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# IllustrationElectrical voltage (general definition) Share — copy and redistribute the material in any medium or format

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This illustration is free to use with indication of the copyright: universaldenker.org

Integration of an electric field vector $$\boldsymbol{E}$$ along the line $$L$$ located in an electric field:\[ U_{\text e} = \int_L \bold symbol{E} \cdot \text{d}\bold symbol{l}\where $$\text{d}\boldsymbol{l}$$ is an infinitesimal line element along the considered line $$L$$. The line integral of the E-field is the general definition of electric voltage $$U_{\text e}$$.

The vector field $$\boldsymbol{E}$$ can be divided into component $$\boldsymbol{E}_{||}$$ parallel to $$\text{d}\boldsymbol{l}$$ and into component $$\boldsymbol{E}_{\perp}$$ orthogonal to $$\text{d}\boldsymbol{l}$$. The scalar product with the orthogonal component does not contribute to the line integral: $$\boldsymbol{E}_{\perp} \cdot \text{d}\boldsymbol{l} = 0$$