question_answer

A current\[i\]ampere flows along an infinitely long straight thin walled tube, then the magnetic induction at any point inside the tube is                                     [AIEEE 2004]

A) infinite

B) zero

C) \[\frac{{{\mu }_{0}}}{4\pi }.\frac{2i}{r}T\]

D) \[\frac{2i}{r}T\]

Correct Answer: B

Solution :

[b] Let R be the radius of a long thin cylindrical shell.

To calculate the magnetic induction at a distance\[r(r<R)\]from the axis of cylinder, a circular shell of radius r is shown.

Since, no current is enclosed in the circle so, from Ampere's circuital law, magnetic induction is zero at every point on the circle. Hence, the magnetic induction at any point inside the infinitely long straight thin walled tube (cylinder) is zero.    \[(\because \oint{B.dl}={{\mu }_{0}}{{I}_{net}})\]