Find intensity of magnetic induction B due to a long current carrying conductor.

Figure shows a long straight conductor carrying a current ‘i’. Let ‘P’ be a point at a perpendicular distance ‘r’ from the conductor. Let a circle of radius ‘r’ passing through P be drawn with the conductor as centre.
The field at any point on the circle is along the tangent drawn at that point in the direction of dl . By symmetry, the magnitude of magnetic induction B is same at all points on the circle.
$\text{∮}\mathrm{B}\cdot \mathrm{d\ell }=\text{∮}\mathrm{Bd\ell cos}{0}^0=\mathrm{B}\text{∮}\mathrm{d\ell }=\mathrm{B}2\mathrm{\pi r}$
According to ampere’s law
$\mathrm{B}2\mathrm{\pi r}={\mathrm{\mu }}_0\mathrm{i},\mathrm{B}=\frac{{\mathrm{\mu }}_0\mathrm{i}}{2\mathrm{\pi r}}$