JEE Main & Advanced Physics Electrostatics & Capacitance Electric Potential

(1) Definition : Potential at a point in a field is defined as the amount of work done in bringing a unit positive test charge, from infinity to that point along any arbitrary path (infinity is point of zero potential). Electric potential is a scalar quantity, it is denoted by V;   \[V=\frac{W}{{{q}_{\mathbf{0}}}}\]  

(2) Unit and dimensional formula

S. I. unit : \[\frac{Joule}{Coulomb}=volt\]

C.G.S. unit : Stat volt (e.s.u.); 1 volt \[=\frac{\mathbf{1}}{\mathbf{300}}\] Stat volt

Dimension : \[[V]=[M{{L}^{2}}{{T}^{-3}}{{A}^{-1}}]\]

(3) Types of electric potential : According to the nature of charge potential is of two types

(i) Positive potential : Due to positive charge.    

(ii) Negative potential : Due to negative charge.

(4) Potential of a system of point charges : Consider P is a point at which net electric potential is to be determined due to several charges. So net potential at P

\[V=k\frac{{{Q}_{1}}}{{{r}_{1}}}+k\frac{{{Q}_{2}}}{{{r}_{2}}}+k\frac{{{Q}_{3}}}{{{r}_{3}}}+k\frac{\left( -{{Q}_{4}} \right)}{{{r}_{4}}}+...\]

In general \[V=\sum\limits_{i=1}^{X}{\frac{k{{Q}_{i}}}{{{r}_{i}}}}\]  

(5) Electric potential due to a continuous charge distribution : The potential due to a continuous charge distribution is the sum of potentials of all the infinitesimal charge elements in which the distribution may be divided i.e.,        

\[V=\int{dV},\,\,\,\,=\int{\frac{dQ}{4\pi {{\varepsilon }_{0}}r}}\]

(6) Graphical representation of potential : As we move on the line joining two charges then variation of potential with distance is shown below

(7) Potential difference : In an electric field potential difference between two points A and B is defined as equal to the amount of work done (by external agent) in moving a unit positive charge from point A to point B  i.e., \[{{V}_{B}}-{{V}_{A}}=\frac{W}{{{q}_{0}}}\]