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  4. A current i is uniformly distributed over the cross-section of a long hollow cylindrical wire of inner radius R1 and outer radius R2 . Magnetic field B varies with distance r from the axis of the cylinder as

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Q. A current $i$ is uniformly distributed over the cross-section of a long hollow cylindrical wire of inner radius $R_{1}$ and outer radius $R_{2}$ . Magnetic field $B$ varies with distance $r$ from the axis of the cylinder as

NTA AbhyasNTA Abhyas 2020

Solution:

$r \, < \, R_{1}, \, B=0$
$r \, > \, R_{2} \, , \, b=\frac{\mu _{0} i}{2 \pi r}$
$R_{1} \, < \, r \, < \, R_{2}, \, B=\frac{\left(\mu \right)_{0} i \left(r^{2} - R_{1}^{2}\right)}{2 \pi r \left(R_{2}^{2} - R_{1}^{2}\right)}$