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1e3test1-2005-solutions - Physics 1E03 Name g0 i ”(eh—l...

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Unformatted text preview: Physics 1E03 January 31, 2005 Name g0 i ”(eh—l W (‘3 Instructors: Student Number: ‘ A. Jopko (section C01) N. McKay {sections C02, C03) Mac email: @memasterca D. Venus (section C04) K. Sills (section C05) Instructor: _ Write your name and student number on your paper before you begin. Multiple-choice questions are worth 2 marks each, and problems are worth 3 marks each. Only the McMaster standard calculator is allowed. Notes and formula sheets are not permitted. Some formulae are given below; if you use them it is your responsibility to know what they mean and when they can be used. 'J . , . . . . -11 C“ Earth's grayitational field :3 = 981$2 permittmty of vacuum :80 = 8.85 x 10 '"‘ N 2 s . m . 1 9 N - m“2 _1, Coulomb s Law constant: kg = = 8.99le) 2 electron charge : e = 1.602x 10 C 47590 C electron mass : me : 9.11X10‘31kg proton mass : mp : 1.67 X 10 3? kg _. k —~ —- - k ,, -: k d A ' F: #1;qu F:qE E: flqr BZJ‘ eqqr I =i=27fi<80 r" r‘ r“ 280 (hr? = If; 0 d}, (DE : QW‘O-md = 47d:edeM, conductor: 1E1 =3 = 47:3230 £0 50 k S);— U:"q1q2 Uqu AV:V(sf)—V(s,)=—jE-d§ AV=—Ed VZk-A' vszedq r r +r + r+1r3 {3 * a 1"? a dlfil 1.: :1: a. x=x v‘_ —a_ :m_(; r_:_.. :_._ K 01' 0 Ex 2 r I df _. 1 q sells-arr K=Emw WC:U,.—Uf K,+U,.+wm,_=r<f+uf PLEASE DO NOT WRITE IN THIS AREA 1—9 to (18) (3) Version 1 Page 2 of 3 Part A (multiple choice): Print the letter corresponding to the best or most nearly correct answer in the box beside each question. Each correct answer is worth 2 marks. An incorrect answer or unanswered question counts as zero marks. 1. Two infinite sheets of charge are parallel to each other and separated by a distance d 2 0.5 em. if the electric field E between the sheets is 500 NC, what is the potential difference between the sheets? A) zero B ___—..__._ J 100 kilovolts _ ,7. ..» [U 1 (g 00 ( )(.§f/F() in) answer __ :2 -( t} C 2. A conducting sphere, carrying charge Q, is in the centre of a spherical conducting shell carrying charge —Q;. To cause the electric field at a point. P half-way between the inner and outer sphere to double, you could ““V ,/ z”: A) double Q], leavin Mu; A unchan ed. / ou e Q2, leaving Q1 unchanged. 7L C) either of the above i D) none of the above 5/ ‘d 115 W Cf Pr 3. Three identical charged particles, each with charge+q, are initially at rest at the vertices of an equilateral triangle of side a. They are released, and accelerate away from each other. When they are very far apart (“at infinity") each will have kinetic energy -- 2 {egg/r: C) 1a a, gf/rt D) Zloty/a / 1 answer 37 K 75 “TOT .F fl lg: if 't ' b \‘1 Tm “a: , i Page 3 of X 4. A total charge Q is spread uniformly over the surface of one hemisphere of a hollow insulating spherical ball of radius R, The magnitude of the electric field at the centre of the ball (point C) will be A} equal to leg/R2 “1 B) lesstllanl'<._.Q/)i€2 ‘/ C) greater than l<..Q/R2 D) zero HIISWBI‘ 5. Charge is added to the surface of a spherical conducting balloon until the potential at its surface is 500 volts (relative to infinity}. The balloon is then inflated until its radius is doubled. The potential at its surface will then Argeemus ta (D K, J $3 250 volts 3 ”a [2 ) 100 volts - D) 125 volts 3.115 W 01' B 6. The electric potential Vtx) at a point on the x axis is given by Wit) 2 l — 2x + 4i:2 volts, wherex is in metres. What is the x component of the electric field at I = l m? f: git—M) D) 13Ntc 1:, : #C/U/C illlSWET l3 Page. 4 of 8 7. The electric potential V(x) at a point on the x axis is given by V(x) = l — 2.1; + 4x2 volts, where x is in metres. How much work does the field do when a charge q = +3pC is moved from x = 1 111 to x : 0'? 323:; ‘ azwr, or: 1w” w: 7/ (“*WS : [9/7- D) 4‘11] i1 [18 WCI' C 8. An uncharged wooden stick is balanced on a pivot so that it can rotate freely. lI' a charged rod is brought close to one end of the stick, the stick will A) feel no electrostatic trace from the charged rod B) 1 - edhythecaaargedm Wtw by the charged r ) will be either a .tracted or repelled, depending on the sign of the charge on the rod 'd 118 WCI‘ C. 9. Electric field lines pass through the three surfaces S 1, SE, and 53 shown. Through which surface is the electric flux the largest“.J A} 81 S B) S: 52 ‘ 3 \ (ELL-83“” ________ _ ...__c._.- .‘_._.._...__,_. 511 I l ‘ f/D) it is the same for all three surface . I ‘, \____ : I I. E. i l I answer ' I I I D " Page 5 ol‘ 8 Part B (Problems): Write a clear solution showing how the answer is obtained. Each problem is worth 3 marks. It}, A straight wire carries a uniform linear charge density +1 (measured in coulombs per metre). Derive an expression for the strength of the electric field a distance r from the wire, using Cams ’3 Law. As a gaussien surface, use the imaginary cylinder of length L and radius r, shown in the diagram. Explain and justify each step with a few words. answer Page (I (ll 8 l 1. Charges —q and +(; are placed at (—a.‘ U) and (+a, 0) Calculate the electric force exerted on a third charge +151 located at the point (+a, +2a). Give the answer in Cartesian vector form, for a = fictltlem and q=U.Z(lU‘uC—’_ —-v £1118 WCI‘ (a “27/3 ”12%) wo’W Page 7 0H? 12. A solid conducting ball of radius a, carrying charge +3 Q, is at the centre of a hollow. cenducting, spherical shell of inner radius :5 and outer radius c. A charge —2Q is placed on the shell. :1) On the diagr a111, indicate how much charge settles on each 01" the three. surfaces. h} On the axes below, sketch a graph of the electric potential V as a function of distance r from the common centre of the spheres. Set V20 at infinity. Surface 1: +39 Surface 2: fl 3 Q" Surface '3: 4" Q _ Page 8 ol' 8 13. A thin wire carrying a uniform linear charge density P» = +3.4 pCr'rn is bent into a semicircle of radius R : 11‘ J cm‘ Use the following steps to calculate the x-component 01‘ the electric field at point 0, the centre of the semicircle: a) Write down an expression for the magnitude IdEI of the field produced by the infinitesimal char element deg on the small arc of length d! =Ra'6, between Band 5 +dt9 on the wire, as shown in t diagram. Indicate the vector dE on the diagram. h) Set up and evaluate an integral to derive an expression for j; at 0 and calculate its numerical value. Mel: ti. ct: ke(¢)~de):%)a[g n. ‘ L. H”, 113- .--'—""' .‘f 12 2L {2. 7,. MHz/QC) T 1:3) eager/ta ...
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