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 $B=\frac{{\mu }_{0}ni\left(\sqrt{5}+3\right)}{\sqrt{K}}$ for $l=4a$ . Find the value of $K$.