Obtain an expression for the magnetic field at a point due to an infinitely long thin conductor or wire by applying Ampere's circuital law.

Explanation

Let I be the current in the wire PQ. Let P be a point at a perpendicular distance r from the wire. Let dI be the element of length of the closed path. The direction of the magnetic field will be tangential to the point P on the element.
Applying Ampere's circuital law, we have
`" "ointvec(B).dvec(l)=mu_(0)I`
i.e., `" "ointBdlcos0^(@)=mu_(@)I, " "theta=0^(@)` between tangent drawn at P to the element of length dl and `vec(B)`.
Thus `" "Bointdl=mu_(@)I`
or `" "B=(mu_(0)I)/(ointdl)=(mu_(0)I)/(2pir)`
Thus `" "B propto 1/r`
Note : B along the axis of the wire = 0