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Electric potential is a fundamental concept in electrostatics that represents the potential energy per unit charge. Think of it as a measure of how much work would be required to bring a positive unit charge from a point at infinity to a specific point within an electric field without producing any acceleration. For a conducting sphere, the electric potential on the surface can be described by the formula:
\( V = \frac{k_e Q}{R} \),
where \(k_e\) is Coulomb's constant, \(Q\) is the total charge on the sphere, and \(R\) is the radius of the sphere. This potential is due to the electric field produced by the charge distributed over the sphere's surface. The electric potential is the same at every point on the surface because a conductor redistributes its charge until it reaches equilibrium, where the surface is an equipotential surface.

Electrostatics is the branch of physics that studies electric charges at rest. The forces between stationary charges are described by Coulomb's law, which states that the magnitude of the electrostatic force between two point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. Conductors are materials that allow charges to move freely. When dealing with a conducting sphere, charges reside on the surface, creating a uniform electric field just outside the surface and no electric field inside the sphere. This uniform distribution is key to understanding the behavior and calculations of potential and energy in electrostatic scenarios.

The work-energy theorem is a fundamental principle that connects the work done on an object to its energy. In the context of electrostatics, the work done to move a charge in an electric field directly relates to the change in electric potential energy of the system. To move a small charge \(dq\) from infinity to the surface of a conducting sphere, the work done is equal to the increase in potential energy of the charge. This work is defined using the concept of the electric potential, and over the process of assembling the sphere's charge, the work done is accumulated. This accumulation is integral to understanding how the energy of the sphere is calculated.

Coulomb's constant \(k_e\) is a proportionality factor that appears in Coulomb's law and electric potential calculations. Its value is approximately \(8.9875 \times 10^9 N m^2 C^{-2}\) in the SI unit system. This constant is crucial for calculating the forces between charged particles and the electric potential due to a particular distribution of charges. In the formula for the energy associated with a conducting sphere \(U = \frac{k_e Q^2}{2R}\), Coulomb's constant links the geometrical and charge properties of the sphere to its electrostatic energy. Understanding \(k_e\) is essential for making precise calculations in electrostatics and comprehending the strength of electric interactions across distances.