Aparallel-plate capacitor is made using two circular plates of radius a, with the bottom plate on the xy plane, centered at the origin. the top plate is located at z = d, with its center on the z axis. charge q is on the top plate; −q is on the bottom plate. dielectric having z-dependent permittivity fills the region between plates. the permittivity is given by ϵ(z) = ϵ0(1 + z2/d2). find (a) d; (b) e; (c) v0; (d) c.

To save energy, the air supply to a 2000 ft office has been shut off overnight and the room temperature has dropped to 40°f. in the morning, the thermostat is reset to 70°f and warm air at 120 f begins to flov in at 200ft'/min. the air is well mixed within the room, and an equal mass flow of air at room temperature (changing with time) is withdrawn through a return duct. the air pressure is nearly 1 atm everywhere. ignoring heat transfer with the surroundings and kinetic and potential energy effects, estimate how long it takes for the room temperature to reach 70°f. plot the room temperature as a function of time.