Ampere's Circutial law:

It states that the line integral of magnetic field over a closed surface is equal to Uo times the total current enclosed by the surface.
i.e {B.dl = UoI

If we consider a straight conductor I, then it will produce a circular magnetic field. Now magnetic field at a point at a distance r from conductor can be give as
B = UoI/2πr
Now {B.dl = {Bdlcosϴ
={Bdl
= {UoI/2πr dl
=UoI/2πr 0{2πr dl
{B.dl = UoI

Applicatiojn of Ampere's law
1) Magnetic field due to straight conductor
Let us consider a straight conductor carrying current I. Consider a point P at distance R from conductor where magnetic field is to be determined. Since this is straight conductor magnetic lines of force are circular. Let us draw a circle of radius r passing through P.
then from Ampere's Law,
{B.dl = UoI
{Bdlcosϴ = UoI
B = UoI/2πr

2) Magnetic field due to solenoid
Let us consider a solonoid having number of turns per unit length n carry current I through it. It produces magnetic field along its axis Now to find magnetic field draw a rectangle of length PQ = l
By ampere's law
{B.dl = UoI
{B.dl = P{Q B.dl + R{Q B.dl + S{R B.dl + P{S B.dl
{B.dl = B P{Q dl =Bl----------1
Now
{B.dl = UoI
{B.dl = UonlI--------2

From I and 2
B = UonI