A Current `I_(0) = 1.9 A` flows in a long closed solenoid. The wire it is wound of is a superconducting state. Find the current flowing in the solenoid when the length of the solenoid is increased by `eta = 5 %`.

Explanation

In a solenoid, the inductance `L = mu mu_(0) n^(2) V = mu mu_(0) (N^(2) S)/(l)`,
where `S` = area of cross section of the solenoid, `l` = its length, `V = Sl, N = nl` = total number of turns.
When the length of the solenoid is increased, for example, by pulling it, its inductance will decrease. If the current remains uncharged, the flux, linked to the solenodi, will also decrease. An induced e.m.f. will then come into play, which by Lenz's law will try to oppose the decrease of flux, for example, by increasing the curent. In the superconducing state the flux wll not chanege and so,
`(I)/(l)` = constant
Hence, `(I)/(l) = (I_(0))/(l_(0))`, or, `I = I_(0) (I)/(l_(0)) = I_(0) (1 + eta)`