Since the rod is uniformly charged, the charge per unit length must be the same over a small length \(dy\) as it is over the whole length of the rod: \[\begin{aligned} \frac{dq}{dy}&=\frac{Q}{L}\\ \th...Since the rod is uniformly charged, the charge per unit length must be the same over a small length \(dy\) as it is over the whole length of the rod: \[\begin{aligned} \frac{dq}{dy}&=\frac{Q}{L}\\ \therefore dq &= \frac{Q}{L} dy\end{aligned}\] It is often useful to introduce a constant charge per unit length, \(\lambda=\frac{Q}{L}\), so that we can write the charge \(dq\) as: \[\begin{aligned} dq = \lambda dy\end{aligned}\] We can also express \(r^2\) and \(\cos\theta\) in terms of \(y\) (and \…
