help with physics.. Any help would be greatly appreciatied. thanks?

Question

An infinite sheet of charge, oriented perpendicular to the x-axis, passes through x = 0. It has area density s1 = -4 µC/m2. A thick, infinite conducting slab, also oriented perpendicular to the x-axis, occupies the region between x = a and x = b, where a = 2 cm and b = 3 cm. The conducting slab has a net charge per unit area of s2 = 6 µC/m2.

(a) Calculate the net x-component of the electric field at the following positions:

At x = -1 cm
At x = 1 cm:
At x = 6 cm

(b) Calculate the surface charge densities on the left-hand (sa) and right-hand (sb) faces of the conducting slab.

Answer 1

The key to answer this problem is to make sure that there is NO e-field inside the bulk of the metal. Hence:
(b) the surface charge density on the left-hand (sa) face of the conducting slab is 5 µC/m2, and on the right-hand (sb) face of the conducting slab is 1 µC/m2.
(a) Let the net x-component of the electric field to be E. Denote epsilon_0 as e_0. According to Gauss's Law:
At x = -1 cm, E = -1x10^(-6)/e_0
At x = 1 cm, E = -5x10^(-6)/e_0
At x = 6 cm, E = 1x10^(-6)/e_0