Contour Integral/Examples/Potential Difference

Example of Contour Integral

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

Let $OA$ be a contour 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 contour integral:

$\ds \int_O^A \mathbf E \cdot \d \mathbf l$

Sources

• 1951: B. Hague: An Introduction to Vector Analysis (5th ed.) ... (previous) ... (next): Chapter $\text {II}$: The Products of Vectors: $3$. Line and Surface Integrals