electromagnetism - Electrodynamics and the Lagrangian density

Could anyone tell me what equations can I obtain from the Lagrangian density

$${\cal L}(\phi,\,\,\phi_{,i},\,\,A_i, \dot A_i,\,\,A_{i,j})~=~\frac{1}{2}|\dot A+\nabla\phi|^2-\frac{1}{2}|\nabla \times A|^2-\rho\phi+J\cdot A$$ by the Euler-Lagrange equations?