Line Integral/Examples/Potential Difference

Example of Line Integral
Let $\mathbf E$ be an electric field acting over a region of space $R$.

Let $OA$ be a curve in $R$.

Let $\d \mathbf l$ be a small element of length of $OA$ at a point $P$.

Then the potential difference between $O$ to $A$ is given by the line integral:
 * $\ds \int_O^A \mathbf E \cdot \d \mathbf l$