Module 2 : Electrostatics
Lecture 8 : Electrostatic Potential

Since the work done by the electric field is independent of path, we may write

\begin{displaymath}\int_A^B \vec E\cdot\vec{dl} = U(A,B)\end{displaymath}

where $U(A,B)$is a scalar function which depends only on the end points A and B of integration. By property of integrals

\begin{displaymath}\int_A^B \vec E\cdot\vec{dl} = \int_A^C \vec E\cdot\vec{dl} + \int_C^B \vec E\cdot\vec{dl} \end{displaymath}

where $C$is any arbitrary point. Thus

\begin{displaymath}U(A,B) = U(A,C) + U(C,A)\end{displaymath}

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