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  4. A coil of Cu wire (radius r, self-inductance L ) is bent in two concentric turns each having radius (r/2). The self-inductance is now

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Q. A coil of $Cu$ wire (radius $r$, self-inductance $L$ ) is bent in two concentric turns each having radius $\frac{r}{2}$. The self-inductance is now

Haryana PMTHaryana PMT 2010

Solution:

As $L \propto N^{2} r$
$\frac{L_{1}}{L_{2}}=\left[\frac{N_{1}}{N_{2}}\right]^{2} \times \frac{r_{1}}{r_{2}} $
$\Rightarrow \frac{L}{L_{2}}=\left[\frac{1}{2}\right]^{2} \times\left[\frac{r}{r / 2}\right]=\frac{1}{2}$
$L_{12}=2 L$