- #1
Safakphysics
- 10
- 2
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