Module 2 : Electrostatics
Lecture 8 : Electrostatic Potential
  Potential Function satisfies Superposition Principle
  Consider a collection of charges $Q_1, Q_2\ldots$. The electric field at a point due to the distrbution of charges obeys superposition principle. If $\vec E_i$is the electric field at a point P due to the charge $Q_i$, the net electric field at P is
 
\begin{displaymath}\vec E = \sum_i \vec E_i\end{displaymath}
  The potential $\phi$at the point P (with respect to the reference point P $_0$) is
\begin{displaymath}\phi(P) = \int_{P_o}^{P} \vec E\cdot d\vec l = \int_{P_0}^P\s... ... = \sum_i \int_{P_0}^P \vec E_i\cdot d\vec l = \sum_i \phi_i(P)\end{displaymath}
  where $\phi_i(P)$is the potential at P due to the charge $Q_i$.
  Determining Electric Field from a knowledge of Potential
  The potential at the position $\vec x$ is given by the expression
 
\begin{displaymath}\phi(\vec x) = -\int_{\vec x_0}^{\vec x}\vec E\cdot\vec{dl}\eqno(A)\end{displaymath}
 
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