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## Homework Statement

Two coencenteric metalic shell has inner radius $r_1$ outer radius $r_2$. We place along axis infinity wire has $\lambda$ charge in per unit length. The inner region of metalic shells inserted with relative permabilitty coefficent $\epsilon$. This system rotates with $\omega$ angular velocity. What is the value of induced magnetic field?

[figure:http://i.stack.imgur.com/ywe4p.jpg

## The Attempt at a Solution

\begin{equation}

\rho_b=-\nabla.{P}

\end{equation}

\begin{equation}

P=(\epsilon-1)\epsilon_0.E

\end{equation}

\begin{equation}

E=\lambda\div({2\pi.\epsilon\epsilon_0.r})

\end{equation}

If we placed to first equation we get:

\begin{equation}

\rho_b=0

\end{equation}

\begin{equation}

\sigma_b=P.n

\end{equation}

where is n is unit vector

for outer metalic shell:

\begin{equation}

\sigma_b(r_2)=P(r_2)=(\epsilon-1)\epsilon_0\lambda\div({2\pi.\epsilon\epsilon_0.r_2})

\end{equation}

for inner metalic shell:

\begin{equation}

\sigma_b(r_1)=-P(r_1)=-(\epsilon-1)\epsilon_0\lambda\div({2\pi.\epsilon\epsilon_0.r_1})

\end{equation}

For charge for the inner shell

\begin{equation}

\sigma_1.2\pi.r_1.h=q_1

\end{equation}

For charge for the outer shell

\begin{equation}

\sigma_2.2\pi.r_2.h=q_2

\end{equation}

For current

\begin{equation}

i=q/T

\end{equation}

when we calculate current inner and outer's effect of magnetic field canceled. Where is the mistake if there is? Or what variables cause to magnetic field? HELP PLEASE