You’ll notice I didn’t even put Coulomb’s law in my crash course. It’s not that fun. Coulomb’s law is technically an equation for Force, but I like the one for the field better.

\[\vec{E} = \frac{1}{4\pi \epsilon_0} \frac{q}{R^2}\hat{R}\]

This \(\vec{R}\) that Griffiths uses (he writes it as a script r) is kind of special. It takes a little getting used to:

\(\vec{R} = \vec{r} - \vec{r^\prime}\) where \(\vec{r^\prime}\) is the location of \(q\) and \(\vec{r}\) is the location where you’re calculating the field. \(\vec{R}\) points from \(q\) to \(\vec{r}\).

If you have a collection of charges then you sum this equation up (but just notice it’s the same equation…)

\[\vec{E} = \frac{1}{4\pi \epsilon_0}\Sigma_{i=1}^n \frac{q_i}{R_i^2}\hat{R}_i\]

And if you have a charge distribution you do the integral… (but please…it’s the same equation…)

\[\vec{E} = \frac{1}{4\pi \epsilon_0}\int \frac{\rho(\vec{r^\prime})}{R^2}\hat{R} d\tau^\prime.\]

Let’s do an example!! Example 2.2 page 64.

———For reference, we did not actually get to do the example in class————-