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EE1 HW 3

# EE1 HW 3 - ρ l 2 π± 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: ρ l / 2 π± ) ln ( r 2 /r 1 ). 4) In spherical coordinates, E = 2 R/ ( R 2 + a 2 ) 2 ˆ R V/m. Find the poten-tial at any point, using the reference: a) V = 0 at inﬁnity. b) V = 0 at R = 0. c) V = 100 V at R = a . 5) A certain potential ﬁeld is given in spherical coordinates by V = V ( R/a ) sinθ . 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 ﬁeld, P , is in the same direction of the electric ﬁeld intensity, E ? Does the electric ﬂux density D always point in the same direction as E ? Why or why not? 1...
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