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.

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