A current I flows along an infinitely long straight thin walled tube. The magnetic induction at a point inside the tube at a distance r from its wall is 

Given Data:

A current I flows along an infinitely long straight thin walled tube. The magnetic induction at a point inside the tube at a distance r.

Formula Used:

$\oint \overrightarrow{B}·\overrightarrow{d}={\mu }_0·I_{\text{enclosed }}......\left(1\right)$

Detailed Solution:

As tube is cylindrical in shape, the cross-sectional area of the tube will be circular in shape.

Now, wake an amperian loop inside the cross sectional area of radius.

Use Ampere circuital law;

$\oint \overrightarrow{B}·\overrightarrow{d}={\mu }_0·I_{\text{enclosed }}......\left(1\right)$

As current is passing only through the boundaries and mot inside, so, Iencloxed $=0$

$$\begin{gathered} {\text{ Put I}}_{\text{endosed}}=0\text{ in (1), we get } \\ \oint \overrightarrow{B}·\overrightarrow{d}=0. \\ \Rightarrow B=0. \end{gathered}$$

Thus $B=0$, for $0<x<R$, i.e Magnetic Induction at any point inside the tube is 0 . 

Hence, the correct optiont is B.