5113 identical spherical droplets of mercury are charged to the same potential of 54 volts.

5113 identical spherical droplets of mercury are charged to the same potential of 54 volts. What will be the potential of the big Carly resulting from the merging of these droplets?

Let:
1.the charge of one drop is q₁,
2.potential – φ₁,
3.radius – r,
4.volume – V₁.
Then:
1. V₁ = 4/3 πr³;
2. V = N * V₁ = 4/3 πR³;
3. R³ = N * r³ ⇒ R = ∛ (N * r³) = r∛N;
We get:
1.q = N * q₁;
2.φ = q / R = N * q1 / r * ∛N;
Then φ:
φ = N ^ {2/3} * φ₁;
Let’s substitute:
φ = 5113 ^ (2/3) * 54;
φ = 296.8 * 54;
φ = 16027 V.
Answer: φ = 16027 V.