discussion6

# discussion6 - 1) Consider a cylindrical volumetric charge...

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1) Consider a cylindrical volumetric charge distribution < < < = a r b b r b r 0 ) / ( 2 0 ρ a) Find the electric field E in the domain ra < and arb < < b) Assume that a surface charge s is distributed at rb = . Find s that lead to 0 = E for > . 2) Consider a line charge distributed on straight line lzl << . Find the electric field E using two methods: a) Find the electric potential V based on superposition and then the magnetic field as V = −∇ E b) Find E directly based on superposition.

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”Electromagnetism” Discussion 6 February 14, 2007 1
February 14, 2007 2 Problem 1: A. Due to symmetry, E has only one component in the b r direction. Using Gauss’s Law: Z S Z ± E · dA = ZZ V Z ρ ε 0 dv For 0 r b The contribution over the envelope is given by: E r 2 π r δz \ = δz \ ρ ε 0 r 0 dr 0 0 (The top and bottom caps do not contribute because E r · ds = 0 on them. ) 2 π r E r = 2 π ε 0 Z r 0 ρ ( r ) r 0 dr 0 2 π \ r E r = 2 π \ ε 0 ρ 0 Z r 0 r 0 3 b 2 dr 0 = 2 π \ ρ 0 ε 0 r 4 4 b 2 Therefore, for the range 0 r < b the electrical ﬁeld is given by: E r = ρ 0 4 ε 0 r 3

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## This note was uploaded on 04/02/2012 for the course ECE 107 taught by Professor Fullterton during the Winter '07 term at UCSD.

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discussion6 - 1) Consider a cylindrical volumetric charge...

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