Let's return to our friend the sphere, with surface charge density σ(θ, f) = σ0sinθcos2f . Find the net polarization of this sphere, assuming the charge density is bound charge. You can assume the sphere is not rotating (f is azimuthal angle). What is the electric potential a large distance from the sphere?

When a book falls from a shelf to the ground without anyone pushing on it, no work is done on the book. true or false

Aperson walking 1 mile everyday for exercise, leaving her front porch at 9: 00 am and returning to her front porch at 9: 25 am. what is the total displacement of her daily walk? a) 1 mileb) 0c) 25 minutes d) none of the above

Suppose water is leaking from a tank through a circular hole of area ah at its bottom. when water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to cah 2gh , where c (0 < c < 1) is an empirical constant. a tank in the form of a right-circular cone standing on end, vertex down, is leaking water through a circular hole in its bottom. (assume the removed apex of the cone is of negligible height and volume.) (a) suppose the tank is 20 feet high and has radius 8 feet and the circular hole has radius 2 inches. the differential equation governing the height h in feet of water leaking from a tank after t seconds is dh dt = − 5 6h3/2 . if the height of the water is initially 8 feet, how long will it take the tank to empty? (round your answer to two decimal places.)