Let us consider two solenoids $A$ and $B$, made from the same magnetic material of relative permeabi

Question

Let us consider two solenoids $A$ and $B$, made from the same magnetic material of relative permeability $\mu_r$ and having an equal area of cross-section. The length of $A$ is half that of $B$ and the number of turns per unit length in $A$ is three times that of $B$. The ratio of the self-inductances of the two solenoids, $L_A: L_B$ is

Professor PC Thomas Classes · Answer

(c) : The self-inductance of a solenoid is $L = \mu_r \mu_o n^2 l A$, where $n$ is the number of turns per unit length, $A$ is the area, and $l$ is the length. We are given $l_A = 0.5 l_B$, $n_A = 3 n_B$, and $A_A = A_B$. The ratio is $\frac{L_A}{L_B} = \frac{n_A^2 l_A}{n_B^2 l_B} = \frac{(3 n_B)^2 (0.5 l_B)}{n_B^2 l_B} = 9 	imes 0.5 = 4.5 = \frac{9}{2}$.