EE325_midterm1_solutions

EE325_midterm1_solutions - I - Fall 2009 EXAM 1 October 8,...

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Unformatted text preview: I - Fall 2009 EXAM 1 October 8, 2009 is a closed book exam. You are allowed to use only the following: I) Pen/pencil 2) Calculator One sheet of notes (front & back) The test is scored out ofa possible 105 points. ""''''AnIA fun credit: I) Clearly show all of your work 2) Show your final answer by putting it inside the box provided. 3) Use the standard Cartesian/cylindrical/spherical coordinate symbols used In the textbook and class. 4) Clearly vectors with hats 5) Turn your formula sheet along with the exam. Print and your name below. Also, print your name in the indicated on ofthe exam. the you are indicating that the work on this exam is yours alone. NAME:__U4LLU~.-l_________ Topic ! Points Problem I Problem 2 Gauss's Law Gauss's Law & Dielectrics 15 30 Problem 3 Conductors Problem 5 NAME:_____ PROBLEM 1 The electric tlux density is given as D(r) =2psin3 p + PCOS3 ,p (C/m 2)_, Find the total charge in the region p 50 2, 0 <; z 50 5 , and 0 <;4> 50 " . ( 15 points) 1 .. --;. 'i/-P"'-JV ( ' '''"'s?5 I""" '" I"''-t fa~ + h '1 \I~&;-ea-( Coofd~~.es ___ ~ V_~~l ~ (S~) tL~t 6rR:J aj J CJf d&) / .. =: 3~~r'~)~ 5 ~ ~}1) / ::: to1"'-4> -5\V\ r 1"f1 :[9-0'= 3,s,-.-4",j'" I ... -7 &, :> ~ Jot '\'l/ -V to (C) I EE 325: Exam 1 Fall 2009 NAME:_______ I PROBLEM 2 A positive point charge Q is at the center of a spherical dielectric shell residing in free space, The shell 's inner radius is R" outer radius RII , and relative permittivity is c, ' a) Determine D(r) I Co and E(r) under static conditions and plot their magnitude for all .-~~ r > 0, In the plot, mark the function values at r = {R;-, R,+, R,~, R(~ } ' / //. "-""" (Hint: Apply Gauss' s integral law with surfaces at different positions) // "..-_, \ /. ~ ~-. \ (20 points) I ~R,(f).1\ \ b Iow~"-.s 'U) ~,w-f j f""""l j Y'"",,-Jry ;,, \ ""--f"\,i"M \ ,: . W'), ) .. v:(e. ~ \'~u;-u:).\ c. CO(J~~ \. --/ .. r / (2-) 6U~)-=-&(('(&, P\ -=-e(r) ($,(W\ML~7' ~;,~~~It~O-->~ \.",....,., _//J .. '~~ ti ~r.I.c...e:-1 e(r ):=-are..(r\ b.uc..M_(..'vo;;r'!lV <:/' e..JIY'f'j b -' t-~~ ~ 1~~ c"'- \1---I I I I I .. I I I L---------J-------~---....
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EE325_midterm1_solutions - I - Fall 2009 EXAM 1 October 8,...

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