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10.1: Radiation from charges and currents
https://phys.libretexts.org/Bookshelves/Electricity_and_Magnetism/Electromagnetics_and_Applications_(Staelin)/10%3A_Antennas_and_Radiation/10.01%3A_Radiation_from_charges_and_currents
51 Let $\overrightarrow{\mathrm{A}}=\nabla \Phi+\nabla \times \overrightarrow{\mathrm{N}}$ ; then \(\nabla \times \overrightarrow{\mathrm{A}}=\nabla \times(\nabla \times \overrightarrow{\mathrm{N}})...51 Let $\overrightarrow{\mathrm{A}}=\nabla \Phi+\nabla \times \overrightarrow{\mathrm{N}}$ ; then $\nabla \times \overrightarrow{\mathrm{A}}=\nabla \times(\nabla \times \overrightarrow{\mathrm{N}})$ and $\nabla \bullet \overrightarrow{\mathrm{A}}=\nabla^{2} \Phi$ , so $\nabla \times \overrightarrow{\mathrm{A}}$ and $\nabla \bullet \overrightarrow{\mathrm{A}}$ can be chosen independently simply by choosing $\overrightarrow{\mathrm{N}}$ and $\Phi$ independently.

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