Electric potential and electric potential energy relationship

Since potential is just work done or energy per unit charge, potential energy will also be same everywhere for a charge Q.

What you want is

$$mathbf{E} = -nabla phi - frac{partial mathbf{A}}{partial t}$$

The energy you might be looking for is: begin{align} E &= epsilon_0 int mathbf{E} cdot mathbf{E} mathrm dV &= epsilon_0 int left(nabla phi + frac{partial mathbf{A}}{partial t}right)left(nabla phi + frac{partial mathbf{A}}{partial t} right) mathrm dV end{align}