# Change in Potential energy moving toward line of charge

I'm analyzing the energy involved with charges moving in an electric field and I'm getting caught up here and I must be missing something. So given that an infinitely long line of charge produces a field

$$E = \frac{2k\lambda}{z}$$

Where $k$ and $\lambda$ (linear charge density) are known constants and $z$ is the distance from the line. So if Electric Potential is

$$V = E\cdot d$$ and Electric Potential Energy is

$$PE = QV$$

And $d$ is the distance from the source($d = z$) then to me it appears this would cause the change in potential energy to remain 0 (it would remain equal to $V$ forever) for any $Q$ as distance changes in either direction. This of course doesn't make sense because it would imply that the wire would exert the same force forever i.e. accelerate particles indefinitely. I'm sure this problem isn't complicated I just can't see what I'm missing in my calculation.

While the formula $V=E\cdot d$ works for parallel plate capacitor, it does not apply for an infinitely long rod. The Formula for calculating potential is $V=\int \vec{E}\cdot\mathrm{d}\vec{l}$. And be aware that we can no longer choose infinity as the zero potential point because the rod itself is infinitely long.