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# exam1solutions - 2049H Spring 2010 Exam 1 Name Grading...

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Unformatted text preview: 2049H Spring 2010 Exam 1 Name: Grading Problem 1 Problem 2 Problem 3 Problem 1 [54 points, 9pts each] Consider an infinite uniformly charged pipe with cross section as depicted below. The volume charge density is p [C/ m3). Calculate electric field (as a function of r: radial position with respect to the center of the pipe) for (a) r > b (b) a<r<b (c) r<a Taking voltage at the center of the pipe to be zero and calculate voltage [as a function of r: radial position with respect to the center of the pipe)for ll\(a)r>b <(b)a<r<b <Q(c)r<a (A) “k 5% ﬁt; “ ZTU’Q— E = @g‘LME" ,, 7t ( b) :wmj} *- 5* ‘ia it ’.. c . NW; 1&5. : 7M”; (ii/Eff Co ,. a: (saw)? ‘7. WEB b7 2m! E 2 it («1-2; M 4,9 g a (New 2 “\$9 C) ”E“: m 3% y) VCcn 3’” .V‘ L “g (Ix‘i V‘Clg VUQ‘““Q(W ; UP 4" J) ‘Qw m 10"?» v a. i'vl_ ole/xvii” b no '3: 5" ’ ‘ F ““V(V) :2 V [V1553 a» 6‘} IQHN j m.......,....m...uw._.MWmW ; WM V: i a‘ﬂr‘ L , I»? 7 Xa‘ém -~ wax/{X (Wm “4’11"” 9’3”: (coxnw (>00 ‘2 Wm Problem 2 [32 points, equally distributed] We have equal charges +Q distance 2d . +Q away from each other as shown in the figure below. A charge, -Q is brought in from infinite distance away to the position {1 shown. . (3) Calculate the force on —Q by the +Q X charges <———————> (b) Calculate the electric potential of -Q (c) Calculate the electric potential energy . +Q Of'Q (d) Calculate the work required to move - Q into the position shown in the figure ’1 sink ““3 ~ \ Q ,,,,, at l, M - ~--—-—~ em , / ~~~~~ \ (lllfa, (Kala?) ON 0i y< Miaﬁwxﬁ REMM" l Q1 x; Fr 1 "7"" a .1-——-—-—- “twine“ W“ 5'5 \ ”ELI - :2 \3 Fr- : l t 2 i M“ 221% a l X M ) Vo‘TEl'J-N (”vb ’ , S2 VtGHVL(v/) a zlcxltvllt' in go ”’1‘; Problem 3 [14 points] Consider two infinite line charge distribution as shown below with opposite charges, Find the direction and the magnitude of electric field at point 1,2, and 3 0 Point 1 0 Point 2 .Point3 A A.“ 7‘ (2‘ (33H TAL‘M“ y mes V \5 > __ A law 4w:- 2 ‘LV 271\$» Y '1 24a WHO «1;: \(L_.»_I_:._,L—_. Argo \z 5% 23,33 3&- q A r; i '1" I“ f d .3 273E; \K ML; 2 ‘ L w F’” " . a (70W 0 (:2 2 t' 3; Z: “j ...
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