- #1
Alem2000
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"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
[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, I am sure I did some of this problem correctly..the part I don't understand is how I would find the electric field? Can anyone please help?
[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, I am sure I did some of this problem correctly..the part I don't understand is how I would find the electric field? Can anyone please help?
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