Question

Draw the magnetic field lines due to a current passing through a long solenoid. Use Ampere's circuital law, to obtain the expression for the magnetic field due to the current I in a long solenoid having n number of turns per unit length.

Answer 1

Let $l$ be the length of the solenoid and $N$ be the total number of turns. So $n=\frac{N}{l}$
Using Ampere's law the magnetic field inside the solenoid : $Bl={\mu }_0{I}_{en}={\mu }_0\left(NI\right)$
$\Rightarrow B=\frac{{\mu }_{0}NI}{l}={\mu }_{0}nI$
As no current flow outside solenoid so practically magnetic field is zero outside the solenoid.