Auniformly polarized dielectric sphere with a radium r=a is located at the origin and has an internal permanent polarization, p = poz , that is pointed along the +z-direction with a magnitude, po. similar to ferromagnetic materials that maintain their internal magnetization even when external magnetic fields are shut off, these ferroelectric materials will maintain their polarization fields in the absence of an external electric field, eext=0, for all parts of this question. 1.1.1.find the volume, ps(r), and surface, os(r), bound charge distributions in this ferroelectric material. [10 pts) 1.1.2.find the displacement field, d(1), both inside (ra) the ferroelectric sphere

Conventional hot-water heaters consist of a tank of water maintained at a fixed temperature. the hot water is to be used when needed. the drawback is that energy is wasted because the tank loses heat when it is not in use, and you can run out of hot water if you use too much. some utility companies are encouraging the use of on-demand water heaters (also known as flash heaters), which consist of heating units to heat the water as you use it. no water tank is involved, so no heat is wasted. a typical household shower flow rate is 2.50 gal/min (9.46 l/min ) with the tap water being heated from 51.0 ˚f (10.6 ˚c) to 120 ˚f (48.9 ˚c) by the on-demand heater. what rate of heat input (either electrical of from gas) is required to operate such a unit, assuming that all the heat goes into the water?