- #1

Ylle

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## Homework Statement

I got this problem (Sectional image of a cylinder):

http://img715.imageshack.us/img715/3448/cylinder.jpg [Broken]

Besides that I know that the cylindrical conductor is infinite long, and the same is the cavity.

And through the conducting material there is a current density that is given by:

[tex]\textbf{J}=J\hat{\textbf{z}}[/tex]

And that is pretty much it.

Now determine the total current

*I*in the conductor.

## Homework Equations

[tex]\[J=\frac{I}{A}\Leftrightarrow I=JA\][/tex]

## The Attempt at a Solution

I really have no idea...

First I thought of doing this:

[tex]I=\int_{0}^{R}{J}\left( 2\pi R \right)dR-\int_{0}^{R}{J}\left( 2\pi \left( R/2 \right) \right)dR[/tex]

But that kinda did not work. So now I'm quite lost :)

A hint would be much appreciated :)

Oh yes, the correct answer should be:

[tex]I=\frac{3}{4}\pi {{R}^{2}}\cdot J,[/tex]

that's what I know.

Thanks in advance.

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