Derive an expression for the electric potential at a distance r from a point charge q. What is the nature of this potential?

Dear student,
The derivation for electric potential due to a point charge is given below :

• Electric Potential Due to a Point Charge

Let P be the point at a distance ‘r’ from the origin O at which the electric potential due to charge +q is required.

The electric potential at point P is the amount of work done in carrying a unit positive charge from∞ to P.

Let ‘A’ be an intermediate point on this path, where OA = x. The electrostatic force on unit positive charge is

, along OA

Small work done in moving through a distance ‘dx’,

∴Total work done in moving unit positive charge from ∞ to point P is

By the definition of potential, this is the potential at P due to the charge at O.

V is inversely proportional to r and therefore as we move away from the point charge electric potential decreases.
Regards