Obtain an expression for the self inductance of a solenoid.

Explanation

Consider a long solenoid of length l, area of cross-section A. Let n be the number of turns per unit length `(n=N/l)`
(ii) Let I be the current flows through it. The magnetic field inside the solenoid is given by `B=mu_(0)ni....(1)`
(iii) Magnetic flux linked with each turn of the solenoid `=B.A=mu_(0)niA ....(2)`
(iv) Total magnetic flux linked with whole solenoid
`phi=mu_(0)niA xx N=(therefore N=nl)`
`phi=mu_(0)niA("where N=Total number of turns in the solenoid")`
`phi=mu_(0)n^(2)iAl .....(3)"Also", phi=Li .....(4)"From eq's" (3) & (4), Li =mu_(0)n^(2)iAl`
`L=mu_(0)n^(2)Al ....(5) (or) L=mu_(0) (N^(2))/(l)A....(6)`