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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 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 from the axis of the cylinder as

NTA AbhyasNTA Abhyas 2020Moving Charges and Magnetism

Solution:

Using Ampere's circuital law
$B \, = \, 0$ for $r\leq R_{1}$
$B=\frac{\mu_0 i}{2 \pi\left(R_2^2-R_1^2\right)}\left(\frac{r^2-R_1^2}{r}\right)$
For $R_{1}\leq r\leq R_{2}$
and $B=\frac{\mu _{0}}{2 \pi }\frac{i}{r}$ $\text{r} \geq \text{R}_{2}$
The corresponding $B-r$ graph will be as shown in
Solution