(adsbygoogle = window.adsbygoogle || []).push({}); 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=epsilon-not

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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# Infinitely extended cylindrical region in free space has volume charge density

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