PX157 - B8a - calculating potentials

introduction

\frac{W_{a \to b}}{q_{0}} = \int_{a}^{b} \frac{\vec{F}}{q_{0}} \cdot d \vec{l} = \int_{a}^{b} \vec{E} \cdot d \vec{l} = V_{a} - V_{b}

∴ V_{a} - V_{b} = \int_{a}^{b} \vec{E} \cdot d \vec{l}

note: in a static situation:$$\oint \vec E\cdot d\vec l = V_{a}-V_{a} = 0$$