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Formula Continuous Charge Distribution in 1d Electric field    Linear charge density   

Formula
Formula: Continuous Charge Distribution in 1d
E-Field - Continuous Charge Distribution (Linear Charge Density)

Electric field

Unit
It indicates the magnitude and direction of the electric force at the location \(\boldsymbol{R}\) that would act on a test charge if it were placed at this location.

Position vector

Unit
It goes from the origin to a location within the one-dimensional charge distribution.

Field vector

Unit
It goes from the origin to the location (field point) where the electric field is to be calculated.

The connecting vector \(\boldsymbol{R} - \boldsymbol{r}\) is the vector going from a point of charge distribution \(\boldsymbol{r}\) to the considered field point \(\boldsymbol{R}\). Here \(\frac{\boldsymbol{R} ~-~ \boldsymbol{r}}{|\boldsymbol{R} ~-~ \boldsymbol{r}|}\) is the unit vector of the connecting vector.

Linear charge density

Unit
Charge per length at location \(\boldsymbol{r}\) within the considered one-dimensional charge distribution.

Length

Unit
The length of the considered one-dimensional charge distribution generating the electric field.

Vacuum Permittivity

Unit
The vacuum permittivity is a physical constant that appears in equations involving electromagnetic fields. It has the following experimentally determined value:$$ \varepsilon_0 ~\approx~ 8.854 \, 187 \, 8128 ~\cdot~ 10^{-12} \, \frac{\mathrm{As}}{\mathrm{Vm}} $$