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### 20115ee101_1_EE 101 Homework 3

Course: ELEC ENGR 101, Fall 2011
School: UCLA
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101 EE Homework 3: DUE NOVEMBER 3TH Thursday 5PM; (THERE IS A COLLECTION HW CABINET MARKED EE101 IN ROOM 67-112 ON THE 6TH FLOOR OF ENGR IV.) 1. Charge is distributed with constant surface charge density on a circular disc of radius a lying in the xy-plane with center at the origin. Show that the potential at a point on the zaxis is given by = 2 + 2 || 20 What is the electric field at that point? What...

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101 EE Homework 3: DUE NOVEMBER 3TH Thursday 5PM; (THERE IS A COLLECTION HW CABINET MARKED EE101 IN ROOM 67-112 ON THE 6TH FLOOR OF ENGR IV.) 1. Charge is distributed with constant surface charge density on a circular disc of radius a lying in the xy-plane with center at the origin. Show that the potential at a point on the zaxis is given by = 2 + 2 || 20 What is the electric field at that point? What does V become as a becomes very large? What is the smallest value of z for which the potential due to this disc can be calculated as if it were a point charge without making an error greater than 1 percent? 2. a) An infinitely long cylinder has a circular cross section of radius a. It is filled with charge of constant volume density ch. Find E for all points both inside and outside the cylinder. b) An infinitely long hollow cylinder with an inner radius a and an outer radius b is filled with -r charge whose volume density in cylindrical coordinates is ch = Ae . Find E everywhere. 3. A cylindrical capacitor consists of an inner conductor of radius a and an outer conductor whose inner radius is b. The space between the conductors filled is with a dielectric of permittivity , and the length of the capacitor is L. Assume that the outer conductor of cylindrical capacitor is grounded and that the inner conductor is maintained at a potential V 0. a) Find the electric field intensity, E, at the surface of the inner conductor (E=E(a)=?). b) With the inner radius, b, of the outer conductor fixed, find a so that E(a) is minimized. 4. An early model of atomic structure of a chemical element was that the atom was a spherical cloud of uniformly distributed positive charge Ne, where N is the atomic number and e is the magnitude of electronic charge. Electrons, each carrying a negative charge e, were considered to be imbedded in the cloud. Assuming the spherical charge cloud to have a radius R0 and neglecting collision effects, find the force experienced by an imbedded electron at a distance r from the center. 5. Assume that the z=0 plane separates two lossless dielectric regions with r1 = 2 and r2 =3. If we know that E1 in region 1 is 2 3 + (5 + ) , what do we also know about E2 and D2 in region 2? Can we determine E2 and D2 at any point in region 2? Explain.
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UCLA - ELEC ENGR - 101
EE 101 Homework 4:DUE NOVEMBER 14TH Monday noon (12pm);(THERE IS A COLLECTION HW CABINET MARKED EE101 IN ROOM 67-112 ON THE 6TH FLOOR OF ENGR IV.)1. A long wire carrying a current I folds back with a semicircular bend of radius b as in figurebelow. De
UCLA - ELEC ENGR - 101
EE 101 Homework 5: DUE NOVEMBER 23TH Wednesday (5pm);(THERE IS A COLLECTION HW CABINET MARKED EE101 IN ROOM 67-112 ON THE 6TH FLOOR OF ENGR IV.)
UCLA - ELEC ENGR - 101
EE 101 Homework 6: DUE NOVEMBER 30TH Wednesday (5pm);(THERE IS A COLLECTION HW CABINET MARKED EE101 IN ROOM 67-112 ON THE 6TH FLOOR OF ENGR IV.)1. A lossy transmission line with characteristic impedance Z0 is terminated in an arbitrary loadimpedance ZL
UCLA - ELEC ENGR - 101
EE 101 Homework 2:DUE OCTOBER 19TH Wednesday 2PM;(THERE WILL BE A COLLECTION CABINET MARK EE101 IN ROOM 67-112 ON THE 6TH FLOOR OF ENGR IV.)1. Three point charges, each with q=3 nC, are located at the corners of a triangle in the x-y plane, with oneco
UCLA - ELEC ENGR - 101
UCLA - ELEC ENGR - 101
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UCLA - ELEC ENGR - 102
UCLAFall 2011Systems and SignalsLecture 18: Sampling Theorem IINovember 30, 2011EE102: Systems and Signals; Fall 2011, Jin Hyung Lee1Administration Project due Wednesday Nov. 30 2011 at 10 am (grace period till 5 pm).Submission Guidelines: A sho
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1EE102Fall Quarter 2011Systems and SignalsJin Hyung LeeHomework #1Due: Wednesday October 05, 2011 at 5 PM.1. Find the even and odd decomposition of this signal:21-2-1x(t)012t2. Given the signal x(t) shown belowx(t )1-2-10-112tdr
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1EE102Fall Quarter 2011Systems and SignalsJin Hyung LeeHomework #2Due: Wednesday, Oct 12, 2011 at 5 PM.1. State whether the following systems are linear or nonlinear; time invariant or time variant;and why.(a) y (t) = x(t) sin(t + )(b) y (t) = x
UCLA - ELEC ENGR - 102
1EE102Fall Quarter 2011Systems and SignalsJin Hyung LeeMatlab Assignment 1Getting Started MatlabFor this lab we only need the basic abilities of matlab to create and manipulate vectors, andplot the results. The documentation for matlab exists in m
UCLA - ELEC ENGR - 102
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1EE102Fall Quarter 2011Systems and SignalsJin Hyung LeeHomework #3Due: Wednesday, October 19, 2011 at 5 PM.1. Analytically compute the convolution (f g )(t), where f (t) and g (t) aref (t) = u(t)etg (t) = rect(t)and sketch a plot of the result.
UCLA - ELEC ENGR - 102
1EE102Fall Quarter 2011Systems and SignalsJin Hyung LeeMatlab Assignment 2Due: Friday, October 21, 2011 at 5 PM.This laboratory will be concerned with numerically evaluating continuous time convolutionintegrals. Matlab provides a function conv() t
UCLA - ELEC ENGR - 102
1EE102Fall Quarter 2011Systems and SignalsJin Hyung LeeMatlab Assignment #2 SolutionThis laboratory will be concerned with numerically evaluating continuous time convolutionintegrals. Matlab provides a function conv() that performs a discrete-time
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1EE102Fall Quarter 2011Systems and SignalsJin Hyung LeeHomework #4Due: Wednesday, November 2, 2011 at 5 PM.1. Suppose that f (t) is a periodic signal with period T0 , and that f (t) has a Fourier series. If is a real number, show that f (t ) can b
UCLA - ELEC ENGR - 102
1EE102Fall Quarter 2011Systems and SignalsJin Hyung LeeMatlab Assignment 3 SolutionIn this lab we will use matlab to compute the Fourier series for several signals, and comparethe errors that results from the approximation of the signals by truncat
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1EE102Fall Quarter 2011Systems and SignalsJin Hyung LeeHomework #5Due: Wednesday, November 9, 2011 at 5 PM.1. Each of these signals can be written as a sum of scaled and shifted unit rectangles andtriangles,a)2x(t)b)210-201-1x(t)12-
UCLA - ELEC ENGR - 102
1EE102Fall Quarter 2011Systems and SignalsJin Hyung LeeHomework #5 Solution1. Each of these signals can be written as a sum of scaled and shifted unit rectangles andtriangles,a)2x(t)b)210-21-1x(t)102-21-1-1-22-1-2Find a simpl
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