Electric field of perpendicular oppositely charged sheets ($\mathbf{E}=\frac{\sigma }{2{ϵ}_0}(\mathrm{sgn}(x),-\mathrm{sgn}(y),0)$)

Infinite sheets at $x=0$ and $y=0$ with surface charge density $+\sigma$ and $-\sigma$ have piecewise uniform electric fields. Gauss's law and superposition give the displayed result outside the sheets. The electric field lines bisect each quadrant and connect the positive sheet to the negative one. Its magnitude is $\sigma /(\sqrt{2}{ϵ}_0)$.