question_answer

The figure shows two infinite semi-cylindrical shells: shell-1 and shell-2. Shell-1 carries current\[{{i}_{1}}\], in inward direction normal to the plane of paper, while shell-2 carries same current\[{{i}_{1}}\], in opposite direction. A long straight conductor lying along the common axis of the shells is carrying current\[{{i}_{2}}\]in direction same as that of current in shell-1. Force per unit length on the wire is

A) zero

B) \[\frac{{{\mu }_{0}}{{i}_{1}}{{i}_{2}}}{2\pi r}\]

C) \[\frac{2{{\mu }_{0}}{{i}_{1}}{{i}_{2}}}{\pi r}\]

D) \[\frac{2{{\mu }_{0}}{{i}_{1}}{{i}_{2}}}{{{\pi }^{2}}r}\]

Correct Answer: D

Solution :

[d] Magnetic field at the centre of the shell\[=2\frac{{{\mu }_{0}}i1}{{{\pi }^{2}}r}\] Force per unit length of the wire \[F=B{{i}_{2}}\times 1\] \[=\left[ 2\frac{{{\mu }_{0}}{{i}_{1}}{{i}_{2}}}{{{\pi }^{2}}r} \right]\]