Electric potential and potential due to point charge

3. Electric Potential

  • We now move towards the electric potential which is potential energy per unit charge.
  • Thus electrostatic potential at any point of an electric field is defined as potential energy per unit charge at that point.
  • Electric potential is represented by letter V.
    V=U/q' or U=q'V                                             (6)
  • Electric potential is a scalar quantity since both charge and potential energy are scalar quantities.
  • S.I. unit of electric potential is Volt which is equal to Joule per Coulumb. Thus,
    1 Volt = 1 JC-1
  • In equation 4 if we divide both sides by q' we have

    where V(r1) is the potential energy per unit charge at point R and V2) is potential energy per unit charge at point S and are known as potential at points R and S respectively.
  • Again consider figure 1. If point S in figure 1 would be at infinity then from equation 7

    Since potential energy at infinity is zero therefore V(∞)=0. Therefore

    Electric Potential
    hence electric potential at a point in an electric field is the ratio of work done in bringing test charge from infinity to that point to the magnitude of test charge.
  • Dimensions of electric potential are [ML2T-3A-1] and can be calculated easily using the concepts of dimension analysis.

4. Electric potential due to a point charge

  • Consider a positive test charge +q is placed at point O shown below in the figure.

    Electric potential due to a point charge

  • We have to find the electric potential at point P at a distance r from point O.
  • If we move a positive test charge q' from infinity to point P then change in electric potential energy would be

  • Electric potential at point P is

  • Potential V at any point due to arbitrary collection of point charges is given by

  • here we see that like electric field potential at any point independent of test charge used to define it.
  • For continous charge distributions summation in above expressin will be replaced by the integration

    where dq is the differential element of charge distribution and r is its distance from the point at which V is to be calculated.

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