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Electric potential, often denoted as 'V', describes the potential energy per unit charge at a point in an electric field and reflects the work done to move a charge to that point from infinitely far away. A critical aspect of electric potential is its relationship with capacitance. Capacitance indicates a system's ability to store electric charge and is quantified by the amount of charge stored per unit of electric potential difference, described by the equation \( C = \frac{Q}{V} \).

Understanding the relationship between electric potential and capacitance is essential when analyzing electric circuits, such as the one involving two spheres with radii \( a \) and \( b \), separated by a distance \( d \). The total electric potential at any point is the sum of potentials due to individual charges or components in the system. This concept is key to deriving the capacitance for complex configurations like spherical capacitors placed at a distance from each other.

A spherical capacitor typically consists of two concentric spherical conductors, separated by an insulating material or vacuum. The capacitance of a simple spherical capacitor with a single gap is given by \( C = 4\pi\epsilon_0\frac{ab}{b-a} \), where \( a \) and \( b \) are the radii of the inner and outer spheres, respectively, and \( \epsilon_0 \) is the permittivity of free space.

When dealing with two separate spheres rather than concentric ones, the potential at the surface of each is influenced by the charge on both spheres, not just the charge on itself. This interaction complicates the calculation of capacitance, as we must account for the composite electric potential resulting from both charges and the geometry of the setup.

Capacitance in an electric circuit can be configured in two primary ways: in series or in parallel. For capacitors connected in series, the total capacitance can be found using the equation \( \frac{1}{C_{\text{total}}} = \sum_{i=1}^{n} \frac{1}{C_i} \), where \( C_i \) represents each individual capacitor's capacitance. In contrast, for capacitors connected in parallel, the total capacitance is the sum of individual capacitances, given by \( C_{\text{total}} = \sum_{i=1}^{n} C_i \).

For two individual spherical capacitors distanced from each other, as in our example, the capacitances are not in series or parallel in the conventional sense. However, when spheres are far apart, we approximate their behavior as if they were in series due to the dominant effect of charge contribution, which leads us to the presented steps in the original solution.

The relationship between an electric field (E) and electric potential (V) is both fundamental and profound. The electric field at any point can be defined as the negative gradient of the electric potential, mathematically described by \( E = -abla V \). This relationship states that the electric field points in the direction where the potential decreases most rapidly and its magnitude corresponds to the rate of decrease.

In the context of two separated spheres, each sphere creates its own electric field, contributing to the potential at any given point in space. The final potential at each sphere is a superposition of the potentials due to both spheres. This concept aids in deriving the equation for the capacitance of a system consisting of two spheres, leading to the expression provided in the original exercise.