EE1 HW 3

EE1 HW 3 - l / 2 ) ln ( r 2 /r 1 ). 4) In spherical...

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EE1: Homework 3: DUE APRIL 30th Wednesday 5PM (THERE WILL BE A COLLECTION BOX IN FRONT OF MY OFFICE ENGR. IV RM# 66-127D) 1) In cylindrical coordinates, let D = ( r ˆ r + z ˆ z ) / [4 π ( r 2 + z 2 ) 3 2 ]. Determine the total flux leaving: a) The infinitely-long cylindrical surface r = 7. b) The finite cylinder, r = 7 , | z | ≤ 10. 2) Charge Q 1 is uniformly distributed over a thin spherical shell of radius a , and charge Q 2 is uniformly distributed over a second spherical shell of radius b , with b > a . Apply Gauss’s law to find E in the regions R < a , a < R < b , and R > b . 3) Show that the electric potential difference V 12 between two points in air at radial distances r 1 and r 2 from an infinite line of charge with density ρ l along the z -axis is V 12 = (
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Unformatted text preview: l / 2 ) ln ( r 2 /r 1 ). 4) In spherical coordinates, E = 2 R/ ( R 2 + a 2 ) 2 R V/m. Find the poten-tial at any point, using the reference: a) V = 0 at innity. b) V = 0 at R = 0. c) V = 100 V at R = a . 5) A certain potential eld is given in spherical coordinates by V = V ( R/a ) sin . Find the total charge contained within the region R < a . 6) What is a dielectric material said to be if the direction of the electric polarization eld, P , is in the same direction of the electric eld intensity, E ? Does the electric ux density D always point in the same direction as E ? Why or why not? 1...
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This note was uploaded on 06/18/2008 for the course EE 1 taught by Professor Joshi during the Spring '08 term at UCLA.

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