A coil of wire of radius $r$ has 600 turns and a self inductance of $108 \mathrm{mH}$. The self inductance of a coil with same radius and 500 turns is

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Aicharya · Accepted Answer

The given, $L_1=108 \mathrm{mH}, N_1=600$ turns, $N_2=500$ turns and $L_2=$ ? By self-inductance of a plane coil $ \begin{aligned} & L_1=\frac{\mu_0 \pi N_1^2 a_1}{2} \ & L_2=\frac{\mu_0 \pi N_2^2 a_2}{2} \end{aligned} $ From the Eqs. (i) and (ii), we get $ \begin{aligned} \frac{L_1}{L_2} & =\left(\frac{N_1}{N_2}ight)^2 \quad\left(\because a_1=a_2ight) \ \frac{108}{L_2} & =\left(\frac{600}{500}ight)^2 \ L_2 & =\frac{108 	imes 25}{36} \ L_2 & =3 	imes 25=75 \mathrm{mH} \end{aligned} $

A coil of wire of radius $r$ has 600 turns and a self inductance of $108 \mathrm{mH}$. The self inductance…

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