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(A) The self-inductance $L$ of a solenoid is given by the formula $L = \frac{\mu_0 N^2 A}{l}$,where $N$ is the number of turns,$A = \pi r^2$ is the cr

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$1: 3$

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(A) The self-inductance $L$ of a solenoid is given by the formula $L = \frac{\mu_0 N^2 A}{l}$,where $N$ is the number of turns,$A = \pi r^2$ is the cross-sectional area,and $l$ is the length of the solenoid.Since $N$ is constant for both solenoids,we have $L \propto \frac{r^2}{l}$.Given the ratio of lengths $l_1 : l_2 = 1 : 3$ and radii $r_1 : r_2 = 1 : 3$.Substituting these values into the ratio:$\frac{L_1}{L_2} = \left( \frac{r_1}{r_2} ight)^2 	imes \left( \frac{l_2}{l_1} ight)$$\frac{L_1}{L_2} = \left( \frac{1}{3} ight)^2 	imes \left( \frac{3}{1} ight)$$\frac{L_1}{L_2} = \frac{1}{9} 	imes 3 = \frac{1}{3}$.Therefore,the ratio of their self-inductance is $1: 3$.

Two solenoids of equal number of turns have their lengths as well as radii in the same ratio $1: 3$. The ratio of their self-inductance will be

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