1.6A: Field of a Point Charge

It follows from equation 1.5.3 and the definition of electric field intensity that the electric field at a distance $r$ from a point charge $Q$ is of magnitude

$$\tag{1.6.2}E=\frac{Q}{4\pi\epsilon_0 r^2}.$$

This can be written in vector form:

$$\textbf{E}=\frac{Q}{4\pi\epsilon_0 r^2}\hat{\textbf{r}}=\frac{Q}{4\pi \epsilon_0 r^3}\textbf{r}.\tag{1.6.3}$$

Here $\hat{\textbf{r}}$ is a unit vector in the radial direction, and $\textbf{r}$ is a vector of length $r$ in the radial direction.