Module 2 : Electrostatics
Lecture 8 : Electrostatic Potential
  Potential and Potential Energy
Potential and Potential energy are different, though they are related. Electric potential at a point is the potential energy of a unit test charge kept at that point.
  Potential is the property of the field and is defined at every point, whether or not a charge is located at the point. It is the potential energy that the unit test charge would have if it happens to be located at that point.
  The potential energy of a positive charge $q$increases if it is taken to a region of higher potential. If electric force is the only force acting on the particle, its kinetic energy would decrease by a similar amount.
  Let the charge have a velocity$v_1$at the position P$_1$ where the electrostatic potential is $\phi_1$.If it moves to a position
  P$_2$, where the potential is $\phi_2$, then, the velocity $v_2$of the particle at this point is given by the energy conservation
 
\begin{displaymath}\frac{1}{2}mv_1^2 + q\phi_1 = \frac{1}{2}mv_2^2 + q\phi_2\end{displaymath}
  The work done on the particle in moving from a potential $\phi_1$to the potential $\phi_2$is given by the ``work-energy theorem"
 
\begin{eqnarray*} {\rm Work\ Done} &=& {\rm Change\ in\ K.E.}\\ &=& \frac{1}{2}m(v_2^2-v_1^2)\\ &=& q(\phi_1 - \phi_2) \end{eqnarray*}
  Volt,the unit of potential difference,may be interpreted as follows.If a charge of one coulomb moves through a potential difference such that in the new position the potential is lower by 1 Volt,the kinetic energy of the charge increases by 1Joule.
   
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