A sphere of mass m, radius a, and uniform density has
Chapter , Problem 38(choose chapter or problem)
A sphere of mass m, radius a, and uniform density has potential u and gravitational force F, at a distance r from the center (0, 0, 0), given by u = 3m 2a mr 2 2a3 , F = m a3 r (r a); u = m r , F = m r 3 r (r > a).Here, r = r, r = xi + yj + zk. (a) Verify that F = u on the inside and outside of the sphere. (b) Check that u satisfies Poissons equation: 2u/x2 + 2u/y2 + 2u/z2 = constant inside the sphere. (c) Show that u satisfies Laplaces equation: 2u/x2 + 2u/y2 + 2u/z2 = 0 outside the sphere.
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer