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Q.

A certain volume of copper is drawn into a wire of radius a and is wrapped in shape of a helix having radius r (>> a). The windings are as close as possible without overlapping. Self-inductance of the inductor so obtained is L1. Another wire of radius 2a is drawn using same volume of copper and wound in the fashion as described above. This time the inductance is L2. FindL1L2 .

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answer is 8.

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Detailed Solution

Length of wire I=volume (V)πa2Winding is as shown in the figure.Number of turns, N=12πrLength of the helix, b=2a, N=alπrNumber of turns per meter length n=12a∴Self-inductance,  L=πμ0n2r2b=πμ012a2.r2.alπr=14μ0rla=14μ0rVaπa2L=μ0r4Va3     ∴L∝1a3∴L1L2=2aa3=81
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