# 1051test2answersW11 - Circle instructor Morrow or Yethiraj...

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Unformatted text preview: Circle instructor: Morrow or Yethiraj 1 Name: 30 L U 7/0 “5 Lab period: Student Number: MEMORIAL UNIVERSITY OF NEWFOUNDLAND DEPARTMENT OF PHYSICS AND PHYSICAL OCEANOGRAPHY Physics 1051 Winter 2011 Term Test 2 March 11, 2011 INSTRUCTIONS: 1. Do all questions. Marks are indicated in the left margin. Budget time accordingly. 2. Write your name and student number on each page. 3. You may use a calculator. All other aids are prohibited. 4. Write answers neatly in space provided. If necessary, continue onto the back of the page. 5. Do not erase or use “whiteout” to correct answers. Draw a line neatly through material to be replaced and continue with correction. 6. Assume all information given is accurate to 3 significant ﬁgures. 7. Don‘t panic. If something isn’t clear, ASK! W SEE LAST PAGE FOR SOME POTENTIALLY USEFUL FORMULAE AND CON STANTS For ofﬁce use only: | 1 2 3 l 4 ltotal Circle instructor: Morrow or Yethiraj 2 Name: Lab period: Student Number: [10] 1. (a) A charge of Q = -8.0 ><1()”6 C is uniformly distributed over a ring of radius a = 2.5 cm. I (i) What is the electric ﬁeld at the centre of the ring? {D We a/ea;,,'¢ /,'g I‘A email/1 0;) Emu-,0 ‘7 (ii) What is the electric potential at the centre of the ring? V5 (4/, /’“’;‘/I‘I75mvpﬂrw q ﬂ/‘M r « 3.79007/“1’41 x30 x/oi‘C 0.0,1rm : ~a.r\$></0‘ \/ (w 4%”) (iii) How much work would you need to do to slowly push an electron into the centre of the ring from a point inﬁnitely far away? W3AU= 304244.50 Art/m (/fym/so- A, 1; 7w , _,¢ 5 ~. W, ; -/.rm 5 x (—grs’xw V) 77'“ = + ‘ﬁé/X/ods .T (b) For each of the four cases shown below, indicate the initial direction in which the charged particle shown will be deﬂected as it enters the region of magnetic ﬁeld. Use arrows for directions in the plane of the page or write “in”, “out”, or “zero” to indicate deﬂection into the page, deﬂection out of the page, or no deﬂection respectively . l Circle instructor: Morrow or Yethiraj 3 Name: Lab period: Student Number: [10] 2. (a) The graph below shows equipotential lines around three point charges; A, B, and C . The lines are drawn in steps of 10 V for all voltages between -30 V and +30 V. The electric potential is taken to be 0 at inﬁnity. y (cm) x (cm) (i) Is the magnitude of the electric ﬁeld larger at point d or at point e? Brieﬂy explain your choice. /1§/:‘s /ér7e,r\ at a. eﬁanﬂdfm/i—m/ ﬂue, q,. r , c/0{e/‘ H7pMA. (Mt/t jw‘e) (ii) Using the scales on the axes and the equipotentials, estimate the magnitude of the electric ﬁeld at point e. FOILeqlLt‘J altar-74\$ ﬂ/‘am "/UV I‘D ‘f‘/0l/ I"! ~ 0-4‘9‘4. ..' /g/: 4! z 9.215, : 5000 V m Mae ’2 A; 00%» m (iii) How much work would be done by the electric ﬁeld if a charge of q : +10 yC were moved from point h to point k? Be careful with the sign. MW 7w : Wm a (b) The electric potential in a region of space is given by V = m where a = 1.7 V/mz. 90’ What is the x-component of the electric ﬁeld at the point x = 2.0 m, y = 3.5 m? q £x€“&i/— -- C? J ‘ _/ 5 + (9% a X 22? . 1/ 1. w gX (3-0)?‘I>‘ £711" =+O-/02/ m-rO/Z/IZ‘ @.0m)/5-§M Circle instructor: Morrow or Yethiraj 4 Name: Lab period: Student Number: [10] 3. (a) The ﬁgure to the right represents a very long, uniformly charged rod I z p with a linear charge density of 2. = 6.3 ><10”9 C/m ‘? ’ (i) Draw a Gaussian surface that could be used to ﬁnd the electric ﬁeld at point P located l0.0 cm away from the rod. (ii) Write an expression for the electric flux through you Gaussian surface in terms of the dimensions of your Gaussian surface, a, and the magnitude of the electric ﬁeld at P. d): A/frxgrfh_ (iii) Use Gauss’s law to ﬁnd the magnitude of the electric ﬁeld at P. QIN x F x g” s M 4., . 