# Problems with electromagnetic fields inside matter

1. Aug 31, 2011

### valleo4

1. The problem statement, all variables and given/known data
see attachment/picture
im having problems with fields inside matter. i get the left side of gaussian surfaces/ampere loops. but for example this first equation's right side i cant understand.

3. The attempt at a solution
i would think the right side should be
$I$
since its the total enclosed current by my ampere loop

but the book says
$I\frac{\pi s^2}{\pi R^2}$
it has something to do with the dependence of the current enclosed and the distance, which you dont have outside the cylinder. but i cant figure it out. can someone explain?
1. The problem statement, all variables and given/known data

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2. Sep 2, 2011

### nickjer

It says $s\leq R$. The loop that you draw is inside the wire, so you get a fraction of the total current. That fraction being the fraction of area of your loop compared to the total area of the wire. Outside the wire, you would just set $s=R$ and get back the total current you were talking about.