A thin nonconducting spherical shell of radius R1 carries a total charge q1 that is uniformly distributed on its surface. A second, larger thin non-conducting spherical shell of radius R2 that is concentric with the first carries a charge q2 that is uniformly distributed on its surface. Required:
a. Use Gauss's law to find the electric field in the regions r < R1, R1 < r < R2, and r > R2.
b. What should the ratio of the charges q1/q2 and their relative signs be for the electric field to be zero for r > R2?

Your starship, the aimless wanderer, lands on the mysterious planet mongo. as chief scientist-engineer, you make the following measurements: a 2.50-kg stone thrown upward from the ground at 14.0 m/s returns to the ground in 5.70 s ; the circumference of mongo at the equator is 2.20×10^5 km ; and there is no appreciable atmosphere on mongo. (a) the starship commander, captain confusion, asks for the following information: what is the mass of mongo? (b) if the aimless wanderer goes into a circular orbit 2.20×10^4 km above the surface of mongo, how many hours will it take the ship to complete one orbit? (c) an unmanned spacecraft is in a circular orbit around the moon, observing the lunar surface from an altitude of 44.0 km . to the dismay of scientists on earth, an electrical fault causes an on-board thruster to fire, decreasing the speed of the spacecraft by 23.0 m/s . if nothing is done to correct its orbit, with what speed (in km/h) will the spacecraft crash into the lunar surface?