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WBJEEAn infinitely long hollow conducting cylinder with inner radius \(R / 2\) and...
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.
$\begin{array}{l}
\text { For } \frac{R}{2} \leq r < R, \\
B=\frac{\mu_{0}}{2}\left[r-\frac{R^{2}}{2 r}\right] J
\end{array}$
$\begin{array}{l}
\text { For } r>R, \quad B=\frac{\mu_{0} i}{2 \pi r} \\
\text { i.e., } B \propto \frac{1}{r}
\end{array}$
Hence graph \((d)\) correctly depicts \(|\vec{B}|\) versus \(r\) graph.
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