First slide

Inductance

Question

A wire of fixed length is wound in such a way that it forms a solenoid of length 'l' and radius 'r'. Its self-inductance is found to be Z. Now if same wire is wound in such a way that it forms a solenoid of length I /2 and radius r /2, then the self-inductance will be

Moderate

A

2L
B

L
C

4L
D

8L

Solution

$L = \frac{μ_{0} N^{2} π r^{2}}{l}$
$Length of wire = N 2 π r = Constant (= C, suppose)$
$∴ L = μ_{0} {(\frac{C}{2 π r})}^{2} \frac{π r^{2}}{l}$
$∴ L \propto \frac{1}{l}$
$∴ Self-inductance will become 2 L .$

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