Aslab of insulating material has thickness 2d and is oriented so that its faces are parallel to the yz-plane and given by the planes x = d and x = -d. the y- and z-dimensions of the slab are very large compared to d and may be treated as essentially infinite. the slab has a uniform positive charge density p.
a. explain why the electric field due to the slab is zero at the center of the slab (x=0).
b. using gauss's law, find the magnitude of the electric field due to the slab at the points 0< = x < = d. express your answer in terms of the variables p, x, d, and e_0.
d. using gauss's law, find the magnitude of the electric field due to the slab at the points x> = d. express your answer in terms of the variables p, x, d, and e_0.
e. what is the direction of the electric field due to the slab at the pints x > = d.

How much work would a child do while puling a 12-kg wagon a distance of 3m with a 22 n force directed 30 degrees with respect to the horizontal? (a) 82j (b) 52j (c) 109j (d) 95j

1. consider the case in which air fills air shocks on a truck trailer. the pressure in the shocks is 2 mpa. the temperature is 300 k. the diameter of the shock piston is 10 cm and the initial length of the cylindrical cavity containing the compressed air is 40 cm. a. the truck is gradually loaded over a period of a day in a static setting. the temperature is held constant for the atmosphere and thus for the gas shock. calculate the compressibility of the air in the shock for this condition when the truck is initially being loaded. b. if the shocks were loaded in a dynamic setting by driving over bumps, what would be the compressibility? state your assumption. c. what is the initial load on the shock if the shock is in an atmospheric 100 kpa? d. if the shock is compressed using the process described in part a, and the air shock compressed air cavity length decreases to 20 cm, what is the additional load applied to the shock?

If you wanted to move an electron from the positive to the negative terminal of the battery, how much work w would you need to do on the electron? enter your answer numerically in joules.