Magnetic field of a uniformly conducting strip ($B(z)$)

For an infinitely long thin strip of width $w$ carrying uniform longitudinal current $I$, the magnetic field a perpendicular distance $z>0$ above its centre has magnitude $B={\mu }_{0}I\arctan (w/(2z))/(\pi w)$. Its near-sheet limit is ${\mu }_{0}I/(2w)$ and its distant line-current limit is ${\mu }_{0}I/(2\pi z)$.