Past exam of the physics 2 paper of the University of Oxford / 2015 resit / 10 / b / c

Inside the uniformly charged slab, its own electric field is $\rho (z+d/2)\hat{\mathbf{z}}/{ϵ}_0$: it vanishes at the slab's midplane and has derivative $\rho /{ϵ}_0$. Everywhere below the negative sheet, that sheet adds $+\sigma \hat{\mathbf{z}}/(2{ϵ}_0)$. ThereforeIts magnitude is the absolute value of this scalar coefficient. The field changes direction atFor $z<z_0$ it points downward; for $z>z_0$ it points upward, towards the negative sheet. Thus it is neither uniform nor directed upwards throughout the slab. The derivative and the field at the lower slab boundary also agree with Gauss's law and the previously found outside field.