A section of solid metal wire of radius R prependicular to its length is represented in the figure.
Let us consider a point P, lying inside the wire at a perpendicular distance r, from the axis of wire. To apply Ampere’s Circuital law, we considers a circular path of radius z around the axis of wire. Over this path, because of symmetry consideractions, the magnetic field produced due to the current in the wire, will be equal at all points on the circular path and will have a tangential direction.
By Ampere’s circuital law, we then have
∵ Current in closed by the circular path is
However, the current enclosed by the circular path would be i when P lies outside the wire.
Hence we have, for z > R,
