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Infinitely extended cylindrical region in free space has volume charge density 
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Oct1711, 03:03 PM

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1. The problem statement, all variables and given/known data
An infinitely extended cylindrical region of radius a>0 situated in free space contains a volume charge density given by: [ ρ(r)= volume charge density ρo=constant=initial volume charge density radius=a>0 ρ(r)=ρo(1+αr^2); r<=a ] with ρ(r)=0 for r>a Questions: 1. utilize gauss law together with the inherent symmetry of the problem to derive the resulting electrostatic field vector E(r) both inside and outside the cylinder 2. Use both Poisson’s and Laplace’s equations to directly determine the electrostatic potential V(r) both inside and outside the cylindrical region. From this potential function, determine the electrostatic field vector E(r). 3. Determine the value of the parameter α for which the electrostatic field vanishes everywhere in the region outside the cylinder (r > a). Plot Er (r ) and V(r ) as a function of r for this value of α. 2. Relevant equations eo=epsilonnot gauss' law : divergence of E(r) = ρ(r)/εo closed∫{E.nda} = 1/εo*∫∫∫{V{ρ(r)d^3r} 3. The attempt at a solution 


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