Consider a magnetic dipole with north and south poles, each of magnetic strength p/2, separated by a distance 2d. what is the magnitude of the magnetic field at a distancex from the middle of the dipole along the axis that connects the north and south poles? ci me: d 15 d tt lit b. consider now a solenoid with n loops, length 2a, radius r and resistance r. calculate the magnetic flux, p, of the magnetic field above through the area of the coil. in doing this, assume one-dimensional geometry in the (x- axis) only.
c. assume that the magnet above is attached to the end of a pendulum, such that x then, calculate the induced emf on the coil a = - x cos wt. dp dt dt dx

Ammonia enters the expansion valve of a refrigeration system at a pressure of 10 bar and a temperature of 18oc and exits at 6.0 bar. the refrigerant undergoes a throttling process. determine the temperature, in oc, and the quality of the refrigerant at the exit of the expansion valve.

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)

Ametal ball with a mass of 0.028 kg is dropped from rest at a height of 1.0 meters above the ground. assuming the energy in the ball is conserved, how much kinetic energy will the ball have when it is 0.5 meters above the ground?