A long thin walled hollow cylinder of radius r is carrying a current I. A very long current carrying straight conductor is passing through the axis of the hollow cylinder, carrying a current `i_(0)`. Find the tension per unit length developed in the hollow cylinder due to the interaction of the straight current carrying conductor.

Explanation

Considering the magnetic forces between `i_(0)` and the differential current di we obtain
`dF = (mu_(0) i_(0))/(2 pi r) (di) (di = (id theta)/(2 pi))`
where dF is the force per unit length .
since the elementary portion is in equilibrium
Since the elementary portion is in equilibrium
`2T sin (d theta //2) = dF` (T is tension per unit length)
`implies T d theta = dF` [as `theta` is very small `sin (d theta)/(2) ~= (d theta)/(2)`]
`implies T d theta = (mu_(0) i_(0))/(2 pi r) ((id theta)/(2 pi))`
`implies T = (mu_(0)i_(0))/(4 pi^(2) r)`