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