Let us consider a positive charge of one coulomb at a distance of s metres from the charge of Q coulombs placed in air. The force acting on this unit + ve charge is given by

E =   Q
    4π∈_os²

Work done in moving this positive charge of one coulomb towards the charge of Q coulombs through distance ds

dw = - Eds = -    Q        ds
                     4π∈_os²

Total work done in bringing the +ve charge of one coulomb from infinity of any point, S metres from the charge f Q coulombs is given by



By definition, potential at any point, V
                                 = The work done in bringing a +ve charge of one coulomb
                                     from infinity to that point

=  Q =  9 X 10⁹ Q volts in air
  4π∈_os            S

and  V = Q  =  X 10⁹ Q
          4π∈_o∈_rs      ∈_rs

Potential at a point due to number of charges.

As already proved, the potential at any point at a distance of S metres from the charge of Q coulombs is given by

V = 9 x 10⁹  Q volts
                 ∈_rs

Similarly the potential at any point due to number of charges Q₁, Q₂,Q₃ etc. placed at distances d₁,d₂,d₃ etc. respectively from it is given by

V = 9 X10⁹ ( Q₁  +  Q₂  +  Q₃ +..........)
                 ∈_r d1  ∈_r d2   ∈_r d3

where ∈_r is the relative permittivity of the surrounding medium.

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