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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

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a

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b

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c

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d

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answer is D.

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Detailed Solution

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r: distance from centre
$r > \frac{R}{2}, B = 0$
$r > R, B = \frac{μ_{0} I}{2 π r}, B α \frac{1}{r},$
$B v / s r$ is rectangular hyperbola
$\frac{R}{2} < r < R, B = \frac{μ_{0} [\frac{I}{(π R^{2} - π \frac{R^{2}}{4})} π (r^{2} - \frac{R^{2}}{4})]}{2 π r}$
$= \frac{μ_{0} I}{2 π} \cdot \frac{4}{3} (\frac{r}{R^{2}} - \frac{1}{4 r})$
$B v / s r$ is not a straight line for $\frac{R}{2} < r < R$

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