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.