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## Main Question or Discussion Point

Hello! I am reading Griffiths derivation for the electric dipole radiation (actually my question would fit for the magnetic dipole radiation too). He considers 2 charged balls connected by a wire with charge going back and forth between them. Now, when he calculates the vector potential he uses this formula: $$A(r,t)=\frac{\mu_0}{4 \pi}\int_{-d/2}^{d/2}\frac{-q_0\omega sin[\omega(t-r'/c)]\hat{z}}{r'}dz$$

However, if I followed it properly through the book, this equation is derived from Biot-Savart law (and a proper choice of gauge). However, when introducing Biot-Savart, Griffiths emphasizes that the current density (or linear current in this case) must be infinite in extent i.e. started infinitely long in the past and uniform. However the current is not infinite in extent, nor uniform. I see that Griffiths takes into account the fact that the potential is retarded, but I am just a bit confused about using this formula derived from Biot-Savart. Is it that obvious that a formula based on a uniform, infinite in extent current is correct just by adding that ##t-r/c## term?

However, if I followed it properly through the book, this equation is derived from Biot-Savart law (and a proper choice of gauge). However, when introducing Biot-Savart, Griffiths emphasizes that the current density (or linear current in this case) must be infinite in extent i.e. started infinitely long in the past and uniform. However the current is not infinite in extent, nor uniform. I see that Griffiths takes into account the fact that the potential is retarded, but I am just a bit confused about using this formula derived from Biot-Savart. Is it that obvious that a formula based on a uniform, infinite in extent current is correct just by adding that ##t-r/c## term?