Question

Using Ampere's law, obtain the expression for the magnetic field clue to a solenoid.

Answer 1

Magnetic field inside the long solenoid can be treated as uniform and parallel to solenoids axis. This is also true for the point just at the end of the solenoid.At all the other points we can take the magnetic field to be 0. Following this assumptions and the Amper's law (in its integrative form)

$$\oint_l{Bdl} = \mu_0 I_{enclosed}$$

we can conclude that

$$B L=\mu_0 N I$$

and after all this

$$B = {\mu_0 N I}/L={\mu_0 n I}$$

where n is a density of the turns of the wire in the solenoid