Electrostatic Potential

To find the potential of the bigger drop formed by the combination of 27 smaller drops, we can use concepts from electrostatics concerning charged spheres. Here's a step-by-step explanation.

1. Understanding the Charge-Potential Relationship:

The potential of a charged spherical drop is given by , where is the electrostatic constant, is the charge, and is the radius of the drop.

1. Initial Conditions:

Each of the 27 smaller drops has a potential of . Assume each drop has a charge and radius .

1. Total Charge Conservation:

The total charge before and after merging remains the same. Hence, .

1. Volume Conservation:

The volume of the combined drop is equal to the sum of the volumes of the 27 smaller drops. Since volume , we have:

Solving for , we get .

1. Potential of the Combined Drop:

Using the potential formula for the bigger sphere:

From the small drop's potential:

Substitute for :

1. Conclusion:

Thus, the potential of the bigger drop is .