Laplace equation in spherical coordinates with some symmetry given a sphere with the radius r and the potential on its surface specified by vo k sin2 (1) where k is a constant and 0 is the polar angle. a) which symmetry does the potential obey? calculate the potential inside and outside the sphere the sphere b) calculate the surface charge density o(0) on hints use the ansatz for the symmetry which is derived in the lectures or from griffths chapter 3. use the boundary conditions to simplify the expression, i. e. get rid of some terms compare the coefficients to get the unknown coefficients using the ansatz and the boundary condition

Dalton’s model of an atom is the best described as a) a solar system b) a solid sphere c) a cloud d) a scoop of chocolate chip ice cream

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?

In positive numbers less than 1, the zeros between the decimal point and non zero are significant