Exam2 April 7, 2003 Page 1 Physics 263: Electromagnetism and Modern Physics Sections0101-0105 Exam 2 Prof JJ Kelly nstructions:. This is a closed book, closed notes exam to be completed in 50 minutes. You may use a basic scientific calculator, but no other aids are permitted. The final page provides a brief compilation ofpossibly useful information, including relevant physical constants.. Work each problem in the space provided. f additional space is needed, use the back of the previous page and indicate that you have done so... Please write your name on each page, including this one. Do not use red ink.. Choose 4 out of 5 problems. Use an X in the table below to indicate which problem to omit. f there is no X, we will grade the first four.. Explain your reasoning and show your work. Partial credit will be awarded when the relevant physical principles are applied even if mistakes are made in execution of the steps. However, correct guesseswithout any explanation may be penalized.. Algebraic answers must have consistent dimensions and numerical answers must have consistent units.. Honor pledge: please copy and sign " pledge on my honor that have not given or received any unauthorized assistance on this examination." Pledge: Signature: Student D number: Printed name: ;:;(!)(fl+/o/ts Section: Problem 1 2 3 4 5 total Score Physics 263 Prof JJ Kelly
Name: Page2 1. A series RLC circuit contains R =100 Q, L=200 mh, and C=50 j.if. a) Compute the impedances for each element at (i)=160radians/sand the net impedance. Draw a phasor diagram (to scale) that shows the net impedance and each of its contributions.( 0pts) X -.-!- = ls"..jl X c-c-)( y.. :: wl = s L... 2... i ;;: J< + (Y-.c. -xl.) J = l$b.bi7- XL '[ R 'f.-l-'f.c y.. c..' b) Compute the phase shift between the voltage and the current. Does the current lead or lag the voltage? Justify your answer using the phasor diagram. ( 0pts) = 'j..'- Xc R. : \J=:J...1.) --tjl ep ;: - 42.9 V<::..J: < "'VR Xc. ';;>XL cp<:0.. L (-t)=r,., t...jt. '? ) c) Compute the resonant frequency for this circuit. )(L =- Xc.. G..h= f Lc..-' - 31L 2 /'5 C'..)o fd :::.;r - S-D. "3 Hl Physics 263 Exam 2 Prof JJ Kelly
Name: Page 3 2. A UHF antenna consists of a single circular loop of radius r. The voltage in the antelma is produced by the changing magnetic flux. a) Sketch the orientation of the antenna relative to the directions of the electric and magnetic fields and the propagation of the electromagnetic signal for the conditions that give the strongest signal in the antenna. Explain. (10 pts) -'" E 71) e.-f -tk. U\iF) tvl B z; -tl % 7i;. ' 1z.t5 -' -"-'" TL q;. E-L fle. 4< :::,.. b) Suppose that the antenna has a radius of 10 cm and is located 100km from a station that broadcasts isotropically (equally in all directions) a total average power of 750 kw using a frequency of 600 MHz. Compute the rms (root mean square) voltage induced in the antenna when it is oriented for best reception.., L.!!- =: - tp = 1t';'" 80 wt t; - Bo ((, C#o'-<Jt E» e.!fp "l.. 'D f3 -'12.JJ < {?t2 / r. p '- ) ) 2 ;;-:) t = 'j('" wdrl'h r",",- D C -= lw DO 7r r r()'\ ) 'he. ( AO P ) /h. -7 J::!.. 7-O 'f<.w \ == 4().1. = --c gr".. ::;> BrfY1(',. = L/if" c.o2 :::.. () {>..'- 3)(/O6'()()t:ttD"'J t> -\0 f5 s -=. "/..(0 T, (!,.."""::.- /8'- 7 71V c) Suppose that the antenna has inductance L and is one element of a series RLC circuit with fixed resistance R and variable capacitance C. How should C be adjusted to receive frequencyf? How does R affect the quality of the tuner? (10pts) 1. - - L-C r. - :;: d"o' -P :-;. C::: [(;;( TT+) LJ VVv, w" - We L r tl.. R - ) Aw - R ). R-='>' Physics 263 Exam 2 Prof JJ Kelly
