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  4. 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, | overset arrow B| as a function of the radial distance r from the axis, is best represented by:

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Q. 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, $\left|\overset{ \rightarrow }{B}\right|$ as a function of the radial distance $r$ from the axis, is best represented by:

NTA AbhyasNTA Abhyas 2022

Solution:

$r < \frac{R}{2}$ , $B=0$
$r>R$ , $B=\frac{\mu _{0} I}{2 \pi r}$
$\frac{R}{2} < r < R$ , $B=\frac{\left(\mu \right)_{0} I}{2 \pi r}\left[\frac{r^{2} - \left(\frac{R}{2}\right)^{2}}{R^{2} - \left(\frac{R}{2}\right)^{2}}\right]$
Solution