"A solid conducting sphere with radius [tex]R[/tex] carries a posative total charge [tex]Q[/tex]. The sphere is surrounded by an insulating shell with inner radius [tex]R[/tex] and outer radius [tex]2R[/tex]. The insulating shell has a uniform charge density [tex]\rho[/tex] a) find the value of [tex]\rho[/tex] so that the net charge of the entire system is zero b) if [tex]\rho[/tex] has the value found in part (a), fnd the electric field (magnitude and direction) in each of the regions(adsbygoogle = window.adsbygoogle || []).push({});

[tex]0<r<R[/tex] [tex]R<r<2R[/tex] and [tex]r>2R[/tex]"

Calculating charge in terms of [tex]\rho[/tex] i got

[tex]\sum Q=\frac{-28\pi\rho R^3}{3}[/tex]

now my problem is trying to fine the [tex]\vec{E}[/tex] below is my work

[tex]\oint\vec{E}d\vec{A}=\frac{Q_inc}{\epsilon_0}[/tex]

there is an electric field only between

[tex]R<r<2R[/tex]

[tex]\vec{E}=\frac{Q}{4\pi R^2 \epsilon_0}[/tex]

and after solving my above value for

[tex]\rho[/tex] in terms of [tex]Q[/tex]

I got

[tex]\vec{E}=\frac{7R\rho}{3}[/tex]

which is soo wrong, im sure I did some of this problem correctly..the part I dont understand is how I would find the electric field? Can anyone please help?

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# Homework Help: Gauss's Law and a conducting sphere

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