# Illustration Electrical voltage (general definition)

Get illustration

Share — copy and redistribute the material in any medium or format

Adapt — remix, transform, and build upon the material for any purpose, even commercially.

Sharing and adapting of the illustration is allowed with indication of the link to the illustration.

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: $$\boldsymbol{E}_{\perp} \cdot \text{d}\boldsymbol{l} = 0$$