1.6A: Field of a Point Charge
- Page ID
- 6322
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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.