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## Homework Statement

http://img209.imageshack.us/img209/1508/problemhd.jpg [Broken]

## Homework Equations

The Ampere law: [itex]\oint_C \vec{B} \cdot d\vec{l} = \mu_0 I_{enc}[/itex]

The field and flux is proportional to the current: [itex]\Phi = LI[/itex]

## The Attempt at a Solution

**(a)**

[itex]\oint_C \vec{B} \cdot d\vec{l} = \vec{B} \oint_C d\hat{l}[/itex]

[itex]= \vec{B} (2 \pi s)= \mu_0 I_{enc}[/itex]

[itex]\therefore \ \vec{B}= \frac{\mu_0 I_{enc}}{2 \pi s}[/itex]

The magnetic field is 0 for s<a. So for the space between the conductors do I have to evaluate this between a<s<b?

[itex]\therefore \ \vec{B}= \frac{\mu_0 I_{enc}}{2 \pi b-2 \pi a}[/itex]

Is this correct?

**(b)**The magnetic flux produced by the current in the conductor in the middle is

[itex]\Phi = \int B.dA = B(2 \pi a h)[/itex]

Here 2πah is the surface area. So how can we evaluate this if we do not know

*h*(height)?

**(c)**[itex]\Phi = LI \implies L = \frac{\Phi}{I} = \frac{B(2 \pi r h)}{I}[/itex]

Is this the correct approach?

Any help is greatly appreciated.

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