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 / 7.696. 6.96 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?
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:. /.55-7.9 5 5.55 Hz viible n (b) The hortet wlength o viible light i n, o that:.97. 9 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
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
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
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