Problem 2. The charge density $\rho(\mathbf{r}, t) = \rho(\mathbf{r}, 0) + \dot{\rho}(\mathbf{r}, 0)t$, so that $\mathbf{J}$ remains a constant in time. Show that the electric field $\mathbf{E}$ can be calculated using Coulombs law, using the charge density $\rho$ without retarded time.