An infinite plane slab of thickness 2d (the slab is located between z=-d and z=d) carries a uniform volume charge density p. Using the Gauss's law, find the electric field as a function of z inside and outside the slab. Plot schematically the dependence of the electric field as a function of z. 2d

An infinite, insulating cylinder of radius ri is surrounded by an air gap and a thin, cylindrical conducting shell of radius r2. The insulating cylinder carries constant volume charge density p and the conducting shell carries a constant area charge density o. Use Gauss's law to calculate the quantity f E•dA for the Gaussian shape (a) most appropriate for this problem. (b) distribution). Find the electric field in the region r < ri (inside the volume charge (c) Find the electric field in the region r1 < r < r2 (air gap region) 2.

An infinitely long, cylindrical, insulating shell of inner radius a and outer radius b has a uniform vol￾ume charge density r. A line of uniform linear charge density l is placed along the axis of the shell. Deter￾mine the electric field for (a) r , a, (b) a , r , b, and (c) r . b.