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Unformatted text preview: PROBLEM (1) (25 points) A cube with side length L is placed with one corner at the Szaop) 56 (back)
origin as shown. The electric ﬁeld is not uniform, but is given by 2': Ax?+b§'+2€zi, where A ,B and C are positive 53 (rightface) constants. (a) (15 pts) Find the electric ﬂux through each of the six cube y faces, i.e. €251, £152, (153, CD4, 475, and C06. 3
: «63+ lei} Ma} 'r 0* AL *0 : (QCteal} : Que/en (c) (5 pts) Find the electric potential difference Vat, = Va — Vb between point a with coordinates (0, 0, O) and point b with coordinates (L, L, 0). 1; 5 EM? : [gtxax + [(9 e137
1:
‘0”.41 L L
:+£E :fAXAx+fBAj
0 O
‘73 a ﬁg} QL Phys 106 First Midterm Examination Page 3 Saturday, April 04, 2009 PROBLEM (2) (25 points)
An insulating sphere of radius R has nonuniform volume
charge density p = Ar2, where A is a positive constant and r is measured from the center. The sphere has total charge Q. Take V = 0 at infinity.
(a) (5 pts) Find A in terms of Q and R. (b) (10 pts) An electron with mass m and charge —e is released from rest at r = 2R. Find its speed at the instant it reaches the surface of the sphere. Ignore gravitational forces. 5. Mi Nisan at, What (mime, r we“ M Wm 932mm ., u: («Wm #515ng river
L a ’J L Q _ EA’W/ : Q/eo “a t I Lﬂl’é’oF; Kﬁ‘ ‘ \l ‘9 \ v7 + (€)\l(£)
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(c)(10pts)Findtheelectricpotentialatr=R/2. E, Mi. (“sac ai’ «awe 443%“ \/(r)’ vew i “(3’ ﬁ> gr
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A Phys 106 First Midterm Examination Page 4 Saturday, April 04, 2009 PROBLEM (3) (25 points) Positive electric charge Q is distributed uniformly (l = constant) along a thin rod of length 2L. Take the X
Q . l<—'L +14 _> P
<——x———>l
7? : 4H, I
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VA 34v, i xvi potential to be zero at infinity. (a) (10 pts) Find the electric potential at point P. 9r: 9,. F:X—7/(
1L (c) (10 pts) Find the electric field at P from Coulomb’s law. A kl JQ \ 33%
a“ 60 (L ._,x)
J, 4' L an’ A ‘ A'L/
Liaea LXbX vL/ :3. (L. A.)
AVG/o X*L_ Xtu Phys 106 First Midterm Examination Page 5 Saturday, April 04, 2009 PROBLEM (4) (25 points) Two identical parallel—plate capacitors (with the same plate area and separation) having capacitances C = 2 nF are connected as shown. A Q1 Q2
material with dielectric constant K = 3 is inserted between the plates
of the capacitor on the right. The capacitors are charged until the charge of the capacitor on the left reaches Q1 = i6 nC. The charging battery is then disconnected from the capacitors. (a) (5 pts) Find the charge Q2 on the capacitor with the dielectric. ................................................................... .. Cat?oxc(‘liars \nqve SQW‘Z Foleﬁh‘m‘ .5 QL5KQ‘
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C ' Kc (b) (5 pts) tEl and E2 be the electricfield magnitudes in the capacitors, respectively. Find the ratio E2/E1. ................ .. Le
i? oi : Sequ H‘M bei'wem Via‘63 (c) (10 pts) Find t e work required to pull the dielectric halfway out of the capacitor. ........................................................... ..
(We, chat/SC C : cf 0/; + KC/Z
QMzQJcCQz :2 (HS! :Z’M '‘\ 6 I:
does moi Cl/QMSC (iwfi‘na We : Q. + 4 + 3 :1 ‘4 [bfoccss ‘ Thi‘eQ Q/“efgj 7. aim: 1A, (19+; : Q‘ix‘ﬁc')
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(Q: : ng Phys 106 First Midterm Examination Page 6 Saturday, April 04, 2009 ...
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This note was uploaded on 04/09/2012 for the course MATH 120 taught by Professor Onurfen during the Spring '12 term at Middle East Technical University.
 Spring '12
 OnurFen

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