The length of a wire required to make a solenoid of length $l$ and self-induction $L$ is

The length of a wire required to make a solenoid of length $l$ and self-induction $L$ is
  1. $\sqrt{\frac{4 \pi L l}{\mu_0}}$
  2. $\sqrt{\frac{L I}{4 \pi \mu_0}}$
  3. $\sqrt{\frac{2 \pi L I}{\mu_0}}$
  4. $\sqrt{\frac{\mu_0 L I}{4 \pi}}$

Solution

Length of wire in solenoid $=2 \pi r \times N$ $ =2 \pi r \sqrt{\frac{L l}{\mu_0 \pi r^2}}\left\{\begin{array}{c} \therefore L=\frac{\mu_0 N^2 A}{l} \\ A=\pi r^2 \end{array}\right\}=\sqrt{\frac{4 \pi L l}{\mu_0}} $

Asked in: AP EAMCET 2018 (22 Apr Shift 2)

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