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Understanding electric potential is critical when studying the behavior of electric fields and their influence on charges. Electric potential, denoted by the symbol V, refers to the electric potential energy per unit charge held by a point in space in the presence of an electric field. It represents the work done in bringing a positive charge from infinity to that point without acceleration.

Imagine placing a charge in an electric field; the electric potential at any given point is akin to the altitude on a hill. Just as the gravity would cause an object to roll down the hill from a point of higher altitude to lower, an electric charge would 'fall' from a point of high potential to low potential, moved by the electric forces. In the case of our raindrops, each charged raindrop has the same electric potential, which means that any charge placed on one drop would need the same amount of work to move to or from infinity.

Permittivity of free space, symbolized as \(\epsilon_0\), is a fundamental constant in electromagnetism representing the ability of the vacuum of space to permit electric field lines. Essentially, it describes how an electric field affects and is affected by a vacuum. Its value is approximately \(8.854 \times 10^{-12}\frac{C^2}{N \times m^2}\).

This constant is essential in the calculation of capacitance as it appears in the capacitance formula for various geometries, including our spherical raindrops. The permittivity dictates how much electric field (and thus potential) is 'allowed' for a given charge in space. The higher the permittivity, the more the space will 'permit' electric field lines to pass through, leading to lower potential for a given charge.

An isolated spherical conductor is a symmetrically charged sphere that is far enough from other conductors so that its charge distribution remains uniform, meaning it is not influenced by external electric fields. This is an ideal model that simplifies the calculations involved in finding various electric properties such as electric field, potential, and capacitance.

In our scenario with raindrops, each drop is considered an isolated spherical conductor if we assume it does not affect or is not affected by neighboring drops. Each raindrop can be treated separately, and it exhibits spherically symmetric charge distribution, making the analysis of its electric properties much simpler. The capacity to store charge in such a conductor is what we refer to as its capacitance.

The capacitance of a conductor is a measure of its ability to hold an electric charge. Capacitance is the ratio of the charge \( Q \) stored on the conductor to the electric potential \( V \) it creates. The formula for the capacitance \( C \) of an isolated spherical conductor is \( C = 4\pi\epsilon_0 a \) where \( \epsilon_0 \) is the permittivity of free space and \( a \) is the radius of the sphere.

When we look at the individual spherical raindrops, each with a radius \( a \) and the same potential, the total capacitance of \( N \) such raindrops is the sum of the individual capacitances, since they are not interacting. However, if we were to combine all \( N \) raindrops into one large spherical drop, its capacitance would be different owing to the change in radius and volume that such a combination would result in, affecting the potential and the ability to store charge.

In three-dimensional geometry, the volume of a sphere is determined by its radius, following the formula \( V = \frac{4}{3}\pi r^3 \). This relationship indicates that the volume of a sphere grows much faster than its surface area as the radius increases. Applied to our raindrops, when combining \( N \) raindrops each of radius \( a \) into one large drop, the volume of the large drop is the sum of all individual volumes.

Since capacitance in spherical conductors depends on the radius, understanding this volume-radius relationship is essential. The combined large drop will have a greater volume and therefore a larger radius, which can be calculated from the total volume. However, as the radius increases, the capacitance does not increase in direct proportion since capacitive effect is more dependent on surface area, meaning the consolidated large drop will have lesser capacitance compared to the sum of individual capacitances of the smaller drops if their total surface area is greater.