Question

Derive an expression for the self inductance of a long solenoid of N number of turns containing a medium of relative permeability

Answer 1

We know that,

\(B = \mu_0ni\)

\(\because n = \frac Nl\)

\(B = \frac{\mu_0Ni}l\)

\(\phi = NB.A\)

\(\phi = \frac{\mu_0N^2iA}{l}\)

\(\because \phi = Li\)

\(Li = \frac{\mu_0N^2 iA}l\)

\(L = \frac{\mu_0AN^2}l\)