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U/J = fU /JdVol = brr PO;', ) 21Ch I'dI' = Po/ ' h In (~) v lls1C r 41C a Since U H = Po [ ' lln(~ ) =.!:.. LJ' , the inductance is 41C a 2 L = Poh In(~) 21C a c) Calculate the inductance of tlus long inductor by usmg the formula (I) = LJ = f B· dA and your results for the magnetic fi eld in (a). To do this you ope" .mrfacl! must choose an appropriate open surface over whi ch to evaluate the magnetic flux. Does yo ur result calculated in this way agree with your result in (b)? cil' / / [ a I ~ ~ ./ The magnetic field is perpendicular to a rectangular surface shown in the figure. The magnetic flux tlu'ough a thin strip of area dA = ldr is , - -- -- r -, - B- ... , , i- - - - - -====::: ~-... ::::~, " -' -- -, '~ , , , , ~ - - -"" , - ....... .. .. "-'0-- -------- I Thus, the total magnetic flux is Thus, the inductance is whi ch agrees with that obtained in (b). ~tJel/ 'M -{) - 90 fo d
Problem 6: Trying to open the switch on an RL Circuit The LR circuit shown in the figure contains a resistor R, and an inductance L in series with a battery of emf Go. The switch S is initially closed. At I = 0, the switch S is opened, so that an additional very large resistance R, (with R, D R,) is now in series with the other elements. I • (a) If the switch has been closed for a long time before I = 0, what is the steady current 10 in the circuit? There is no induced emf before I = O. Also, no current is flowing on R2. Therefore, I -~ o- R' (b) While this current 10 is flowing, at time I = 0, the switch S is opened. Write the differential equation for /(1) that describes the behavior of the circuit at times I ~ O. Solve this equation (by integration) for Jet) under the approximation thatG o = O. (Assume that the battery emf is negligible <strong>com</strong>pared to the total emf around the circuit for times just after the switch is opened.) Express your answer in terms of the initial current /0' and R" R" and L. The differential equation is d/(I) Go -/(t)(R, +R,)=L- dl Under the approximation that Go = 0, the equation is - I(I)(R, + R,) = L dl(t) dl The solution with the initial condition /(0) = 10 is given by
Page 1: Problem 5: Inductor An inductor con
Page 5 and 6: Problem 7: Le Circuit An inductor h
Page 7 and 8: The greatest potential difference a
Page 9 and 10: PRS:Loop The magnetic field through
Page 11 and 12: PRS: Stopping a Motor Consider a mo
Page 13 and 14: If you increase the resistance in t
Page 15 and 16: Class 31: Outline Hour 1: Concept R
Page 17 and 18: PRS Questions: Faraday's & Lenz's L
Page 19 and 20: Maxwell's Equations [jJE.dA = Q. ,
Page 21 and 22: PRS Questions: Inductors & Circuits
Page 23 and 24: PRS: RC Circuit 0 An uncharged capa
Page 25 and 26: PRS: LC Circuit Consider the LC cir
Page 27 and 28: Plot I, V's vs. Time ." Resonance I
Page 29 and 30: ill PRS: Leading or Lagging? The gr
Page 31 and 32: PRS Questions: Poynting Vector Clas
Page 33 and 34: Rtv'(~\V Se76'O') ~->t 3 Dorfll IJ
Page 35 and 36: " dr~wl 'J ~ 6 ods -Vlo 1- f lfd h4
Page 37 and 38: ~ I\ ~ h 5(1\11 II r trs At o S: Cr
Page 39 and 40: - f\J 5~ B 'd~ loop 1 fi ~ ~ tl-trP
Page 41 and 42: for 6(J'; d(lo;J ncA,Ie.. V\ bJ- Ir
Page 43 and 44: t ftJ{ :~"y ; Lao' :'> ChUAa:AJ flv
Page 45 and 46: @ I~ E f i~ ~ Yes (' /0.. F -J~ =-
Page 47 and 48: Co thro~ ~ 0- fvl) c tcl e 5o~ er
Page 49 and 50: [1\ Q 1 -l L I dl ~ 0 " - d I c Q 1
Page 51 and 52: ----....... (~~i(Aj JI( ) (hv(9Y'~
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, • Problem 1: (25 points) Five C
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Question 3 (5 points): A circuit co
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Question 5 (5 points): A coil of wi
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iii) inside the slab, -d / 2 < z <
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Problem 3 (25 points) NOTE: YOU MUS
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(c) What is the total charge Q that
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(b) What is the self-inductance L o
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MASSACHUSETTS INSTITUTE OF TECHNOLO
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Question 3 (5 points): A circuit co
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Q uestion S (S points): A coil of w
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Problem 2 (25 points) NOTE: YOU MUS
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) Make a carefully labeled graph sh
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(c) What is the total charge Q that
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So (b) What is the self-inductance
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~ !hi'> (lo.~ " before ~)(G{Ii" vtf
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I d "7 ( ~ B cl~ 0- lP ~ ( e 601--
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Summary of Class 32 8.02 Topics: Ma
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Hour 1: Class 32: Outline Energy Fl
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Traveling E & B Waves Wavelength: A
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Poynting Vector and Intensity Direc
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(t! ((e.lto VI ~ ~ f") r :~(i 00 .
