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## Homework Statement

Consider an infinitely long cylindrical rod with radius a carrying a uniform charge density ##\rho##. The rod is surrounded by a co-axial cylindrical metal-sheet with radius b that is connected to ground. The volume between the sheet and the rod is filled with a dielectric, ##\epsilon##.

Calculate the free and bound surface charges at r=a and r=b

## Homework Equations

## The Attempt at a Solution

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I tried to use discontinuity in E.

From Gauss. ##\nabla \cdot E = \frac{\rho}{\epsilon_0} \Rightarrow \oint E \cdot ds = \frac{Q}{\epsilon_0} ##

##\Rightarrow (E_{above}-E_{below}) = \frac{\sigma_b}{\epsilon_0}##.

For r= a, ##\sigma_b = \frac{Q}{2 \pi s*l} (\frac{1}{\epsilon_r} - 1)##

So now we have the bound charge per unit area.

By integrating we ca get the total bound surface charge, ##\sigma_{bt} = Q(\frac{1}{\epsilon_r}-1)##.

I'm not sure this is right. But if it is, how do I now get the ##free## surface charge?

And I do remember that either the bound charge or free charge should be zero for a grounded material, but not which one.