Electric Charge

The electrostatic potential energy of a system of point charges is given by:

where: is the Coulomb constant, and are the charges, is the distance between the charges.

Step 1: Identify charge pairs.

In the given system, there are three charges at the vertices of an equilateral triangle of side . The potential energy is due to the pairwise interactions between the charges. The charge pairs are:

Between charges at vertices 1 and 2,

Between charges at vertices 2 and 3,

Between charges at vertices 3 and 1.

Step 2: Calculate the potential energy for one pair.

The potential energy for one pair of charges is:

Step 3: Sum the potential energy for all pairs.

Since there are three pairs of charges in an equilateral triangle:

Thus:

When the drops coalesce, their total volume remains unchanged. Let: - be the radius of each small drop, - be the radius of the combined drop.

Step 1: Apply Volume Conservation The total volume of eight small drops is: Simplify:

Step 2: Terminal Velocity Relation The terminal velocity of a drop is proportional to the square of its radius: Let be the terminal velocity of the small drops, and be the terminal velocity of the combined drop. Then: Substitute :

Step 3: Calculate Rearrange to find :

Final Answer: