Question

A closely wound coil of $100$ turns and area of cross-section $100{\text{cm}}^2$ has a coefficient of self-induction $1\text{mH}$. What is the length of the solenoid?

• A. $\frac{\pi }{2}\text{cm}$
• B. $\pi \text{cm}$
• C. $2\pi \text{cm}$
• D. $4\pi \text{cm}$

Answer 1

The correct option is D $4\pi \text{cm}$

The coefficient of self induction is given by,

$L=\frac{{\mu }_o{N}^{2}A}{l}$

$\Rightarrow {10}^{-3}=\frac{4\pi \times {10}^{-7}\times {100}^2\times {10}^{-2}}{l}$

$\therefore l=4\pi \times {10}^{-2}\text{m}=4\pi \text{cm}$

Hence, $\left(D\right)$ is the correct option.