A long narrow solenoid of radius a has n turns per unit length and resistance of the wire wrapped on it is R. The solenoid is connected to a battery of emf V through a variable resistance `R_(x)`. There is a conducting ring of radius 2a held fixed around the solenoid with its axis coinciding with that of the solenoid. The relaxation time of free electrons inside the material of the conducting ring at given temperature is `tau` and specific charge of an electron is `alpha`. The variable resistance `R_(x)` is changed linearly with time from zero to R in an interval `Delta t`. Calculate the drift speed of the free electrons in the ring during this interval. [Neglect inductance]

Answer

`(alpha mu_(0)an V tau)/(8R Deltat)`