= Negative sheet on a positive volume-charged slab
{title2=$E_z=[\rho(2z+d)+\sigma]/(2\epsilon_0)$}
Place a fixed sheet of charge density $-\sigma$ at $z=0$ and a uniform fixed volume charge $\rho$ in $-d<z<0$. With no imposed uniform background field, the above-sheet and below-slab fields are $\pm(\rho d-\sigma)/(2\epsilon_0)$. The interior field is the title expression, obtained by adding the slab's linear field to the sheet's constant field. If $0<\sigma<\rho d$, it vanishes at $z=-(d+\sigma/\rho)/2$, inside the lower half of the slab. At the sheet it jumps down by $\sigma/\epsilon_0$, while it remains continuous at the slab's uncharged lower face.
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