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Unformatted text preview: ECE311 Test 1
October 2, 2007 Name: ID: Problem 1 ABET Outcome  Points  Score
1 1 10
2 1 10
L 3 1 4f 10 1
4 +7 1 10 +
L_’I‘_otal 4O (i) 1. (10 points) A uniform charge density p0 C / m2 exists on the a: = a plane and —p0 C /m2 on the x = —a
plane, and these are inﬁnite in extent in the y and 2 directions. . T
(In Fez. 3pm) fa
_ 501°
IE’.’=I§..\
r: 113: 0
260 260 “ﬁnch, $L26+ 1'7 E "1‘ 331mm 31313 ‘5? Et" qr. 4’; 3C2? E3: ‘51.— f2 2:, ’E‘ﬁ at: 2&0 . (b) (2 points) Find the force on an electron located somewhere between the two sheets.
Please retain the variable q = —e, where e is the magnitude of the charge on an electron. E: F “€Fo 5: _ éo (c) (2 points) How much work was done in assembling this charge distribution, per unit area ofcharge? L15 ,1. [3.13 0h:
Z
 .LéolélL 1.24
’ z 2. (10 points) A coaxial system with two concentric inﬁnitely long conducting cylinders is shown.
Assume that the inner conductor (,0 = a) has a uniform change density of p50 C / mgrAssume N that there is no charge on the surface p = c. ksm at“) M tLa .  (a) (5 points) Find the electric ﬁeld everywhere, in terms of p50. Caqss‘s Lam + saw/\th 03' a W «WM . (b) (3 points) Find the potential in the region a g p g b, assuming that V(p = b) = 0, in
terms of p30. (c) (2 points) Find an expression for the capacitance per unit length. 0 V:
(3—.— 3. (10 points) A semicircular ring of charge in the z = 0 plane7 as shown, has uniform charge
density p0 C {ind an expressioii for the electric ﬁeld at the origin (0,0,0). y Assume CW 'sfsu; ﬁzz space.
—:0 ( t; oES'W'Ca’: Point); 4. (10 points) Two inﬁnitely long concentric conducting cylinders are shown. The inner cylinder
is at potential V0 and the outer at V = 0. The material in the region a g p S b has
conductivity 0 and permittivity e. (a) (5 points) Solve Laplace’s equation for the potential as a function of position in the
region a S p S b. 3.2. 3.! =0.
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 Fall '08
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 Electric charge, Fundamental physics concepts, charge density, uniform charge density, 1 1 10 2 1 10 L

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