An infinitely long hollow conducting cylinder with inner radius $R / 2$ and outer radius $R$ carries a…
An infinitely long hollow conducting cylinder with inner radius $R / 2$ and outer radius $R$ carries a uniform current density along its length. The magnitude of the magnetic field, $|\vec{B}|$ as a function of the radial distance $r$ from the axis is best represented by
Solution
For $r < \frac{R}{2}, \quad B=0$
$\begin{array}{l}
\text { For } \frac{R}{2} \leq r < R, \\
B=\frac{\mu_{0}}{2}\left[r-\frac{R^{2}}{2 r}\right] J
\end{array}$
$\begin{array}{l}
\text { For } r>R, \quad B=\frac{\mu_{0} i}{2 \pi r} \\
\text { i.e., } B \propto \frac{1}{r}
\end{array}$
Hence graph $(d)$ correctly depicts $|\vec{B}|$ versus $r$ graph.
