work a ollow: [ ] T F/A A T F C/ ( N /C ) ( C /J) J N ( N ) N / 4. THE ELECTROMAGNETC SPECTRUM. A radio tation utilize requenie between oerial AM and FM. What i the requeny o a.- - wlength hannel? Uing the equation, we an olve or the requeny ine we know the peed o light and are given the wlength;.99 / MHz 7. the Sun uddenly turned o, we would not know it until it light topped oing. How long would that be, given that the Sun i.5 away?

2 College Phyi Student Manual Chapter 4 d We know that v, and ine we know the peed o light and the ditane ro the t d.5 un to the earth, we an alulate the tie: t 5. /. (a) What i the requeny o the 9- n ultraviolet radiation ued in laer eye urgery? (b) Auing the auray with whih thi EM radiation an ablate the ornea i diretly proportional to wlength, how uh ore aurate an thi UV be than the hortet viible wlength o light? (a) Uing the equation we an alulate the requeny given the peed o light and the wlength o the radiation:. / Hz viible n (b) The hortet wlength o viible light i n, o that: n n other word, the UV radiation i 97% ore aurate than the hortet wlength o viible light, or alot twie a aurate. UV 4.4 ENERGY N ELECTROMAGNETC WAVES. Find the intenity o an eletroagneti w having a peak agneti ield trength o 4. T. Uing the equation we ee that: µ (. /)( 4. T) ( T /A).9 W/ µ The unit work a ollow: [ ] ( /) T T A ( N/A )( A) T /A N. J/ W

3 College Phyi Student Manual Chapter 4 6. Laer an be ontruted that produe an extreely high intenity eletroagneti w or a brie tie alled puled laer. They are ued to ignite nulear uion, or exaple. Suh a laer ay produe an eletroagneti w with a axiu eletri ield trength o. V / or a tie o. n. (a) What i the axiu agneti ield trength in the w? (b) What i the intenity o the bea? () What energy doe it deliver on a. - area? E (a) Uing the equation, we an deterine the axiu agneti ield trength given the axiu eletri ield trength: E. N/C T, realling that V/ N/C.. / (b) Uing the equation reult ro part (a): ε E, we an alulate the intenity without uing the ε E (. /)(.5 C /N )(. N/C) 9. W/ () We an get an expreion or the power in ter o the intenity: P A, and ro the equation E Pt, we an expre the energy in ter o the power provided. Sine we are told the tie o the laer pule, we an alulate the energy delivered to a. area per pule: E PΔt AΔt 9 (. W/ )(. ) (. ). 4 J. kj 4. ntegrated Conept What apaitane i needed in erie with an - µ H indutor to or a iruit that radiate a wlength o 96? Uing the equation, we an ind the apaitane in ter o the π LC 4

4 College Phyi Student Manual Chapter 4 reonant requeny: C L. Subtituting or the requeny, uing the equation give: C L ( 96 ) 4 (. H)(. /).5 F.5 pf The unit work a ollow: [ C ] ( ) H / H Ω Ω V/A A V C V F 44. ntegrated Conept Eletroagneti radiation ro a 5.- W laer i onentrated on a. - area. (a) What i the intenity in W/? (b) Suppoe a.- nc tati harge i in the bea. What i the axiu eletri ore it experiene? () the tati harge ove at 4 /, what axiu agneti ore an it eel? P (a) Fro the equation A, we know: P 5. W 5. W/ 6 A. (b) Uing the equation εe, we an olve or the axiu eletri ield: (5. W/ ) E.94 (. /)(.5 C /N ) ε N/C. So, uing the equation F qe F E we an alulate the ore on a. nc harge: q 6 (. C)(.94 N/C). N E () Uing the equation F qvinθ and, we an write the axiu agneti ore in ter o the eletri ield, ine the eletri and agneti ield are related or eletroagneti radiation: F,ax qv qve (. C)( 4 /)(.94 N/C) 5. N. / So the eletri ore i approxiately 6 order o agnitude tronger than the agneti ore. 5

5 College Phyi Student Manual Chapter 4 5. Unreaonable Reult An LC iruit ontaining a.- pf apaitor oillate at uh a requeny that it radiate at a - n wlength. (a) What i the indutane o the iruit? (b) What i unreaonable about thi reult? () Whih auption are unreaonable or inonitent? (a) Uing the equation and, we an olve or the indutane: π LC, o that π LC L C (. ) (. F)(. /).5 H (b) Thi indutane i unreaonably all. () The wlength i too all. 6