A solenoid of radius R has n turns per unit length, then the self-inductance of the solenoid per unit length is

Options

A. `mu_(0) nR^(2)`
B. `mu_(0) n R^(2)`
C. `mu_(0) n R^(2)`
D. `mu_(0) n ^(2) piR^(2)`

Answer

D

Explanation

Self-induction of solenoid, `L =(N phi)/(i)`
where `phi=` magnetic flux,
N = total numbers of turns and I = current.
Here, N = nl, n = number of turn per unit length and l = length of solenoid.
`phi = BA= (mu_(0)m) piR^(2),` [where R= radius]
Self-inductance per unit length,
`L/l = mu_(0) n ^(2) piR^(2)`