Name: Page4 3. An object is placed at distance 15 cm to the right of a thin converging lens with focal length 12 cm. Construct a ray diagram that includes at least two of the principal rays and determine the position, orientation, and magnification (or reduction) ofthe image. s the image real or virtual? (25 pts) Note: although you may check your answers using the thin-lens equation, to obtain full credit you must produce a neat ray diagram and derive your answers from it geometrically. mage type:(feabr virtual? (circle one) mage position = /; (;) C n' 1; mage orientation: erect o@ert Magnification factor = - tf- Diagram: (circle one) f B c he - h.6 AJ:F.lJBVF ::> s: - f + "'-' - - -+- - J;:: '2 c.)'v) - h: 1--0 S'c S: 6.A\J 1. "-' 6cVB s/ S1) - ::;. ' -. l' -h' So::: S-c."", SL ::: 'D Co.,.." M =-4 -tv-tx,/t). An Physics 263 Exam 2 Prof JJ Kelly 6" -
Name: Page 5 4. A series RC circuit consists of a switch that is initially open, a battery with potential E, a resistor R, and a parallel-plate capacitor that has circular plates of radius a separated by distance. Assume that a» such that the electric field within the capacitor is nearly uniform. The switch is closed at t = 0. a) Determine the time dependence of the electric field within the capacitor. /!? - C;; + 6 0 Q (t":j \ ==0 c. - C. 1'-) ( _7/1::\,-+1 't'- RC '[3 Q (t) = C 1- e ) - -::::- +-l\' E r:' & t -=- - Q = -i1:h: =- e- => G<«. t =, e. v (9. - -5.. - c ::: EtzA A-=rraL R D e ( -t:-/7: E=- - -eo..r. j. E == E A - C - '>...e b) Determine the magnetic field as a function of the distance r from axis of the capacitor.(6pts). - 0- cy6 y- H-- de '- Q,) vr- E =- v to J.t- ::: /lto f... 7"\-r co'"... B::: C! - tit:..)'\\ 0- '!.. R. e (6pts) -"-...:l. Tll E E B cg) 0 S S c) Compute the electromagnetic energy flux at the cylindrical surface ofthe capacitor. What is its direction? (6pts) S tjv<,. e"l- - tj't:( - -t-t'"\,-= A- S - - -::::. e. l \ ) - D C):rrA.J.R d) Compare the total energy that enters the capacitor with the stored energy as t 00.(7pts) u.:::,,.. 'Z. CoP -tit: -J1:'\ - e2... 1"" r d t L 't-) -:2 11Q 1- ;::..f.. f oft e. ( - e J - -- "2- c) R D R 2.. U -=- L(.... CVJr.. a 7L.' fe U - "2. Jl a - <="" 2 1- (J) c.. - C.?. - - ( e. tf C - '20 "2- - - - Jt Ct --'"-.2. - - '!TO- E. 2...{ Physics 263 Exam 2 Prof JJ Kelly
Name: Page 6 5. The apparent position of the sun is affected by refraction in the earth's atmosphere. Suppose that we represent the earth as a sphere of radius R surrounded by a thin atmospheric shell of thickness h with unifonn refractive index n. The local horizontal plane is tangent to the observer's position on the surface. a) At sunset the sun appears to be in the horizontal plane. s its actual position above or below the horizontal plane? Explain. lu. fl J (VJ tl.ct. ) ) d-. t;l b) Find an expression for the angle ()that the sun's rays outside the earth's atmosphere make with respect to the horizontal plane at sunset. (10 pts) Bi -::::. (-t+&) -= n& R.' 9t;::: +\\._'fnr\.-1 ( 1< \ :. ::: ;a l f..+).,. ) - fc.+j) t x /<. kor;tl?y' v- R R c) Find a simple approximation for () assuming that h «R, 0 < n -1 «1. (5 pts) c <" e (et t- S)?C et -+ & f}t./-.. d t?;= (n-\ \ Ut h«r :::> let-\6\ -= h.al,..';..$f h 8-t \ - f)t:. -;:,J;;;t'" j(. / kbt ;::... (t'1-')j;h' d) Compute 0 using n -1 = 3 x 10-4, h = 20 km, R = 6.4 x 106m. Compare your result with the angular diameter of the sun, approximately half a degree. -=-3. f q 'ry\r--a.o::=-0."1-1 1L- ti tla2. Physics 263 Exam 2 Prof JJ Kelly
Name: Page 7 Possibly useful information J - Q 'j da. E = --;;- "0 fda..8=o fas. E =- d<d B dt - -- D = GE= GoE+P - 1 static: E = f fdq2 41Z"Go r G E2 B2 u=+-. 2 2J.10 1. 1 1 - = (n-l)(---) f R R2 ds' B- 110( Ho d:e) B = J.1H= J.10(H + M) static:.8 = J.10 f asx f S = Ex.8/ J.10 1 1 1 -+-=- So s; f 41Z" r 2 2 1 c =-'--- GoJ.1o c=2.9979xl08 m s Go =8.8542xlO-12 F m e = 1.6022 x 10-19 C me =9.109xlO-31 kg=0.511mevlc2 J.10= 41Z"X10-7 A NA = 6.022xl023 mp =1.672xlO-27 mole- kg=938.27mevlc2 J.1B=9.27xlO-24 J T J.1N= 5.05xlO-27 J T Dimensions and S Unitsfor Basic Electromagnetic Quantities Quantity Unit Abbreviation Conversions Dimensions Charge Coulomb C Q Electric potential Volt V JC ML2T-2Q-l Electric field Voltlmeter Vim NC MLT-2Q-l Capacitance Farad F CV M-1 L-2T2Q2 Current Ampere A Cis QT-1 Magnetic field Tesla T N (A m) MT-1Q-l Magnetic flux Weber Wb JA ML2T-1Q-l nductance Henry H JA" ML2Q-2 Resistance ohm Q VA ML2T-1Q-2 Physics 263 Exam 2 Prof JJ Kelly