Asolid insulating sphere of radius r = 1.0 m that carries a positive charge q1 = 1.0 mc uniformly distributed over it is concentric with a very thin insulating shell of radius 2r that carries the charge q2 = -1.0 mc. the charge q2 is distributed uniformly over the shell.

use gauss's law to obtain the magnitude of the electric field:

a. e1 inside the sphere, r < r

b. e2 between the sphere and the shell, r < r < 2r

c. e3 outside the shell, r > 2r

d. plot the electric field in the radial direction on a graph. be sure to label the actual magnitude of the electric field at r = 0, r= r, and r = 2r.

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?