Problem:

In identical spherical droplets of water, each charged to the same potential V, merge to form a larger droplet.  What will be its potential?

Solution:

• Concepts:
  The potential of a spherically symmetric charge distribution of finite radius R.
• Reasoning:
  The potential at the surface of a spherically symmetric charge distribution is V = kQ/R.
  As we combine n drops, Q and R change.
• Details of the calculation:
  We assume that initially the drops are very far apart, so that we can neglect their interactions.
  For one drop: V = kQ/R
  For n drops: R --> R' = n^(1/3)R,  Q --> Q' = nQ
  V' = kQ'/R' = knQ/(n^(1/3)R) = n^(2/3)V.