Calculate the time constant `tau` of a straight solenoid of length `l` having a single layer winding of copper wire whose total mass is equal to `m` . The cross-sectional dimater of the solenoid is assumed to be considerably less than its length. Given desity of copper `p_(0)` and resistivility `p` .

Explanation

Inductor `L=mu_(0)n^(2)pir^(2)l=(mu_(0)N^(2)pir^(2))/(l)`
`N` : total number of turns
Resistance `R=(pN.2pir^(2))/(A)A` , : area of cross-section of wire
Time constant `tau=(L)/(R)=(mu_(0)N^(2)pir^(2))/(l.(pN2pir)/(A))=(mu_(0)NrN)/(2pl)`
`m=p_(0)AN2pir` implies `NrA=(m)/(2pip_(0))`
`tau=(mu_(0)m)/(2pl.2pip_(0))=(mu_(0)m)/(4pipp_(0)l)`