The uniform charge density inside the 2d-thick endless plate in the figure is p(unit: Coulomb/m^3). The x-y plane is in the middle of the plate. An infinite cylindrical cavity of radius a is carved around the x-axis. Find the electric field everywhere (outside and inside the plate, in the hollowed out space). Give your answer in terms of (ε, p, d, a, x, y, z, î, j, k(unit vectors)).

The uniform charge density inside the 2d-thick endless plate in the figure is p(unit: Coulomb/m^3). The x-y plane is in the middle of the plate. An infinite cylindrical cavity of radius a is carved around the x-axis. Find the electric field everywhere (outside and inside the plate, in the hollowed out space). Give your answer in terms of (ε, p, d, a, x, y, z, î, j, k(unit vectors)).