A slab of insulating material of uniform thickness d, lying between -d/2 to +d/2 along the x axis, extends infinitely in the y and z directions. The slab has a uniform charge density rho. The electric field is zero in the middle of the slab, at x = 0.

(a) What is Eout, the magnitude of the electric field outside the slab? As implied by the fact that Eout is not given as a function of x this magnitude is constant everywhere outside the slab, not just at the surface. Express your answer in terms of d, rho, and ε_0.

(b) What is Ein, the magnitude of the electric field inside the slab as a function of x? Express your answer in terms of x, rho, and ε_0.