Some charged particles are suspended inside a hollow metal object by supports made of a material that is an electrical insulator. The metal object has charge +q distributed over its outer surface and charge ?2q distributed over its inner surface. A. How much charge is suspended in the cavity?

B. What is the charge on the object? (Hint: What is the electric field a very large distance r from the center of the object?)

After the near spacecraft passed mathilde, on several occasions rocket propellant was expelled to adjust the spacecraft's momentum in order to follow a path that would approach the asteroid eros, the final destination for the mission. after getting close to eros, further small adjustments made the momentum just right to give a circular orbit of radius 45 km (45 × 10^3 m) around the asteroid. so much propellant had been used that the final mass of the spacecraft while in circular orbit around eros was only 545 kg. the spacecraft took 1.04 days to make one complete circular orbit around eros. calculate what the mass of eros must be.

According to an observer on earth, planet x is stationary. maria and samir depart earth on their spaceships at the same time, each flying at 0.5c. maria flies toward planet x and samir flies in the opposite direction. according to maria, her voyage to planet x takes 9 years. how many years does maria's voyage take according to samir?

Suppose astronomers built a 140-meter telescope. how much greater would its light-collecting area be than that of the 10-meter keck telescope? express your answer using two sign