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\sect{Nyquist theory for a ring RL-circuit}

Derive the Nyquist expression for the current-current correlation
function in a closed ring, taking into account its inductance.
Use the following procedure:

\begin{enumerate}

\item Cite an expression for the inductance $L$ of a torus shaped ring 
given its radius~$R$ and its cross-section radius~$r$. 

\item Write the R-L circuit equation for the current $I$, 
where the flux $\Phi(t)$ through the ring is the driving parameter.

\item Identify the generalized susceptibility $\chi(\omega)$, 
and observe that it is formally the same expression as in the problem of Brownian motion.

\item Calculate the current-current correlation function $\langle I(t)I(0)\rangle$,  
taking the classical / high temperature limit.

\item Verify that $\langle I^2 \rangle $ agree with the canonical result.

\end{enumerate}