The self-inductance of a long solenoid of cro | vedclass

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Question

(B) The magnetic field $B$ inside a long solenoid is given by $B = \mu_0 n I$,where $n$ is the number of turns per unit length and $I$ is the current.

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$\mu_0 n^2 Al$

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(B) The magnetic field $B$ inside a long solenoid is given by $B = \mu_0 n I$,where $n$ is the number of turns per unit length and $I$ is the current.The magnetic flux $\phi$ through a single turn of the solenoid is $\phi = B \cdot A = \mu_0 n I A$.The total number of turns $N$ in a solenoid of length $l$ is $N = n \cdot l$.The total magnetic flux linkage $\Phi$ is given by $\Phi = N \cdot \phi = (nl) \cdot (\mu_0 n I A) = \mu_0 n^2 I A l$.By definition,the self-inductance $L$ is given by $\Phi = L I$,so $L = \frac{\Phi}{I} = \mu_0 n^2 A l$.

The self-inductance of a long solenoid of cross-sectional area $A$,length $l$ and $n$ turns per unit length is given by

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