physics question 152

  1. Two concentric spherical shells are hooked up to a battery (voltage V = 10.0 V) and charged. The inner shell becomes negatively charged while the outer shell becomes positively charged. The radius of the outer shell is three times the radius of the inner shell. The capacitance of the system is C = 10.0 pF.
    1. Assuming this has been connected a long time, how much charge is on the outer shell?
    2. A particle of charge q = 2.0 μC (microcoulombs) and mass m = 4.0 x 10-7 kg gets fired from the inner shell towards the outer shell. Ignoring gravity, what is the minimum initial velocity the particle must have, to ensure that it reaches the outer shell?
    3. What is the radius of the inner sphere? Derive any formulas you use from basic laws such as Gauss’ Law or Coulomb’s Law.