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ECE 2317 Exam 2 Spring 2005

# ECE 2317 Exam 2 Spring 2005 - Problem 1(25 pts Consider the...

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Unformatted text preview: Problem 1 (25 pts) Consider the two spherical perfect conductors as shown in the Figure. The inner one has radious a [m]. The inner surface of the outer one is at a distance b [m] from the center of this spherical structure. The outer conductor is grounded, and the space between the two conductors is filled with a material with relative dielectric constant a; . Suppose that on the inner conductor there is a net charge Q [C] distributed uniformly on its surface. 3) Find the suigergharge distribution on the inner conductor. b) Find the potential difference between the two conductors. 0) what is the potential of the outer conductor? d) what is the potential of the inner conductor? ,9 tet- _ L[ Jiﬂ — l I ,1 ROOM FOR EXTRA WORK ___ QEWC : Q ,3 §w * QC“: melbr: Q ’3‘» Rb 1": /’ a Elng r3 b Ci. ffmf; ho " m \g \_. 5 . ' C E01 _\ Problem 2 (25 pts) A planar distribution of charge p30 [ C/mz] is located on the disk region as shown in Figure. The inner radius of the disc isg [m], and the outer one is__b., [m]- a) Find the potential at any point along the z axis. b) Fine the 2 component of the electric field, E, by using the gradient, at any point along the z axis. :1 k .1 ROOM FOR EXTRA WORK ;-..-':_0/‘\-‘ H j a) — EYE.“ ‘1 1 Va” (LWOJL [2 7(9 n ) . _ Problem 3 (30 pts) Consider a non_-i_.in_ifgm__volume charge distribution py : Mp): 3/2 [Clm31- Z ‘7 T [— p[p2 +9] g , a part-g. a 3) Determine the electric field vectorE everywhere. b) Find the electric potential (I) everywhere, assume that (I) = 0[\/] atp= O[m]. F ‘4 c) Find the eliectric potential (I) everywhere, assume that a (I)=2[V] atp=4[m]. ' \ -,— a r .4 a I‘ - at; I s”? . V - I - Li‘s ' .1 i - "-- “ a L—_ ww‘ by: {lg-2 J «=7: 3 (1’? I .. , i ﬁll? l __ I 3 ‘1," r 1—". ‘K '4 9: , ’99 I J \$1.5" \ . K?! 3‘ r i \ ,_ u ._‘:}1 {4 I .E r. i ‘1 i ' 1 a. 2?": ﬁns:- H : a ' m r“ g B IE “#1: _ s 35’ — G j ff qx (I L iF \ r k I ['5 I ‘3 . r —- — __ :' 553‘ I IE I —7 -" ___.._'(.—___..._ E" I m ‘ '_ l 1. 7r. go I a! x r- l 3’ l (a —- H; 2 Problem 4 (20 pts) Consider 3 parallel slabs made of dielectric materials with different electric permitivities eh, 82?, and 53?, as shown in the figure. Determine the electric field vectors E2 and E3 in slabs 2 and 3 if the electric field vector in slab 1 is E1:(2, 3)[V/m]. y F" X ’ _ I? u y" 3: as / i4: "' .9" I ’ “J J ' Ea=? { I I :ﬂ/V 1,4, . ‘ . C ‘ \ I g” ‘L.\,‘- girl-L '2 _ r: r g '- If i T'gf r- ’z- r d , . U j t \ N W25 ’ Eh I y ¥ ...
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ECE 2317 Exam 2 Spring 2005 - Problem 1(25 pts Consider the...

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