The self-inductance of solenoid of length $31.4 \mathrm{~cm}$, area of cross section $10^{-3} \mathrm{~m}^2$ having total number of turns 500 will be nearly $\left[\mu_0=4 \pi imes 10^{-7} ight.$ SI unit $]$

Question

The self-inductance of solenoid of length $31.4 \mathrm{~cm}$, area of cross section $10^{-3} \mathrm{~m}^2$ having total number of turns 500 will be nearly $\left[\mu_0=4 \pi 	imes 10^{-7}ight.$ SI unit $]$

Aicharya · Accepted Answer

$\begin{aligned} & \ell=31.4 \mathrm{~cm}=0.314 \mathrm{~m} \ & \mathrm{~A}=10^{-3} \mathrm{~m}^2, \mathrm{~N}=500 \end{aligned}$ Self-inductance, $L=\mu_0 n^2 \ell A$ $\begin{aligned} & =\frac{\mu_0 \mathrm{~N}^2 \mathrm{~A}}{\ell}, \quad 	ext { where } \mathrm{n}=\frac{\mathrm{N}}{\ell} \ & =\frac{4 \pi 	imes 10^{-7} 	imes(500)^2 	imes 10^{-3}}{0.314} \ & =\frac{4 	imes 3.14 	imes 25 	imes 10^{-6}}{0.314} \ & =10^{-3} \mathrm{H} \end{aligned}$

The self-inductance of solenoid of length $31.4 \mathrm{~cm}$, area of cross section $10^{-3} \mathrm{~m}^2$…

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