Alocalized region of space has a charge density ρ(r). use the general solution of poisson's equation: ρ(r) 4tteo and the expansion of 1/ir -r'| in terms of legendre polynomials p (cos α), tr to calculate the first two terms in multipole expansion for the scalar potential in the region where the charge density is zero. the angle α is the angle between r and r'.you may assume the charge density is azimuthally symmetric about the z- axis. calculate the electric field produced by the first two terms in the multipole expansion. show that the monopole terms for v and e are independent of your choice of origin. follow the argument in sections 3.4.2 - 3.4.4. show that the dipole terms for v and e depend on your choice of origin, except in the case where the total charge in the localized region vanishes

Many machines- including inclined planes such as ramps- increase the strength of the force put into the machine but decrease the distance over which the force is applied.

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?

Choose the most likely outcome of this scenario: jen decided to go bike riding without a helmet. while no one is around during her ride, she is thrown from her bike when her wheel goes into a pothole. she is not injured, but she is terrified to get back on her bike. what happens next? a. her physical health is affected even though she wasn't hurt. b. her mental and emotional health are affected because she is afraid to get back on her bike. c. her social health is affected because she is worried her friends saw the fall. d. her overall health is not affected at all by her fall.