Derive an expression for the self inductance of a long solenoid of N n

1.	Derive an expression for the self inductance of a long solenoid of N number of turns containing a medium of relative permeability
Answer» We know that, \(B = \mu_0ni\) \(\because n = \frac Nl\) \(B = \frac{\mu_0Ni}l\) \(\phi = NB.A\) \(\phi = \frac{\mu_0N^2iA}{l}\) \(\because \phi = Li\) \(Li = \frac{\mu_0N^2 iA}l\) \(L = \frac{\mu_0AN^2}l\)

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

Answer»

We know that,

\(B = \mu_0ni\)

\(\because n = \frac Nl\)

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

\(\phi = NB.A\)

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

\(\because \phi = Li\)

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

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

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

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