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Page 97 and 98:
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Summary of Class 33 8.02 sky under
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PRS I ) - is (U(rh l t/ Vt,t ,,7c1.
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Generating Electric Dipole Radiatio
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Spark Gap Generator: An LC Oscillat
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Spark Gap Antenna Demonstration: An
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PRS Questions: Angular Distribution
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Interference Interference: Combinat
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A Extra Path Length Mi~~oor"'-"" /
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Two Transmitters Microwave Interfer
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Group Problem: Lecture Demo We just
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OBJECTIVES MASSACHUSETTS INSTITUTE
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Detecting (Receiving) the Radiation
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IN-LAB ACTIVITIES EXPERIMENTAL SETU
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IN-LAB ACTIVITIES MEASUREMENTS MASS
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10(1 '+ ,,"or (7 ctboJt-- JeN)", t{
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l' \ L] (6 ~~ oJ ~1~Jnr~ f o./('o;v
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lJ> ; r1 () olv+ to "1 ~ Y ~ f yo S
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,. ~ ,r,ve l i~j X (J ir pM '9 ctti
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X ~ E l/OV (l{l. ~jt)~b\lj Jf -I- d
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(b) What is the width of the centra
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Problem 3: Slalldillg Waves The ele
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(d) If the path difference is 0 = A
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8.02 MASSACHUSETTS INSTITUTE OF TEC
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3. Another Way to Measure Hair Side
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(c) Derive an equation for calculat
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Problem 3: Siandillg Waves The elec
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~ ' // r;" E~(( c, (iL&;l' L '>! if
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- F x, • J!,::=
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Problem S. Electromaglletic Waves T
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EI;nt/J...I (x=c) =- c. 6 0 S01 (-w
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(e) In the double-slit interference
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v: =- ;3 w7f 2- o • "- 7fT=. R r
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) What is the total energy stored i
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-f-6\ «/7,.....-/?' x,d ...... ~ 1
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Summary of C lass 34 S.02 Topics: E
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t , l • --"77"--- t 4' ~I P--..!-
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t t I t l"k... t-'e l \ ~ - C v tl
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When ordinary light is emitted from
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Question 2: Draw a picture of two t
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Question 8: Why are the phase sh~ t
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Question 12: Since the energy of th
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Summary of Class 35 8.02 Here Ih e
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Two In-Phase Sources: Geometry I I
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Intensity Distribution Destructive
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Coherent monochromatic r . (j 1 t I
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Experiment 10, Part I: Measure Lase
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PRS: Lower Limit? _ Using diffracti
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Two Slit Interference ----- L. ---.
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APPARATUS 1. Optical bench Wooden S
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Part 2: Interference from a CD In t
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Summary of Class 36 Vinal Exam lnfo
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Class 36: Outline Final Exam Review
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Undriven LC Circuit " . " Oscillati
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If you increase the resistance in t
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PRS Questions: Driven RLC Circuits
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PRS: Leading or Lagging The graph s
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Traveling E & B Waves Wavelength: A
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PRS EM Wave The E field of a plane
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PRS: Spark Gap At the time shown th
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ICc)he,rerlt monochromatic waves im
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PRS: Headlight Resolution J '.lu {
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SUNSET: What's wrong with this pict
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(J~ / {f\ II -:: CvJ 07 f1- {o613_
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~(d [5 \ £{)("'~1 " €eV ! ~ 2 ~/
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- p e o~l~ Pfl tpr;11 j -t lfo/i/'j
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...>- B f ~~ldJ dot1 t JQ V"JJrk -
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'- -- - --- I Ī ....:> t ::-1... r
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~f cl d Q L d~ ~ Jr Ap kA~ - I ~ ~
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® CcN1L fo,!" t \~9 V(t(~ r f1CA.Y
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~ lIz .M.{ := roJl4't> /sec bv·l J
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, , , l 0.-) t :; c) (I{J~Q s,,,,,J
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SIf\(O) ~ 0 )A( * + ~ ===- 0 )At =-
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---------- v, ~ Ios;, ~A-f£) - " ,
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\ III V{~ I~ T( k) = Va Sift JA.{)-
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1(\ V 1 ~LC I;; fit weird OVl( \;V~
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