Aconducting sphere of radius r carries positive charge q. calculate the amount of work that would be required to move a small positive test charge q0 slowly from r=5r to r=3r. assume that the presence of q0 has no effect on how the charge q is distributed over the sphere.

express your answer in terms of the electric constant ϵ0 and some or all of the variables q, q0, and r.

Steam is generated in a boiler of a cogeneration plant at 10 mpa and 450°c at a steady rate of 5 kg/s. in normal operation, steam expands in a turbine to a pressure of 0.5 mpa and is then routed to the process heater, where it supplies the process heat. steam leaves the process heater as a saturated liquid and is pumped to the boiler pressure. in this mode, no steam passes through a condenser, which operates at 20 kpa. (a) determine the power produced in the turbine and the rate at which process heat is supplied in this mode. (b) determine the power produced in the turbine and the rate of process heat supplied if only 60 percent of the steam is routed to the process heater and the remainder is expanded to the condenser pressure. (3.32 mw; 9.69 mw; 4.25 mw; 5.82 mw)

Awave is produced in a rope. the wave has a speed of 33 m/s and a frequency of 22 hz. what wavelength is produced?

In positive numbers less than 1, the zeros between the decimal point and a non-zero number are blank significant