The ratio of the number of turns per unit len | vedclass

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(C) The self-inductance $L$ of a solenoid is given by the formula $L = \mu_0 n^2 A l$,where $n$ is the number of turns per unit length,$A$ is the cros

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$1: 18$

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(C) The self-inductance $L$ of a solenoid is given by the formula $L = \mu_0 n^2 A l$,where $n$ is the number of turns per unit length,$A$ is the cross-sectional area,and $l$ is the length of the solenoid.Given for solenoids $A$ and $B$:Ratio of turns per unit length: $\frac{n_A}{n_B} = \frac{1}{3}$Ratio of lengths: $\frac{l_A}{l_B} = \frac{1}{2}$Cross-sectional areas are equal: $A_A = A_B = A$Since $L \propto n^2 l$,the ratio of self-inductances is:$\frac{L_A}{L_B} = \left(\frac{n_A}{n_B}ight)^2 	imes \left(\frac{l_A}{l_B}ight)$Substituting the given values:$\frac{L_A}{L_B} = \left(\frac{1}{3}ight)^2 	imes \left(\frac{1}{2}ight) = \frac{1}{9} 	imes \frac{1}{2} = \frac{1}{18}$Therefore,the ratio is $1: 18$.

The ratio of the number of turns per unit length of two solenoids $A$ and $B$ is $1: 3$ and the lengths of $A$ and $B$ are in the ratio $1: 2$. If the two solenoids have the same cross-sectional area,the ratio of the self-inductances of the solenoids $A$ and $B$ is

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