Question

A circular coil of radius $5\text{cm}$, has $500$ turns of a conducting wire. The approximate value of the coefficient of self induction of the coil will be -

• A. $25\text{mH}$
• B. $5\text{mH}$
• C. $0.5\text{mH}$
• D. $2.5\text{mH}$

Answer 1

The correct option is A $25\text{mH}$

The magnetic flux through the coil is,

$N\varphi =LI$

$\Rightarrow NBA=LI$

$\Rightarrow N\left(\frac{{\mu }_{o}NI}{2r}\right)\pi r^2=LI$

$\Rightarrow L=\frac{{\mu }_o{N}^2\pi r}{2}$

$=\frac{4\pi \times {10}^{-7}\times {500}^2\times \pi \times 0.05}{2}$

$\approx 25\times {10}^{-3}\text{H}=25\text{mH}$

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