3 z '- £114 /\ 5/.13w0 y W /./3//0 5. a774,» C (b) A point charge Q] is located at the centre of a spherical conducting shell with with an inner radius of a = 0.15 m and 93 an outer radius of b 2 0.20 m . The net charge on the conducting shell is Q2 2 2.0 ><10’12 C. At r = 0.25 m from the centre of the shell, an electric ﬁeld of magnitude 0.719 V/m points radially outward. ‘ (i) What is the total charge, Q, + Q2 of the point charge and the surrounding shell. (Hint: Q, + Q2 is the total charge enclosed b by a concentric spherical Gaussian surface of radius 0.25 m and r area Aspmre = 47rr2 .) I37 Gent's [w fﬂqufﬂ: 6:31» Go . 7 — ’ 2 2 .. Q, + at : % xgryx(0,gfm) )( 8-{5'1/0 64M: . l , 11 = 4f. 7 77x10 C r 0 X/0-nc (ii) What is the total charge on the inner surface of the conducting shell? Brieﬂy justify your answer. /2 ,5 5mm"? ’2. X/o'nc : + 3 x15 C. (err/r can/‘ch _ Claw]; an I‘d/78f fur/m /coaa/ac/;17 5W mmgtL Le ’3X/0-I25. (62a) 1 ﬂéasm: [‘0 Msl‘cg com/«alfrr. r‘ﬂ/MX ILA/‘r/tzwjj‘ 5/Affl‘ce/ fer/‘f/M /\V\ (Dazué WW :c9r' Zinc/agar” 5W :5 0. ya = -62/ em Circle instructor: Morrow or Yethiraj 5 Name: Lab period: Student Number: [10] 4. A rod of length L = 15.0 cm runs along the x~axis y from x = —7.5 cm to x = +7.5 cm as shown. A charge T Q = +2 ><10'6 C is uniformly spread along the rod. R? p Point P is located a distance h = 10.0 cm above the rod \ centre as shown. :vé\\ h=10.0 cm \x a What is the linear char e densit , xl , on the rod? i ‘\ H g y Q=2xlO‘C l i * flwljd‘ *6 -\$ ,,,, :_' ,,,,,,,,,, , ,,,, (a %‘ QX/O Z0” : [.33 200 («44 (b) On the diagram, show the direction of the contribution, dE , to the electric ﬁeld at P from the charge on segment dx located a distance x from the centre of the rod as shown. (23> (0) Write an expression for a’Ey , which is the y—component of (IE , in terms of the variable x, the segment length dx , the charge density 2., and the distance 17 from the rod. , a k A 457: AQ.J%X 605&' A Y [‘1 ((A4? HIV-2H,» :;\ (2/ : AMA M / 3 (x3?) 1 (d) Calculate the y-component of the electric ﬁeld, Ey , at P due to the entire rod? 4.075910“?t -" £7; A‘XA j (Kit/‘1')?” ’.07f~: 0.077“ ‘F -r x a \$.7‘U/ﬂ ’C’i'ﬂx #33100 ﬁxalm x [1 6 h 4,7an1, ’0’y7rm‘ z -r 7 m t 3-77 k/DT’VLE’ (/.‘53X/V a x 0.],97 X a? x 0-0 { (0 Mm)" *’ (0-97Y¢)L *wv/mf 3 /'43)(/06 % m/.‘/’2X/O I Z, (c) What is the total electric ﬁeld at P due to the rod? Give your answer in unit vector notation. [(70 Wadi/'7 50 5?: 1 flé’jx/pbg; Circle instructor: Morrow or Yethiraj Lab period: Name: Student Number: Some Potentially Useful Formulae and Constants: Vzkczgi , 1: Vszfig ,. C Me = 27rr (circumference) A =7rr2 circle Physical constants: k, = I =8.99><109N.m2 /C2 4m:O so =8.85><10‘” C2 /N.m2 Mathematical formulae: 55"-}. r2 r dx J-m—tlnx x dx /2 2 [szln[x+ x +y] dx x “*3 2 2 2 (x2+y2 y x+y 21-13 = AB c030 = AXBX + AyBy + AZBZ Em (j12 : k8 qlqE r12 B —- AU = ~qu d? e : l.602><10‘19 C me =9.11x10*3' kg xdx 1 l<x2+y2)3/2 _- x2 +y2 IsinQdG : ~cos€ [cosﬁdﬂ : sin8 x B = (A‘VBZ — A213}, )5 + (,4sz — AXBZ )j' + (141.3}, — AyBx ...
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1051test2answersW11 - Circle instructor Morrow or Yethiraj...

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