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  4. If self inductance of air core solenoid increases from 0.04 mH to 16 mH on introducing an iron core into it, then what is relative magnetic permeability of the core?

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Q. If self inductance of air core solenoid increases from $0.04 mH$ to $16 mH$ on introducing an iron core into it, then what is relative magnetic permeability of the core?

Electromagnetic Induction

Solution:

As $L_{0}=\frac{\mu_{0} N^{2} A}{\ell}$,
$L=\frac{\mu N^{2} A}{\ell} (L \propto \mu)$
$\mu_{ r }=\frac{\mu}{\mu_{0}}$
$\mu_{ r }=\frac{ L }{ L _{0}}=\frac{16}{0.04}=400$