(1) A solid sphere is centered at the origin with radius R and volume charge density Psphere. Separately, a slab of charge with width w, but infinite in the x and z dimensions is oriented so that it is centered at the point (0, -yo, 0). The slab has charge density Pslab. (a) Use Gauss' law to find the electric field created by the slab at the point (0, - R, 0). Note: This point is outside of the slab. [5pts] (b) Use Gauss' law to find the electric field created by the sphere at the point (0, - R, 5pts] (c) In the case where w = 57.5mm, yo = 36.8cm, R = 54.5mm, Psphere = 229nC/m3, Pslab = 617nC/m', what is the electric field at the point (0, - 2, 0)? [3pts] (d) Using the numbers from part (c), what would the charge density of the slab need to be in order to make the electric field at (0, -, 0) equal to zero? [3pts] (e) A spherical cavity is cut into the solid sphere. The cavity is centered at (To, 0, 0) and has radius . Is it possible for the electric field in this cavity to be zero? If so, use the numbers (unchanged) from part (c) to find what To needs to be to make this happen. If it is not possible, explain why it is not possible. [4pts]