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Q.
A coil of wire of radius $ r $ has $ 600 $ turns and a self inductance of $ 108 \,mH $ . The self inductance of a coil with same radius and $ 500 $ turns is
EAMCETEAMCET 2014
Solution:
The given,
$L_{1}=108\, mH , \, N_{1}=600$ turns,
$N_{2}=500$ turns and
$L_{2}=?$
By self-inductance of a plane coil
$L_{1}=\frac{\mu_{0} \, \pi \, N_{1}^{2}\, a_{1}}{2} \,\,\,...(i)$
$L_{2}=\frac{\mu_{0}\, \pi\, N_{2}^{2}\, a_{2}}{2}\,\,\, ...(ii)$
From the Eqs. (i) and (ii), we get
$\frac{L_{1}}{L_{2}} =\left(\frac{N_{1}}{N_{2}}\right)^{2} \,\,\,\left(\because a_{1}=a_{2}\right) $
$\frac{108}{L_{2}} =\left(\frac{600}{500}\right)^{2}$
$L_{2} =\frac{108 \times 25}{36} $
$L_{2} =3 \times 25=75\, mH$