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  4. Two solenoids of same cross-sectional area have their lengths and number of turns in ratio of 1: 2. The ratio of self-inductance of two solenoids is

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Q. Two solenoids of same cross-sectional area have their lengths and number of turns in ratio of $1 : 2$. The ratio of self-inductance of two solenoids is

JIPMERJIPMER 2019Electromagnetic Induction

Solution:

From $L =\frac{\mu_{0} N ^{2} A }{1}$
$\Rightarrow L \propto \frac{ N ^{2}}{1}$
we get, $\frac{ L _{1}}{ L _{2}}$
$=\frac{(1 / 2)^{2}}{1 / 2}=\frac{1}{2}$