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  4. An air-cored coil has a self-inductance of 0.1 H. A soft-iron core of relative permeability 1000 is introduced and the number of turns is reduced to 1 / 10 text th . The value of self-inductance now is

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Q. An air-cored coil has a self-inductance of $0.1 H$. A soft-iron core of relative permeability 1000 is introduced and the number of turns is reduced to $1 / 10^{\text {th }}$. The value of self-inductance now is

Electromagnetic Induction

Solution:

$L_{0}=\frac{\mu_{0} \pi N^{2} \cdot r}{2}=0.1 H$
$L=\frac{\mu_{0} \mu_{r} \pi\left(\frac{N}{10}\right)^{2} \cdot r}{2}$
As $\mu_{r}=1000$
$L=\frac{1000}{10^{2}}\left(\frac{\mu_{0} \pi N^{2} \cdot r}{2}\right)=10 L_{0}=10 \times 0.1 H =1 H$