(a) Find E in the plane z = 0 that is produced by a uniform line charge, rhoL, extending along the z axis over the range −L < z < L in a cylindrical coordinate system. (b) If the finite line charge is approximated by an infinite line charge (L → [infinity]), by what percentage is Erho in error if rho = 0.5L? (c) Repeat (b) with rho = 0.1L.

If the thermal strain developed in polyimide film during deposition is given as 0.0044. assume room temperature is kept at 17.3 c, and thermal coefficient of expansion for the film and the substrate are 54 x 10^-6c^-1 and 3.3 x 10^-6c^-1respectively. calculate the deposition temperature.

The force on a cutting tool are 2600n vertically downward and 2100 horizontal. determine the resultant force acting on the tool and the angle at which it acts.

An external consultant recommends that a plant installs a bank of capacitors for power factor correction. this will reduce the peak electrical demand charges by an average of 93 kw every month. the plant current pays $13 per kw in peak demand charges. the capacitor bank will include 223 kw of fixed capacitors, and 183 of variable capacitors. the fixed capacitors cost $59 per kw, and the variable capacitors will cost $65 per kw. the consultant charges 21% of the equipment costs to install the capacitors. because this project will reduce the demand for the electric utility, they are prepared to provide a one-time rebate of $42 per kw of reduced demand. what is the simple payback period for this project (in years)?