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jmtome2
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Homework Statement
A conducting wire carrying a charge [tex]\lambda[/tex] per unit length is embedded along the axis of the cylinder of Class-A dielectric. The radius of the wire is a; the radius of the cylinder is b.
Show that the bound charge on the outer surface of the dielectric is equal to the bound charge on the inner surface, except for sign.
Homework Equations
[tex]\int \vec{E}\cdot \vec{da}=\frac{Q_{enc}}{\epsilon_0}[/tex]
[tex]\vec{P}=\epsilon_0 X_{e}\cdot \vec{E}[/tex]
[tex]\sigma_{b}=\vec{P}\cdot \hat{n}[/tex]
The Attempt at a Solution
Using Gauss' Law, we get that [tex]\vec{E}=\frac{\lambda}{2\pi r} \cdot \hat{r}[/tex]
Therefore, [tex]\vec{P}=\frac{\epsilon_0 X_{e}\lambda}{2\pi r} \cdot \hat{r}[/tex]
Therefore, [tex]\sigma_{b}=\frac{\epsilon_0 X_{e}\lambda}{2\pi b}[/tex] on the outer surface and [tex]\sigma_{b}=-\frac{\epsilon_0 X_{e}\lambda}{2\pi a}[/tex] on the inner surface...
These are not equal in magnitude! Can someone explain where I went wrong?
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