Arectangular slab with uniform volume charge density rho has thick- ness 2l in the x direction and infinite extent in the y and z direc- tions. let the x coordinate be measured relative to the center plane of the slab. for values of x both inside and outside the slab: (a) find the electric field e(x) (you can do this by considering the amount of charge on either side of x, or by using gauss’s law); (b) find the potential φ(x), with φ taken to be zero at x = 0; (c) verify that rho(x) = ε0∇ · e(x) and rho(x) = −ε0∇2φ(x).

Agymnast dismounts off the uneven bars in a tuck position with a radius of 0.3m (assume she is a solid sphere) and an angular velocity of 2rev/s. during the dismount she stretches out into the straight position, with a length of 1.5m, (assume she is a uniform rod through the center) for her landing. the gymnast has a mass of 50kg. what is her angular velocity in the straight position?

In the 1980's, congress authorized the u. s. department of energy to build the wipp facility in the chicuahuan desert in new mexico. what is the purpose of wipp?

Acoal-fired plant generates 600 mw of electric power. the plant uses 4.8 x 10^6 kg of coal each day, and the heat of combustion of coal is 3.3x 10^7 j/kg. the steam that drives the turbines is at a temperature of 300° c, and the exhaust water is at 37° c. (a) what is the overall efficiency of the plant for generating electric power? (b) how much thermal energy is exhausted each day? (c) what is the change in entropy of the universe for this heat engine? (d) using the same heat reservoirs, what is the maximum possible (carnot) efficiency for a heat engine?