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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. Multiplechoice 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‘Omd = 47d:edeM, conductor: 1E1 =3 = 47:3230
£0 50 k S);—
U:"q1q2 Uqu AV:V(sf)—V(s,)=—jEd§ AV=—Ed VZkA' 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
sellsarr 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 halfway 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 \
(ELL83“” ________ _ ...__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 xcomponent 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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