Chapter 24, Problem 21P

It is shown in Example 24.7 that the potential at a point P a distance a above one end of a uniformly charged rod of length ℓ lying along the x axis is

$V=k_e\frac{Q}{\mathcal{l}}\ln \left(\frac{\mathcal{l}+\sqrt{a^2+{\mathcal{l}}^2}}{a}\right)$

Use this result to derive an expression for the y component of the electric field at P.