An electron beam shaped like a circular cylinder of radius r0 carries a charge density given by rhov = (−rho0/1 + r^2) (C/m^3),
where rho0 is a positive constant and the beam’s axis is coincident with the z axis.
(a) Determine the total charge contained in length L of the beam.
(b) If the electrons are moving in the +z direction with uniform speed u, determine the magnitude and direction of the current crossing the z-plane.

Amass of m 1.5 kg of steam is contained in a closed rigid container. initially the pressure and temperature of the steam are: p 1.5 mpa and t 240°c (superheated state), respectively. then the temperature drops to t2= 100°c as the result of heat transfer to the surroundings. determine: a) quality of the steam at the end of the process, b) heat transfer with the surroundings. for: p1.5 mpa and t 240°c: enthalpy of superheated vapour is 2900 kj/kg, specific volume of superheated vapour is 0. 1483 m/kg, while for t 100°c: enthalpy of saturated liquid water is 419kj/kg, specific volume of saturated liquid water is 0.001043m/kg, enthalpy of saturated vapour is 2676 kj/kg, specific volume of saturated vapour is 1.672 m/kg and pressure is 0.1 mpa.

Apiston-cylinder with a volume of 0.25 m3 holds 1 kg of air (r 0.287 k/kgk) at a temperature of 100 c. heat transfer to the cylinder causes an isothermal expansion of the piston until the volume triples. how much heat is added to the piston-cylinder?

If you were designing a bumper for a car, would you prefer it to exhibit elastic or plastic deformation? why? consider the functions of a bumper in both a minor "fender-bender" and a major collision.