Question

A tightly wound solenoid of radius $‘a’$ and length $‘l’$ has n turns per unit length. It carries an electric current i. Magnetic field at a distance $\frac{l}{4}$ from one of the end (inside the solenoid on its axis) is $B=\frac{{\left(\mu \right)}_{0}ni\left(\sqrt{5}+3\right)}{\sqrt{K}}$ for $l=4a$ . Then find the value of K.

Answer 1

Answer: 40

Hint: $B=\frac{{\mu }_{0}ni}{2}\left[sin{\theta }_1+sin{\theta }_2\right]$

$\Rightarrow B=\frac{{\mu }_{0}ni}{2}\left[\frac{1}{\sqrt{2}}+\frac{3}{\sqrt{10}}\right]$
$\Rightarrow B=\frac{{\mu }_{0}ni(\sqrt{5}+3)}{\sqrt{40}}$
$\therefore K=40$