Q152 / 160 · TS EAMCET 2018 (07 May Shift 1) · Physics
A solenoid of radius $R$ has $n$ turns per unit length, then the self-inductance of the solenoid per unit length is
- A$\mu_0 m \pi R^2$
- B$\mu_0 r R^2$
- C$\mu_0 n^2 R^2$
- Correct answerD$\mu_0 n^2 \pi R^2$
Solution
Self-induction of solenoid, $L=\frac{N \phi}{i}$
where, $\phi=$ magnetic flux,
$N=$ total numbers of tums and $i=$ current.
Here, $N=n l, n=$ number of turn per unit length and $l=$ length of solenoid.
$$
\begin{gathered}
\phi=B A=\left(\mu_0 n i\right) \pi R^2, \quad \text { [where, } R=\text { radius] } \\
L=\frac{(n i)\left(\mu_0 n i\right) \pi R^2}{i} \Rightarrow L=\left(\mu_0 n^2 \pi R^2\right) l
\end{gathered}
$$
Self-inductance per unit length,
$$
\frac{L}{l}=\mu_0 n^2 \pi R^2
$$
Hence, the correct answer is option: 'D'.