What is the self-inductance of a solenoid of | vedclass

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(A) The formula for the self-inductance $(L)$ of a solenoid is given by: $L = \frac{\mu_0 N^2 A}{l}$ Given: Permeability of free space $\mu_0 = 4 \pi

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$4$ mH

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(A) The formula for the self-inductance $(L)$ of a solenoid is given by: $L = \frac{\mu_0 N^2 A}{l}$ Given: Permeability of free space $\mu_0 = 4 \pi 	imes 10^{-7} \ T \cdot m/A$ Number of turns $N = 10^3$ Area of cross-section $A = 10^{-3} \ m^2$ Length $l = 31.4 \ cm = 31.4 	imes 10^{-2} \ m$ Substituting the values: $L = \frac{4 	imes 3.14 	imes 10^{-7} 	imes (10^3)^2 	imes 10^{-3}}{31.4 	imes 10^{-2}}$ $L = \frac{4 	imes 3.14 	imes 10^{-7} 	imes 10^6 	imes 10^{-3}}{31.4 	imes 10^{-2}}$ $L = \frac{12.56 	imes 10^{-4}}{31.4 	imes 10^{-2}} = \frac{12.56}{31.4} 	imes 10^{-2} = 0.4 	imes 10^{-2} \ H$ $L = 4 	imes 10^{-3} \ H = 4 \ mH$

What is the self-inductance of a solenoid of length $31.4 \ cm$,area of cross-section $10^{-3} \ m^2$,and total number of turns $10^3$?

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