# Formula Continuous Charge Distribution in 2d Electric field    Surface charge density

## Electric field

Unit
The E-field indicates how large and in which direction the electric force at the location $$\boldsymbol{R}$$ would act on a test charge if it were placed at the location under consideration.

## Position vector

Unit
It goes from the origin to a location within the two-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 running from a point of the 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.

## Surface charge density

Unit
Charge per area at location $$\boldsymbol{r}$$ within the considered two-dimensional charge distribution.

## Surface

Unit
The surface of the considered two-dimensional charge distribution, which generates 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:$$\varepsilon_0 ~\approx~ 8.854 \, 187 \, 8128 ~\cdot~ 10^{-12} \, \frac{\mathrm{As}}{\mathrm{Vm}}$$